ENGINEERING YOUR FUTURE An Introduction to Engineering: A Comprehensive Approach

The History of Engineering CHAPTER 1 The History of Engineering

1.1 Introduction Definition of Engineering The profession in which knowledge of the mathematical and natural sciences, gained by study, experience, and practice, is applied with judgment to develop ways to use, economically, the materials and forces of nature for the benefit of mankind.

1.2 Getting Started Prehistoric Culture Our Computer Age The Speed of History Quick Overview

1.3 The Beginnings of Engineering The Earliest Days Egypt and Mesopotamia (add picture)**

1.3 Pictures of Pyramids Insert Figure 1.2 The Great Pyramid of Khufu

1.4 The Overview Approach Engineering the Temples of Greece The Roman Roads and Aqueducts The Great Wall of China **FROM HERE MIGHT WANT TO ADD PICTURES FROM BOOK

1.5 Traveling Through the Ages 1200 B.C. – A.D. 1 Quality of wrought iron is improved Swords are mass produced Siege towers are perfected Greeks develop manufacturing Archimedes introduces mathematics in Greece Concrete is used for arched bridges, roads and aqueducts in Rome.

1.5 Traveling Through the Ages: A.D. 1-1000 Chinese further develop the study of mathematics Gunpowder is perfected Cotton and silk manufactured

1.5 Traveling Through the Ages: 1000-1400 Silk and glass industries continue to grow Leonardo Fibinacci, a medieval mathematician, writes the first Western text on algebra

1.5 Traveling Through the Ages: 1400-1700 First toilet is invented in England Galileo constructs a series of telescopes, with which he observes the rotation about the sun Otto von Guerick first demonstrates the existence of a vacuum Issac Newton constructs first reflecting telescopes Boyle’s Gas Law, stating pressure varies inversely with volume, is first introduced.

1.5 Traveling Through the Ages: 1700-1800 Industrial Revolution begins in Europe James Watt patents his first steam engine Society of Engineers, a professional engineering society, is formed in London First building made completely of cast iron built in England

1.5 Traveling Through the Ages: 1800-1825 Machine automation is first introduced in France First railroad locomotive is designed and manufactured Chemical symbols are developed, the same symbols used today (Au, He) Single wire telegraph line is developed

1.5 Traveling Through the Ages: 1825-1875 Reinforced concrete is first used First synthetic plastic material is created Bessemer develops his process to create stronger steel in mass quantities First oil well drilled in Pennsylvania Typewriter is perfected

1.5 Traveling Through the Ages: 1875-1900 Telephone is patented in the US by Alexander Graham Bell Thomas Edison invents the light bulb and the phonograph Gasoline engine developed by Gottlieb Daimler Automobile introduced by Karl Benz

1.5 Traveling Through the Ages: 1900-1925 Wright brothers complete first sustained flight Ford develops first diesel engines in tractors First commercial flight between Paris and London begins Detroit becomes center of auto production industry

1.5 Traveling Through the Ages: 1925-1950 John Logie Baird invents a primitive form of television The VW Beetle goes into production First atomic bomb is used The transistor is invented

1.5 Traveling Through the Ages: 1950-1975 Computers first introduced into the market, and are common by 1960 Sputnik I, the first artificial satellite, put into space by USSR First communication satellite—Telstar—is put into space The U.S. completes the first ever moon landing

1.5 Traveling Through the Ages: 1975-1990 The Concord is first used for supersonic flight between Europe and the U.S. Columbia space shuttle is reused for space travel First artificial heart is successfully implanted

1.5 Traveling Through the Ages: 1990-Present Robots travel on Mars The “Chunnel” between England and France is finished GPS is used to predict and report weather conditions, as well as many other consumer applications

1.6 Case Study of Two Historic Engineers Leonardo Da Vinci Gutenberg and His Printing Press

1.7 The History of the Disciplines Aerospace Eng. Agricultural Eng. Chemical Eng. Civil Eng. Computer Eng. Electrical Eng. Industrial Eng. Mechanical Eng.

1.7 History: Aerospace Engineering “Aerospace engineering is concerned with engineering applications in the areas of aeronautics (the science of air flight) and astronautics (the science of space flight).

1.7 History: Agricultural Engineering Agricultural engineering focuses on: Soil and water Structures and environment Electrical power and processing Food engineering Power and machinery

1.7 History: Chemical Engineering Chemical engineering applies chemistry to industrial processes, such as the manufacture of drugs, cements, paints, lubricants, and the like.

1.7 History: Civil Engineering Civil engineering focuses on structural issues, such as: Bridges and Highways Skyscrapers Industrial Plants and Power Plants Shipping Facilities and Railroad Lines Pipelines, Gas Facilities, Canals

1.7 History: Computer and Electrical Engineering The world’s business is centered around computers, and their uses are only increasing Electrical is the largest branch of engineering Involved in: Communication Systems Computers and Automatic Controls Power Generation and Transmission Industrial Applications

1.7 History: Industrial Engineering Industrial engineers design, install, and improve systems that integrate people, materials, and machines to improve efficiency.

1.7 History: Mechanical Engineering Deals with power, the generation of power, and the application of power to a variety of machines, ranging from HVAC to space vehicles.

CHAPTER 2 Engineering Majors

2.1 Introduction Several characteristics of students that might have an interest in engineering are: Proficient skills in math and physical science An urging from a high school counselor Knows someone who is an engineer Knows that engineering offers literally dozens, if not hundreds of job opportunities Is aware that a degree in engineering is quite lucrative

2.1 Engineers and Scientists Scientists seek technical answers to understand natural phenomenon Engineers study technical problems with a practical application always in mind For example “Scientists study atomic structure to understand the nature of matter; engineers study atomic structure to make smaller and faster microchips”

2.1 The Engineer and the Engineering Technologist Main difference between the two is: Engineers design and manufacture machines and systems, while engineering technologists have the technical know-how to use and install the machines properly An example: “The technologist identifies the equipment necessary to assemble a new CD player; the engineer designs said CD player”

2.1 What Do Engineers Do? Ways to get information about careers: Visit job fairs Attend seminars on campus by various employers Contact faculty with knowledge of engineering fields Get an intern or co-op position Enroll in an engineering elective course

2.1 What Engineers Do Insert Figure 2.1 Engineering positions

2.2 Engineering Functions: Research Research engineers are knowledgeable in principles of chemistry, biology, physics, and mathematics Computer know-how is also recommended A Masters Degree is almost always required, and a Ph. D is often strongly recommended

2.2 Engineering Functions: Development Development engineers bridge the gap between the laboratory and the production facility They also identify problems in a potential product An example is the development of concept cars for companies like Ford and GM

2.2 Engineering Functions: Testing Testing engineers are responsible for testing the durability and reliability of a product, making sure that it performs how it is supposed to, every time. T.E.s simulate instances and environments in which a product would be used Crash testing of a vehicle to observe effects of an air bag and crumple zone are examples of a testing engineer’s duties

2.2 Engineering Functions: Design Design aspect is where largest number of engineers are employed Design engineers often work on components of a product, providing all the necessary specifics needed to successfully manufacture the product Design engineers regularly use computer design software as well as computer aided drafting software in their jobs

2.2 Engineering Functions: Design Design engineers must also verify that the part meets reliability and safety standards required for the product A concern always on the mind of design engineers is how to keep the development of a part cost effective, which is taken into account during a design process

2.2 Engineering Functions: Analysis Analysis engineers use computational tools and mathematic models to enrich the work of design and research engineers Analysis engineers typically have a mastery of: heat transfer, fluid flow, vibrations, dynamics, acoustics, and many other system characteristics

2.2 Engineering Functions: Systems Responsible on a larger scale for bringing together components of parts from design engineers to make a complete product Responsible for making sure all components of a product work together as was intended by design engineers

2.2 Engineering Functions: Manufacturing & Construction Work individually or in teams Responsible for “molding” raw materials into finished product Maintain and keep records on equipment in plant Help with design process to keep costs low

2.2 Engineering Functions: Operations & Maintenance Responsible for maintaining production line Must have technical know-how to deal w/ problems Responsible for inspecting facility and equipment, must be certified in various inspection methods

2.2 Engineering Functions: Technical Support Works between consumers and producers Not necessarily have in depth knowledge of technical aspects of product Must have good interpersonal skills

2.2 Engineering Functions: Customer Support Often have more of a technical knowledge than Tech. Support, because they must be able to work with basic customers Evaluate whether or not a current practice is cost effective via feedback from customers

2.2 Engineering Functions: Sales Sales engineers have technical background, but are also able to communicate effectively w/ customers Job market for sales engineers is growing, due to the fact that products are becoming more and more technically complex

2.2 Engineering Functions: Consulting Are either self-employed, or work for a firm that does not directly manufacture products Consulting engineers might be involved in design, installation, and upkeep of a product Sometimes required to be a registered professional engineer in the state where he/she works

2.3 Engineering Majors: Aerospace Engineering Previously known as aeronautical and astronautical engineering First space flight Oct. 4, 1957 (Sputnik I) KEY WORDS: Aerodynamics: The study of the flow of air over a streamlined surface or body. Propulsion engineers: develop quieter, more efficient, and cleaner burning engines.

2.3 Engineering Majors: Aerospace Engineering KEY WORDS: Structural engineers: use of new alloys, composites, and other new materials to meet design requirements of new spacecraft Control systems: systems used to operate crafts Orbital mechanics: calculation of where to place satellites using GPS

2.3 Engineering Majors: Agricultural Engineering Concerned with finding ways to produce food more efficiently KEY WORDS Harvesting Equip. - removes crops from field, and begins processing of food Structures: used to hold crops, feed, and livestock; Agricultural engineers develop and design the structures that hold crops

2.3 Engineering Majors: Agricultural Engineering Food process engineers: concerned with making healthier processed food products Soil/Water Resources: working to develop efficient ways to use limited resources

2.3 Engineering Majors: Architectural Engineering Structural: primarily concerned with the integrity of the building structure. Evaluates loads placed on buildings, and makes sure the building is structurally sound Mechanical systems: control climate of building, as well as humidity and air quality (HVAC)

2.3 Engineering Majors: Biomedical First recognized in 1940’s Three basic categories: Bioengineering, Medical, and Clinical Bioengineering is application of engineering principles to biological systems Medical engineers develop instrumentation for medical uses Clinical engineers develop systems that help serve the needs of hospitals and clinics

2.3 Engineering Majors: Chemical Emphasizes the use of chemistry and chemical processes in engineering Chemical engineers develop processes to extract and refine crude oil and gas resources Chemical engineers also develop circuit boards, and work in the pharmaceutical industry, where processes are designed to create new, affordable drugs

2.3 Engineering Majors Civil Engineering First seen in pyramids of Egypt Structural engineers most common type of civil engineer Transportation engineers concerned w/ design and construction of highways, railroads, and mass transit systems Surveyors start construction process by locating property lines and property areas

2.3 Engineering Majors Computer Engineering Focuses primarily on computer hardware, not software Work w/ electrical engineers to develop faster ways to transfer information, and to run the computer Responsible for the “architecture” of the computer system

2.3 Engineering Majors Electrical Engineering More engineers are electrical than any other discipline With an ever growing technological society, electrical engineers will ALWAYS have a job Work in communications, microelectronics, signal processing, bioengineering, etc

2.3 Engineering Majors Environmental Engineering Often coupled with Civil Engineering 3 aspects of environmental engineering: Disposal: disposing of industrial/residential waste products Remediation: clean up of a contaminated site Prevention: working with corporations to reduce and/or prevent emissions and work to find ways to “recycle” products to be used again to reduce waste

2.3 Engineering Majors Industrial Engineering “Design, improvement, and installation of integrated systems of people, material, and energy” Emphasis placed on: Production, Manufacturing, Human Factors Area, and Operations Research Production focuses on plant layout, scheduling, and quality control Human Factors focuses on the efficient placement of human resources within a plant/facility

2.3 Engineering Majors Marine and Ocean Engineering Concerned with the design, development, and operation of ships and boats Marine engineer designs and maintains the systems that operate ships, I.e. propulsion, communication, steering and navigation Ocean engineer design and operates marine equipment other than ships, such as submersibles. O.E.s might also work on submarine pipelines and/or cables and drilling platforms

2.3 Engineering Majors Materials Engineering Study the structure, as well as other important properties of materials, I.e. strength, hardness, and durability Run tests to ensure the quality of the performance of the material Material Engineers also study metallurgy, and the development of composites and alloys

2.3 Engineering Majors Mechanical Engineering Concerned with machines and mechanical devices Work in design, development, production, control, and operation of machines/devices Requires a strong math and physics background. Often 4 or more math classes required for graduation

2.3 Engineering Majors Mining Engineering Work to maintain constant levels of raw minerals used every day in industrial and commercial settings Must discover, remove, process, and refine such minerals

2.3 Engineering Minerals Nuclear Engineering Most concerned with producing and harnessing energy from nuclear sources Propulsion and electricity are the main uses of nuclear power Engineers also responsible for disposal of the nuclear waste byproduct, and how to keep people safe from harmful nuclear products

2.3 Engineering Majors Petroleum Engineering Discover, remove, refine, and transport crude and refined oil around the world PE’s design and operate the machinery used to refine crude oil into its many forms

Chapter 3 Profiles of Engineers

3.1 Introduction Diversity of the engineering work force Wide range of engineering careers that are possible

3.1 Profile of a Biomedical Engineer Sue H. Abreu, Ft. Bragg, North Carolina Occupation: Lieutenant Colonel, Medical Corps, United States Army Medical Director, Quality Assurance, Womack Army Medical Center Education: IDE (BSE, Biomedical Engineering), 1978 MD, Uniformed Services University of the Health Sciences, 1982

3.1 Profile of an Aerospace Engineer Patrick Rivera Anthony Occupation: Project Manager, Boeing Space Beach Education: BS, Aerospace Engineering

3.1 Profile of a Civil Engineer Sandra Begay-Campbell, Boulder, Colorado Occupation: AISES Executive Director Education: BSCE, 1987; MS, Structural Engineering, 1991

3.1 Profile of an Electrical Engineer Ryan Maibach, Farmington, Michigan Occupation: Project Engineer at Barton Malow Company Education: BS-CEM (Construction Engineering and Management), 1996

3.1 Profile of an Agricultural Engineer Mary E. Maley, Battle Creek, Michigan Occupation: Project Manager, Kellogg Company Education: BS, Agricultural Engineering (food engineering)

A Statistical Profile of the Engineering Profession Chapter 4 A Statistical Profile of the Engineering Profession

4.1 Statistical Overview How many people study engineering? What are the most common majors? What kind of job market is there for engineers? How much do engineers earn? How many women and minorities study engineering?

4.2 College Enrollment Trends of Engineering Students 1950s-1960s: 60,000-80,000 engineering students 1970s marked the lowest number of students, at 43,000 Engineering peaked in 1980s, with around 118,000 students

4.3 College Majors of Recent Engineering Students Of approximately 350,000 full-time undergrad engineering students, just less than 1/3 (124,000) were majoring in computer and electrical engineering Just over 32,000 were “undecided”

4.4 Degrees in Engineering Steady decline in Engineering degrees awarded between 1986 and 1995. Since then, there have been many fluctuations, but as of data of 2000, there were 63,300 engineering degrees awarded For a long time, electrical awarded the highest number of degrees, but that was eventually replaced by mechanical engineering

4.5 Job Placement Trends 1999-2000 was the hottest year for engineering majors to find jobs As the number of engineering students declines, employers must “fight” harder to get whatever students they can get their hands on to fill vacant positions. This has led to a very promising job placement ratio

4.6 Salaries of Engineers On the whole, engineers make more money than any other graduate with another degree Electrical, computer, and computer science recently have led the way, with average salaries from a Bachelor degree starting at around $52,000 A Ph.D. in computer science will earn a starting average of around $84,000

4.7 Diversity in the Profession For a long time, white males dominated engineering Recently, women, foreign nationals, and various minority students have entered colleges and universities with an engineering diploma in mind

4.8 Distribution of Engineers by Field of Study Electrical engineering employs the highest number of engineers, nearly 25%, numbering close to 375,000 Mechanical employs almost 250,000 Civil is the next highest “populated”, with 200,000 workers

4.11 Words of Advice from Employers Looking for graduates who possess: Excellent communication skills Teamwork Leadership Computer/Technical proficiency Hard working attitude

Global and International Engineering Chapter 5 Global and International Engineering

5.1 Introduction After WWII, engineering became a more “global” business. Taking a few foreign language classes in college cannot hurt, but only help your chances at getting a job after college.

5.2 The Evolving Global Market: Changing World Maps & Alliances Breakup of former USSR New laws, regulations, policies have affected the spread of international engineering

5.2 NAFTA 1994 North American Free Trade Agreement (US, Mexico, Canada) Designed to reduce tariffs, and increase international competition Manufacturing trade has increased by 128% between Canada, US, and Mexico since 1994

5.3 International Opportunities For Engineers Engineers are employed internationally in: Automobile Industry Manufacturing Construction Pharmaceuticals Food Industry Petroleum and Chemical Industry Computer and Electronics Industry Telecommunications

5.4 Preparing for a Global Career Students who look to work internationally should: Be language and culturally proficient Should participate in study abroad programs Look into work international work experience and Co-Op opportunities

Chapter 6 Future Challenges

6.1 Expanding World Population 1900-2000, world population climbs from 1.6 billion to 6 billion people Places new stress on conservation of resources, and gives engineers new challenges to compensate for high population

6.2 Pollution Engineers concerned with management and the control of pollution, especially: Air pollution Water pollution and the depletion of freshwater resources Management of solid waste

6.3 Energy It is predicted that energy usage in the Developing Countries will more than double in the next 30 years Engineers must find new ways to generate power in an effort to conserve natural resources (fossil fuels)

6.5 Infrastructure With mass transportation an ever-present problem, engineers will be responsible in the future for designing and maintaining a system by which the transportation of raw materials, as well as the human capital that process them, can easily and efficiently move from place to place

Succeeding in the Classroom CHAPTER 7 Succeeding in the Classroom

7.2 Attitude Success in an engineering curriculum depends largely on a student’s attitude and work ethic If the student’s attitude is one of failure, the student will most likely fail Keep an open mind, and be willing to “work” with the professor in order to best understand the material

7.3 Goals Set goals that will be difficult to attain, but not impossible This will motivate the student to work hard, not just hard enough to do the minimum, but to reach their higher standard/goal Set short, intermediate, and long term goals GPA for a semester, grade on an upcoming exam, GPA for a year/college career

7.4 Keys to effectiveness GO TO CLASS Allow 2 hrs. of study time outside of class for every hour in class Re-read sections of book covered in class Keep up with class and reading Take good notes Work lots of problems, not just the minimum amount for homework Study in groups

7.5 Test Taking Obtain past exams Ask professor for practice exams Work problems in book Start with problems you know how to do, then work on the harder problems Skim test first, to see what will basically be covered

7.6 Making the Most of Your Professor Don’t wait until the end of the semester to go for help If you make yourself visible in class and during office hours, the professor may remember you while grading Teaching is not professors only responsibility, often the are researchers and advisors as well, so give them the benefit of the doubt

7.7 Learning Styles Each person’s brain is unique to him or her Proper nutrition, stress, drugs and alcohol are some of the factors that can affect a developing brain Each person is born with all the brain cells, or neurons, they will ever have (estimated at 180 billion neurons)

7.7 Learning Styles None of us is ever too old or too dumb to learn something new! People think and memorize in several different ways

7.7 Learning Styles Memorizing: Refers to how people assimilate new material to existing knowledge and experience How we accommodate, or change our previous way of organizing material

7.7 Learning Styles Thinking: Refers to how we see the world, approach problems and use the different parts of our brain.

7.7 Learning Styles We all have different learning styles Memory Languages: Auditory Visual Kinesthetic

7.7 Learning Styles Auditory Learner: Buy a small tape recorder and record lectures Sit where you can hear the professor well Focus on what is said in class, take notes from the tape recorder later Ask the professor questions Read out loud to yourself Keep visual distractions to a minimum

7.7 Learning Styles Visual Learner: Sit where you can see the professor and board or screen clearly Write notes during lecture with lots of pictures and meaningful doodles Rewrite notes later in a more organized fashion and highlight main ideas Write out questions to ask the professor Highlight and take notes in your book

7.7 Learning Styles Kinesthetic Learners: TAKE Labs! Make connections between what is being said and what you’ve done in the past Talk to professor about ways to gain more hands-on experience, such as volunteering in his/her lab Use models or experiments at home

7.7 Learning Styles Thinking Skills: Refers to how we see the world, approach problems and use the different parts of our brain Different people think differently Two hemispheres in our brain, and four quadrants generally categorize how we think

7.7 Learning Styles Insert Figure 7.1 Herrmann’;s “whole brain model” describing four quadrants of the brain

7.8 Well Rounded Equals Effective Make sure to balance social, intellectual, and physical activities in your schedule Well rounded students are generally more effective than students with a “one-track” mind

7.9 Your Effective Use of Time Decide in advance what to study and when Make schedules Use calendars effectively Organize tasks by priority level Stay focused on task **Remember, everyone will “fail” at some point, it’s how you respond to a failure that determines your future success or failure

Chapter 8 Problem Solving

8.1 Introduction Problem solving requires many “tools” and skills. Make sure that you have them, or at least know where to find them and how to use them

8.2 Analytic and Creative Problem Solving Two basic types of problem solving involved in design process: creative and analytic More students familiar with analytic, where there is one right answer Creative problem solving has no right answers

8.2 Analytic and Creative Problem Solving Steps that typically help w/ problem solving Make a model/figure Identify necessary, desired and given info Work backwards from answers Restate problem in one’s own words Check the solution and validate it

8.3 Analytic Problem Solving Six steps to analytic problem solving: Define the problem and create a problem statement Diagram and describe the problem Apply theory and any known equations Simplify assumptions Solve necessary problems Verify accuracy of answer to desired level

8.4 Creative Problem Solving Use divergence and convergence to gather and analyze ideas. Divergence is brainstorming. Convergence is analyzing and evaluating the ideas, seeking out the best possible solutions What is wrong? What do we know? What is the real problem? What is the best solution? How do we implement the solution?

Visualization and Graphics Chapter 9 Visualization and Graphics

9.1-9.2 Visualization Visualization is often used as a mode of communication between engineers Sketches, tables, graphs, computer generated drawings, blueprints are various ways in which engineers communicate via visual mediums

9.3 Sketching Although most final drawings are computer generated, initial and freehand sketches are vital to the design process Freehand does not mean messy. Sketches should display an adequate amount of detail, and any pertinent notes/comments pertaining to the drawing For instance, if a line is supposed to be straight, make it as straight as possible. A square will not pass for a circle.

9.7 Graphical Communication Oblique and isometric drawings are 3D and general Orthographic drawings are 2D, more detailed, and often have dimensions for the part Object, Hidden, Centerline, and Construction are 4 common types of lines used in engineering graphics

Chapter 10 Computer Tools

10.1-10.6 Computer Tools for Engineers There are many aspects to the design process of a product Engineers must be competent in basic computer tools such as the internet, word processing, and basic spreadsheets Engineers will most likely be required to have some knowledge of mathematical software, such as MatLab Engineers also make computer presentations using most commonly, Microsoft PowerPoint

10.7-10.8 Operating Systems and Programming Language Engineers may be required to have experience or be expected to be able to work in UNIX, MS-DOS, or a Microsoft Windows System Computers work on series of 1’s and 0’s, called binary code FORTRAN, BASIC, C, and C++ are all programming languages used by engineers to communicate with the computer

Chapter 11 Teamwork Skills

11.1 Teamwork Corporations develop teams for many reasons Projects are becoming increasingly complex Projects often span international borders, and require workers all over Projects are requiring more speed, which require more workers

11.2 What Makes a Successful Team? A common goal Leadership Each member makes unique contributions Effective communication Creativity Good planning and use of resources

11.4 Team Leadership Structures Traditional: One leader, who directs subordinates. Leader typically is the only one who “speaks”. Participative: Leader is closer to individual workers. Flat: There is no “leader”. All members are equal. The leadership “moves” with the situation to the worker with the most expertise in a given subject

11.5 Decisions within a Team Consensus: All team members agree on a decision Majority Rule Minority/Committee decision Expert input

11.7 Grading a Team Effort Did the team accomplish its goal? Were results of a high quality? If not, why? Did the team grow throughout the process? Evaluate the team leader Evaluate the other members of the team Evaluate your own contribution to the project

Chapter 12 Project Management

12.1 Introduction “Failure to plan is planning to fail.” A good plan is one of the most important attributes of successful teams and projects. Projects should be organized systematically.

12.1 Eight Questions that can be Addressed with a Plan What to do first? Next? How many people? What resources? How long? Time table? Deadlines? Objectives?

12.2 Creating a Project Charter A project summary Defining what your project is and when you will know when it is done Elements include Deliverables Duration Stakeholders Team members

12.3 Task Definitions Identify the completion tasks to achieve the objectives and outcomes Plan Design Build Deliver

12.3 Plans Plans should include: Who to hold accountable for progress Needed materials, resources, etc. How to determine if the project is on schedule Manage people and resources Determine the end!

12.4 Milestones Monitoring of your plans progress Deadlines for deliverables Completion of subcomponents

12.5 Defining Times Include the full time needed for tasks As a student, you don’t have a full eight-hour work day every day Break tasks into week segments Weekday and/or weekend Class periods Break tasks into short time periods No more than a week or two

12.6 Organizing the Tasks Determine task relationships and sequencing Relate the task groups from your outline

12.7 PERT Charts Insert Figure 12.1 PERT Chart for Project Planning

12.7 PERT Charts Each task is represented by a box containing a brief description of and duration for the task The boxes can be laid out just as the project plan is laid out Useful as a “what if” tool during planning stages

12.8 Critical Paths The longest string of dependant project tasks Ex. – prerequisites such as the math curriculum for engineering Some tasks can be accelerated by using more people, others cannot Ex. – nine people cannot have the same baby in one month

12.9 Gantt Charts Popular project management charting method Horizontal bar chart Tasks vs. dates

12.9 Gantt Charts Insert Figure 12.2 Sample Gantt Chart from an Engineering Student Team

12.10 Details, Details Remember Murphy’s Law - “Anything that can go wrong, will.” Leave time to fix debug or fix errors

12.10 Details, Details Don’t assume things will fit together the first time Order parts well in advance to leave time for shipping, errors, or backorders Leave time for parts malfunction Push delivery times back to a week before they’re actually due – this will help to avoid panic if things go badly

12.11 Personnel Distribution Get the right people on the right tasks Assign people after developing a draft of the plan Balance the work between everyone Weekly updates – does everyone understand what they’re doing and is everyone still on task?

12.12 Money and Resources Develop a budget Extra costs Estimate with high, middle, and lower quality products – offer a range of solutions Extra costs Shipping Travel Extra parts such as nails, screws, resistors Material costs and labor Have someone be responsible for managing the budgets and financial aspects

12.13 Document As You Go Document milestones as they occur Leave time at the end for reviewing, not writing

12.14 Team Roles Roles Project Management Software Project Leader or Monitor Procurement Financial Officer Liaison Project Management Software

12.14 – Project Leader or Monitor Designate a leader, or rotate leaders Monitor and track progress of milestones Maintains timelines Increases likelihood of meeting goals

12.14 – Procurement Learns purchasing system Tracks team orders

12.14 – Financial Officer Manages teams expenses Creates original budget Makes identifying budgetary problems easier

12.14 – Liaison Responsible for keeping everyone informed about the progress of the plan and any changes This includes outside customers, management, professors, etc.

Chapter 13 Engineering Design

13.1 Engineering Design Engineering design is the process of devising a system, component, or process to meet desired needs. It is a decision making process in which the basic sciences and mathematics and engineering sciences are applied to convert resources optimally to meet a stated objective. Among the fundamental elements of the design process are the establishment of objectives and criteria, synthesis, analysis, construction, and testing….

13.2 The Design Process Identify the problem Define the working criteria/goals Research and gather data Brainstorm ideas Analyze potential solutions Develop and test models Make decision Communicate decision Implement and commercialize decision Perform post-implementation review

Chapter 14 Communication Skills

14.1 Why do we Communicate? Transfers important information Provides basis for judging one’s knowledge Conveys interest and competence Identifies gaps in your own knowledge

14.2-14.3 Oral and Written Communication Skills Present communication on a level that you believe will be easily understood by whomever is to be receiving your communication Don’t use big words if a smaller, easier-to-understand word will suffice.

14.5 Power of Language Be as clear as possible Avoid clichés Avoid redundancy Avoid using jargon specific to a certain group of people Don’t make sexual generalizations, I.e. his, hers, he, she

14.6 Technical Writing Identify thesis early Follows a specific format Follows a problem solving approach Uses specialized vocabulary Often incorporates visual aids Complete set of references Be objective, not biased either way

14.9 Formal Reports Should include: Analysis Title; short and concise Summary of what will be discussed Table of Contents (not including abstract) Introduction Analysis Procedure and Results Discussion of results Conclusions References Appendices

14.10 Other forms of Communication E-mail Progress reports Problem statements Cover letters Resumes

Chapter 15 Ethics

15. The Nature of Ethics Ethics is generally concerned with rules or guidelines for morals and/or socially approved conduct Ethical standards generally apply to conduct that can or does have a substantial effect on people’s lives

Chapter 16 Units

16.1 History of Units A common denomination of units is essential for the development of trade and economics around the world National Bureau of Standards, established by Congress, adopted the English system of measurement (12 inches, etc) Majority of nations in the world today operate on the metric system because of its simplicity (multiples of 10)

16.1 History of Units - SI Units Le Systeme International d’Unites, French for the International System of Units Improvements in the definitions of the base units continue to be made by the General Conference of Weights and Measures as science dictates

16.2 The SI System of Units Modernized metric system adopted by the General Conference, a multi-national organization which includes the United States Built on a foundation of seven base units, plus two supplementary ones All other SI units are derived from these nine units

16.2 The SI System of Units Multiples and sub-multiples are expressed using a decimal system Generally, the first letter of a symbol is capitalized if the name of the symbol is derived from a person’s name, otherwise it is lowercase

16.2 The SI System of Units Base Units in the SI system Meter = m Kilogram = kg Seconds = s Ampere = A Kelvin = K Mole = mol Candela = cd

16.3 Derived Units Expressed algebraically in terms of base and supplementary units Several derived units have been given special names and symbols, such as the newton (N).

Kilogram per cubic meter 16.3 Derived Units Quantities whose units are expressed in terms of base and supplementary units Quantity SI Unit SI Symbol Area Square meter m2 Speed, velocity Meter per second m/s Density Kilogram per cubic meter Kg/m3

Electrical Resistance 16.3 Derived Units Quantities whose units have special names Quantity SI Name SI Symbol Other SI Units Frequency hertz Hz cycle/s Force newton N kg*m/s2 Electrical Resistance ohm W V/A

16.3 Derived Units Units used with the SI System Name Symbol Value in SI Units Minute min 1 min = 60 s Hour h 1 h = 3600 s Degree ° 1° = p/180 rad

16.4 Prefixes Defined for the SI system Used instead of writing extremely large or very small numbers All items in a given context should use the same prefix, for example in a table Notation in powers of 10 is often used in place of a prefix

Multiplication Factor 16.4 Prefixes Multiplication Factor Prefix Symbol Term (USA) 1000000 = 106 mega M One million 1000 = 103 kilo k One thousand .001 = 10-3 milli m One thousandth .000001 = 10-6 micro One millionth

16.5 Numerals A space is always left between the numeral and the unit name or symbol, except when we write a degree symbol 3 m = 3 meters; 8 ms = 8 milliseconds SI units a space is used to separate groups of three in a long number 3,000,000 = 3 000 000 .000005 = .000 005 This is optional when there are four digits in a number (3456 = 3 456; .3867 = .386 7)

16.5 Numerals A zero is used for numbers between -1 and 1 to prevent a faint decimal point from being missed Rounding Significant Digits

16.6 Conversions To convert from: To: Multiply by: Degrees Radians 0.017 453 Inches Centimeters 2.54 Newtons Pounds 0.224 81

Chapter 17 Mathematics Review

17.1 Algebra Three basic laws Commutative: a + b = b + a Distributive: a ( b + c ) = a b + a c Associative: a + ( b + c ) = ( a + b ) + c

17.1 Algebra Exponents Logarithms Used for many manipulations Examples xa xb=xa+b xab=(xa)b Logarithms Related to exponents bx = y then x = logby Table 17.1.5

17.1 Algebra Quadratic Formula Binomial Theorem Partial Fractions Solves ax2 + bx + c = 0 Formula 17.1.6 Binomial Theorem Used to expand (a+x)n Formula 17.1.7 Partial Fractions Used for simplifying rational fractions Formulas 17.1.8, 17.1.9, 17.1.10, 17.1.11 Examples

17.2 Trigonometry Involves the ratios between sides of a right triangle sine, cosine, tangent, cotangent, secant, and cosecant are the primary functions Trigonometry identities are often used 17.2.3, 17.2.4, 17.2.5, 17.2.6, 17.2.7 For all triangle we can also use the laws of sines and cosines Some other equations that can be found in your book are Pythagorean Theorem 17.2.10 Hyperbolic Trig Functions 17.2.11 Examples

17.3 Geometry Used to analyze a variety of shapes and lines The equation for a straight line Ax + By + C = 0 This equation can also be written in Pint-slope, Slope-intercept, and Two-intercept forms Distance between a line and a point is given in Formula 17.3.5 The general equation of the second degree is

17.3 Geometry This equation is used to represent conic sections Classified on page 473 Ellipse, Parabola, Hyperbola More information on pages 474-475 Examples

17.4 Complex Numbers Complex numbers consist of a real (x) and imaginary (y) part x+iy where i= In electrical engineering j is used instead of i because i is used for current Useful to express in polar form Euler’s equation is also commonly used Other useful equations can be found on page 477 Examples

17.5 Linear Algebra Used to solve n linear equations for n unknowns Uses m x n matrices Many manipulations of this basic equation are shown on page 479 Determinants of matrices are often used in calculations Illustrated on page 480 Eigenvalues are used to solve first-order differential equations Examples

17.6 Calculus We first write derivatives using limits Some basic derivatives are shown on pages 484-485 Used to indicate points of inflection, maxima, and minima L’Hospial’s rule when f(x)/g(x) is 0 or infinity 17.6.6

17.6 Calculus Inversely we have integration Examples Used for finding the area under a curve Equation 17.6.7 Can be used to find the length of a curve Used to find volumes Definite when there are limits When indefinite a constant is added to the solution Basic Integrals on page 486 Examples

17.7 Probability and Statistics The probability of one events’ occurrence effects the probability of another event Probabilities Many combinations can occur P(A or B) = P(A)+P(B) P(A and B)=P(A)P(B) P(not A) = 1-P(A) P(either A or B)=P(A)+P(B)-P(A)P(B)

17.7 Probability and Statistics Probability ranges from 0 to 1 Additional equations on page 490 Arithmetic Mean Median Mode Standard Deviation Variance Examples

Engineering Fundamentals Chapter 18 Engineering Fundamentals

18.1 Statics Concerned with equilibrium of bodies subjected to force systems The two entities that are of the most interest in statics are forces and moments.

18.1 Statics Force: The manifestation of the action of one body upon another. Arise from the direct action of two bodies in contact with one another, or from the “action at a distance” of one body upon another. Represented by vectors

18.1 Statics Moment: Equilibrium: Can be thought of as a tendency to rotate the body upon which it acts about a certain axis. Equilibrium: The system of forces acting on a body is one whose resultant is absolutely zero

18.1 Statics Free Body Diagrams (FBD): Neat sketch of the body showing all forces and moments acting on the body, together with all important linear and angular dimensions. Insert figures from Example 18.3

18.2 Dynamics Separated into two sections: Kinematics Kinetics Study of motion without reference to the forces causing the motion Kinetics Relates the forces on bodies to their resulting motions

18.2 Dynamics Newton’s laws of motion: 1st Law – The Law of Inertia 2nd Law – F=ma 3rd Law – Fab=-Fba Law of Gravitation

18.3 Thermodynamics Involves the storage, transformation and transfer of energy. Stored as internal energy, kinetic energy, and potential energy Transformed between these various forms Transferred as work or heat transfer

18.3 Thermodynamics There are many definitions, laws, and other terms that are useful to know when studying thermodynamics.

18.3 Thermodynamics A few useful definitions: System A fixed quantity of matter Control Volume (open system) A volume into which and/or from which a substance flows Universe A system and its surrounding

18.3 Thermodynamics Some Laws of ideal gases: Boyle’s Law Charles’ Law Volume varies inversely with pressure Charles’ Law Volume varies directly with temperature Avagadro’s Law Equal volumes of different ideal gasses with the same temperature and pressure contain an equal number of molecules

18.4 Electrical Circuits Interconnection of electrical components for the purpose of: Generating and distributing electrical power Converting electrical power to some other useful form Processing information contained in an electrical form

18.4 Electrical Circuits Direct Current (DC) Alternating Current (AC) Steady State Transient circuit

18.4 Electrical Circuits Quantity Symbol Unit Charge Q coulomb Current ampere Voltage V volt Energy W joule Power P watt

18.4 Electrical Circuits Circuit Components: Resistors Inductors Capacitors Sources of Electrical Energy Voltage Current

18.4 Electrical Circuits Kirchhoff’s Laws Ohm’s Law Kirchhoff’s Voltage Law (KVL) Kirchhoff’s Current Law (KCL) Ohm’s Law V=IR

18.4 Electrical Circuits Reference Voltage Polarity and Current Direction Circuit Equations Using Branch Currents Using Mesh Currents Circuit Simplification DC Circuits

18.5 Economics Value and Interest Cash Flow Diagrams The value of a dollar given to you today is of greater value than that of a dollar given to you one year from today Cash Flow Diagrams Cash Flow Patterns Equivalence of Cash Flow Patterns

Chapter 19 The Campus Experience

19.1 Orienting Yourself to Your Campus Introduction to Campus Life Tools to assist students to adjusting to the college lifestyle

19.2 Exploring Begin by becoming familiar with some different locations on campus Offices Dorms Classroom Buildings Engineering Building Sample map of Michigan State University Campus

19.3 Determining and planning your Major Narrow down to a few different majors Ask questions of insightful people Look for any opportunity to learn more about each field

19.4 Get into the Habit of Asking Questions Active questioners learn the most Questions help students understand and complete tasks Communication skills are vital to engineers Understanding information given Giving information that is understandable

19.5 The ‘People Issue’ Meeting People Academic Advisor Make friends of other engineers Helpful as study partners Offer perspective on engineering Academic Advisor Advisors are an excellent resource Discuss problems Information about the school, classes, and instructors Offer guidance for graduating and careers

19.5 The ‘People Issue’ Instructors Networking Ask other students about an Instructor before signing up for the class Sit in on a class to see their teaching style Networking Keep in contact with friends and acquaintances Useful for assistance and support in and out of the classroom

19.6 Searching for Campus Resources Every school has a document or website that lists activities and opportunities Examples Things to Do, Places to Go Planetarium, Gardens, Museum, Union What’s Happening Academic calendar, calendar of events Library locations and hours Services Legal aid, counseling, financial aid Extracurricular Activities

19.7 Other Important Issues Managing Time Control time to achieve success Recommended Reading The Usefulness of Reading Engineering requires the extensive use of technical and non-technical materials Read each paragraph for its central point Create outlines for each reading assignment

19.7 Other Important Issues Fulfilling Duties Engineers have a responsibility to society Contributing to Society brings its own reward Using the Web Use the internet to look up more information on topics of interest outside the classroom Sending e-mail Most contacts use email for some part of their interaction

19.7 Other Important Issues Test-taking Skills Preparing outlines as subject matter is presented will make studying easier Form study groups Ask questions Taking Notes Organize information Highlight essential information

19.7 Other Important Issues Study Skills Should be calm, structured, and routine Remember to get up and move a few times in an hour Reward yourself for studying Teaching Styles Variety of Instructors including graduate students Fully engage professors and ask questions Learning Styles Discover your Learning Style and use it to your advantage

19.7 Other Important Issues Perspectives of others Learn to listen to others respectfully Be open to discussion of a variety of topics Listening Skills Dialogue does not need to be confrontational Allow others to express their opinions Listen carefully to what other people say

19.7 Other Important Issues Handling Stress Include time to relax in your schedule Take classes for the right reason Do not resent required classes Approach weak points with a positive attitude Focus on learning instead of grades Be patient for results of increased studying Stress can not be avoided Talking out problems can help

19.8 Final Thoughts Use the concepts from this chapter to make the college experience all it can be. Don’t forget to ask questions!!!

Chapter 20 Financial Aid

20.1 Intro What costs are involved in going to college? Tuition Other college or university fees Cost-of-living expenses Other “extras”

20.2 Parental Assistance Some parents are able and willing to cover all of your college expenses On average, nine million students must find ways to fund their college education every fall

20.3 Is Financial Assistance for You? Applying for Financial Aid Three areas: Grants and scholarships Loans Work Need vs. Non-need Academic qualifications Why apply?

20.3 Is Financial Assistance for You? Budgeting Advisors available to assist with personal budgeting Help estimate costs and income and develop a plan How to apply Free Application for Federal Student Aid (FAFSA)

20.3 Is Financial Assistance for You? FAFSA http://www.fafsa.gov First thing to complete to become eligible for aid Can apply as early as January for the following fall semester Look up the information required before starting to fill out the form

20.4 Scholarships Educational funds that do not need to be repaid Public, private, or university sources Local high school, professional groups, corporations, service organizations, government, college, etc. It is your responsibility to seek out private scholarships/grants

20.5 Loans May be secured from lending institutions and state and federal loan programs Students who apply for financial aid will be notified of their eligibility for both student and parent federal loans Loans can be obtained from parents or relative who feel that you should repay the money that is required to put you through school

20.6 Work-Study “Earning money the old-fashioned way” On- or off-campus employment during school Summer jobs Internships Co-ops Requires careful management of time

20.6 Work-Study Work-Study: “Just Plain Work” Volunteering Employment subsidized by the federal or state government Will be listed on your financial aid award letter is you are eligible “Just Plain Work” Volunteering Full Semester Off-Campus Employment

20.6 Work-Study Cooperative Education Academic program in which college students are employed in positions directly related to their major field of study Alternating, Parallel, and Back-to-back semesters

20.7 Scams to Beware Do your own homework to avoid scholarship service rip-offs Check with the Federal Trade Commission (FTC) http://www.ftc.gov/bcp/menu-jobs.htm

20.8 The Road Ahead Awaits Examine the many different sources available to you for obtaining the funds needed for your college expenses How much do you actually need? Correct forms and deadlines

Engineering Work Experience Chapter 21 Engineering Work Experience

21.1 A Job and Experience “How do you get experience without a job, and how do you get a job without experience?” Graduate schools and employers look for experiences outside the classroom Incorporating career experience is a worthwhile consideration May extend college to 6 years Many Economic shifts have happened in a college students lifetime 1980-1983: Major Recession 1983-1986: Revival of U.S. Economy 1988-1994: Restructuring of Corporate America 1994-2001: Vigorous Rebound of Economy 2001-2003: Recession 2004- : Signs of improvement in the labor market for engineers

21.1 A Job and Experience In good and bad times employers look for Engineers with job-related experience Engineers require less training Faster results Many different Experiences are available

21.2 Summer Jobs Even jobs such as baby-sitting and mowing lawns is a place to start All jobs help develop basic employable skills Provide stepping stone to better, more career related jobs Skills include teamwork, communication, and problem solving Help you discover what working environments you like

21.3 Volunteer Especially useful to freshmen and sophomores to gain experience Generally volunteer positions are with non-profit organizations Not a paid experience Useful in developing skills Able to experiment with different career related fields

21.4 Supervised Independent Study Designed for the advanced undergraduate Preparatory for grad school or a career in Research Some are paid and others award credit Provides a unique experience Challenging in many different areas To learn more Talk to professors that share similar interests

21.5 Internships Paid or unpaid experience for a set period of time Usually during the summer No obligations for future employment Sometimes they support other engineers Other times they are given individual projects No official evaluation or credit given Short term projects Obtain a description of these projects prior to employment to assure it is of interest Great for students with time, curriculum, and location constraints

21.6 Co-operative Education Cooperative Education is often the preferred form of experimental Learning Co-ops are considered to be academic and are administered by the college Assignments are directly related to field of study Detailed job descriptions are used to create the best possible matches School and work are closely integrated Alternating terms of school with work at the same company Projects become more extensive throughout the experience Term in school followed by a term at work followed by a term at school and so on

21.6 Co-operative Education Parallel co-ops is an alternative Students are partially enrolled in classes and spend 20 to 25 hours at work Difficulties arise in allowing ample time for both areas Sometimes a longer alternating approach is used Students work two consecutive semesters then attend class for a semester or two Allows for longer projects Some schools use all three methods Co-ops are rarely summer only Break between work assignments is too long Requires a three or four semester commitment

21.6 Co-operative Education Advantages for Students Consideration for employment and grad school Improved technical skills Helps determine career path Excellent pay Advantages for Employers Recruiting Co-op students is more cost efficient Many students accept full time positions with their employer More diverse and dedicated students Students free up other engineers and bring in fresh approaches

21.6 Co-operative Education Advantages for Schools Integrates theory and practice Keeps faculty informed of trends in industry Creates relationships between schools and businesses Improves a schools reputation Other Benefits Communication Skills Networking Self-discipline Management Experience Interactions with a variety of people

21.7 Which is Best for You? Some Questions to help determine which is best for you Am I willing to sacrifice convenience for the best experience? How flexible can I be? How committed do I want to be? Seek out advice from professors, academic advisors, and campus placement officers

Connections: Liberal Arts and Engineering Chapter 22 Connections: Liberal Arts and Engineering

22.1 What are Connections? Connections exist between engineering and liberal arts Literature History Music Art Social studies Philosophy

22.1 What are Connections? Look closely at what engineers really are and what they really do “liberal” comes from liberty, so that liberal arts means “works befitting a free man” Need for a general education Developed because people have a need for a strong, open mind in addition to a specialty in order to be well-rounded Not trapped by cultural blind-spots

22.2 Why Study Liberal Arts? Liberal arts help improve your broadness Look in many directions at once Questions about areas that do not have pre-set answers Expected to be a leader

22.2 Why Study Liberal Arts? The Arts Improve: Your Perspective See the “big picture” Your Balance Practice dealing with a variety of diverse ideas Your People Skills Be aware of things that modern tendencies avoid or neglect

22.2 Why Study Liberal Arts? The Arts Improve: Your Sense of Duty and Responsibility Elevate, integrate, and unify the standards of the profession Fulfill your duty in life, so society respects you more

The Basics of Power Point Appendix A: The Basics of Power Point

A.1 Introduction The purpose of this section is to introduce a user to PowerPoint Learn 20 key procedures Be able to do 80% of everything you will ever need to do To learn more experiment with the software

A.2 The Basics of PowerPoint To begin open a blank presentation Activate the standard, formatting, drawing, picture, and WordArt toolbars Select a slide type for the first slide Select a background Enter text into given text blocks Edit the text and box sizes and shapes Add additional text boxes selecting Insert-TextBox Insert WordArt as necessary

A.2 The Basics of PowerPoint Insert any pictures Click Insert-Picture-From File Format the picture using the Picture toolbar Insert Clip Art Click Insert-Picture-Clip Art Picture Toolbar is used for formatting Change visibility of an object by right clicking on an object and then selecting Order from the menu To Delete objects click on it and press backspace or delete

A.2 The Basics of PowerPoint To begin a new slide click the new slide button Repeat from the beginning to format View slides by thumbnails in the Slide Sorter View Useful for arranging or hiding slides for presentations Can be used when copying or deleting whole slides Save your work when finished Change slide transitions and animations View the entire Show

Introduction to MATLAB Appendix B: Introduction to MATLAB

B.1 Introduction MATRIX LABORATORY Powerful tool in performing engineering computations Many engineering curricula have moved to making MATLAB the primary computing tool in its undergraduate program Can be run on many different platforms, including UNIX, PC, and Macintosh.

B.2 MATLAB Environment Command window Command History window Use to run your programs and see the results Command History window Shows a history of the commands that have been entered into the command window Launch Pad window Allows you to start applications and demonstrations by clicking the icons in the window

B.2 MATLAB Environment Demonstration Programs Help Files >>help <command name> >>lookfor topic >>helpwin MATLAB is case sensitive Apple ≠ apple ≠ APPLE ≠ aPPle

B.2 MATLAB Environment Helpful commands >>who >>clear Allows the user to see the variables currently in memory >>clear Erase the memory >>clear <variable> Clears just that variable

B.2 MATLAB Environment MATLAB has some predefined functions that should not be used to name variables A few variable names to avoid: ans Inf NaN i j realmin

B.3 Symbolic Manipulations To declare variables as a symbol >> syms x y Algebraic expressions >>solve (x^2-4) Symbolic derivatives >>diff (y^3) Symbolic integrals >>int (sin(x))

B.4 Saving and Loading Files To find out the identity of your working directory, type pwd (print working directory) Use cd to change the working directory >>cd c:\matlab\mystuff The file can be saved using save at the MATLAB prompt

B.4 Saving and Loading Files Use the command load followed by the file name to retrieve your file. >>load my_workspace path lists the directories that MATLA will search for files addpath <pathname> will add the location to the path listing

B.5 Vectors A vector is simply a row or column of numbers Vectors are enclosed in square brackets >>row_vector = [1 2 6 9 12] >>col_vector = [2;4;6;8;10] To change a column vector into a row vector and vice versa, use transpose

B.5 Vectors For vectors to be added and subtracted, they must be of the same type and size To multiply or divide vectors, special MATLAB symbols must be used “.*” is used for multiplication “./” is used for division

B.6 Matrices A matrix is a group of numbers arranged in columns and rows Each element in a matrix is identified by the use of two numbers or indices The first index is the row number The second index is the column number MATLAB can extract an entire row or column, or specific elements

B.7 Simultaneous Equations Put the equations to be solved into standard form To solve for matrix x from Ax=b X=A\b

B.9 Plotting To generate linear xy plots use plot >>plot(x axis values, y axis values, ‘symbol or line type’) Use hold on to plot multiple data sets The axes can be labeled using the commands xlabel, ylabel, and title To generate multiple plots on a single figure use subplot

B.9 Plotting Semi-log and log plots semilogx semilogy loglog

B.9 Plotting Add Table B.1 Line and Symbol Options

B.10 Programming Programs, called scripts, consist of a series of MATLAB commands that can be saved to run later Select new, M-file to open the programming editor Enter MATLAB commands just like you would type them into the workspace Add comments by using the % symbol

B.10 Programming Save the file with a .m extension Remember to avoid file names that MATLAB already uses The file can then be executed by typing the file name at the MATLAB prompt

B.10 Programming Input commands To ask the user to input a number >>W=input(‘Enter a number to be used by the program’) To ask the user to enter a string >>my_word=input(‘Enter a word:’,’s’) The function disp can be used to display data