1. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections

2. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections CHAPTER 2 Math and Science Connections Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. What are some basic to advanced math concepts that engineers use in the regular course of their work, and what are four science disciplines that are addressed in this chapter.

3. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science ConnectionsCopyright © by The McGraw-Hill Companies, Inc. All rights reserved.  Describe three levels of mathematics that engineers use.  Discuss how probability and statistics affect the choices applied to engineers’ designs.  List applications of geometry and trigonometry in engineering.  Describe how engineers work within four fields of science.  Identify three main physics topics of interests to engineers. CHAPTER 2 Math and Science Connections

4. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science ConnectionsCopyright © by The McGraw-Hill Companies, Inc. All rights reserved. Regardless of the field of engineering, one or more fields of science along with various levels of mathematical concepts, are applied in the design and analysis of products and systems. CHAPTER 2 Math and Science Connections

5. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science ConnectionsCopyright © by The McGraw-Hill Companies, Inc. All rights reserved.  probability  quadratic  iteration  space  waveforms  derivatives  potential energy  kinetic energy  force  fluid mechanics  hydrology  hydrocarbons CHAPTER 2 Math and Science Connections

6. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science ConnectionsCopyright © by The McGraw-Hill Companies, Inc. All rights reserved. Draw this table for each section. Write key terms and phrases under Cues. Write main ideas under Note Taking. Summarize the section under Summary. CHAPTER 2 Math and Science Connections

7. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections Math Connections and Applications Basic Mathematics 2.1 Section A ratio is a comparison of two numbers and is expressed as a fraction. Five-Speed Manual Transmission Gear Ratios Ratios

8. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections Math Connections and Applications Basic Mathematics 2.1 Section In a reciprocal, the numerator of a fraction becomes the denominator and the denominator becomes the numerator. Reciprocals

9. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections Math Connections and Applications Basic Mathematics 2.1 Section Logic is the study of mathematical reasoning, and can be applied to various engineering problems. Logic What is the length of the diagonal inside the cube? Will the fishing rod meet airline regulations? The airline will not allow any baggage that measures more than three feet in any direction.

10. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections Math Connections and Applications Basic Mathematics 2.1 Section An algorithm is a process for performing a task and is closely related to mathematical logic. AlgorithmsControl System Algorithm

11. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections Math Connections and Applications Basic Mathematics 2.1 Section Extremely accurate measurements are vital to engineering projects, whether these are measurements of distance and size, or quantities. Dimensions and Units

12. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections Math Connections and Applications Basic Mathematics 2.1 Section At the heart of the study of statistics is an understanding of the normal distribution, also known as Gaussian distribution. Statistics

13. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections Math Connections and Applications Basic Mathematics 2.1 Section Determining probability begins with taking a random sample. Probability

14. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections Math Connections and Applications Algebraic Applications 2.1 Section Engineers use inverse functions to determine values. The equation in standard form of a quadratic function is y = ax 2 + bx + c x is the independent value. y is the dependent variable. a,b, and c are constants.

15. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections Math Connections and Applications Algebraic Applications 2.1 Section A parabola is the graph of a quadratic function.

16. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections Math Connections and Applications Algebraic Applications 2.1 Section

17. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections Math Connections and Applications Geometry and Trigonometry 2.1 Section There are 446 iterations of the shape “X “ in the fractal antenna shown. In each small square there are 21 iterations, and there are 21 small squares, plus there are 4 “X” shapes connecting small squares, and one large “X” shape overall [21 × 21) + 4 + 1 = 446]. iteration a succession of approximations used to develop accuracy; a repetition >

18. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections Math Connections and Applications Geometry and Trigonometry 2.1 Section space the three-dimensional extent of an object or area > In the fractal antenna, the surface area of the antenna can be maximized relative to its length. This enables an effective antenna to occupy a much smaller overall space.

19. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections Math Connections and Applications Geometry and Trigonometry 2.1 Section The Cycloid

20. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections Math Connections and Applications Geometry and Trigonometry 2.1 Section Key Concepts Area and VolumeVectorsTrigonometry Applied in the analysis of waveforms waveforms the shapes and forms of signals moving through a solid, liquid, or gas >

21. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections Math Connections and Applications Geometry and Trigonometry 2.1 Section Global PositioningIndirect Measurement Sine Wave

22. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections Math Connections and Applications Calculus Applications 2.1 Section Logarithms Differential Equations Derivatives derivatives in mathematics, measures of how a function changes when its input changes >

23. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections 1.Identify the three main areas of math used by engineers. Math Connections and Applications 2.1 Section

24. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections 2.Explain the key statistical concept used in quality control and why it is used. Math Connections and Applications 2.1 Section

25. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections 3.Analyze how a GPS works in the mathematical sense. Math Connections and Applications 2.1 Section

26. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections Physics Concepts Science Connections and Applications 2.2 Section

27. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections Physics Concepts Science Connections and Applications 2.2 Section Common Formulas for Work, Energy, and Power potential energy stored energy, based on an object’s position > kinetic energy active energy, based on the movement of an object from a stationary position >

28. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections Physics Concepts Science Connections and Applications 2.2 Section Nuclear Power Plant

29. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections Physics Concepts Science Connections and Applications 2.2 Section Thermodynamics

30. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections Physics Concepts Science Connections and Applications 2.2 Section Kinematics is the study of the motion of objects. Torque is the measure of the turning force acting on an object. Elements of Torque

31. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections Physics Concepts Science Connections and Applications 2.2 Section Optics is the study of the behavior and properties of light.

32. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections Physics Concepts Science Connections and Applications 2.2 Section Acoustics is the study of sound waves. Noise-Canceling Headphones

33. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections Earth Science Applications Science Connections and Applications 2.2 Section GeologyWater Geotechnical EngineeringFluid Mechanics Hydrology Ocean Engineers Flood Control Systems fluid mechanics the study of fluids and the forces that act on them > hydrology the study of water and its occurrence, circulation, and distribution on earth >

34. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections Chemistry Concepts Science Connections and Applications 2.2 Section Atomic and Molecular Structure Materials Science Organic Chemistry Electrochemistry Environmental Chemistry

35. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections Chemistry Concepts Science Connections and Applications 2.2 Section hydrocarbons molecules that consist only of hydrogen and carbon atoms >

36. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections Biological Applications Science Connections and Applications 2.2 Section BotanyGeneticsAnatomy PhysiologyBioremediation

37. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections Biological Applications Science Connections and Applications 2.2 Section

38. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections 1.Describe what is studied in the science of thermodynamics. Science Connections and Applications 2.2 Section

39. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections 2.Analyze why knowledge of geology is important to engineers. Science Connections and Applications 2.2 Section

40. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections 3.Justify why groups of electrochemical cells are often used together in a device. Science Connections and Applications 2.2 Section

41. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Chapter 2 Math and Science Connections End of