1. Developing a Solution
How to create the computer-based solution for a real-world problem.
The steps
- Examples for each step

2. General Idea of This Lesson
Give you methodology (i.e. a recipe)
Example problems:
“Find the optimum nozzle dimensions for …”
“Solve for the optimum path for the robot …”
“Find the range of temperatures adequate for …”
In EGR115, most tasks will be:
“Develop a program that ……”

3. General Terms Keep in mind there are 2 sides to software
The person who writes software: the programmer
The person who uses software: the user (i.e. client)

4. “The programmer should make the user’s life easy.”
General Terms
Keep in mind there are 2 sides to software
The person who writes software: the programmer
The person who uses software: the user (i.e. client)
As you (the student) develop software, you will constantly jump back and forth between the two roles.
Your goal:
“The programmer should make the user’s life easy.”
Clear directions
Clear units
Examples of answers
Clean presentation

5. Scientific Problem-Solving Method
An everyday part of the engineer’s thought process.
“If these steps are properly executed during the solution of problems in this text and all other courses, it is our belief that you will gradually develop an ability to solve a wide range of complex problems.”
Engineering Fundamentals and Problem Solving, Eide, Jenison, Mashaw and Northup

6. Where do I even start?
ME408 Clean Thermal Power Systems

7. Scientific Problem-Solving Method
Problem Statement
Diagram
Theory
Assumptions
Solution Steps
Identify Results & Verify Accuracy
Computerize the solution
Deduce the algorithm from step 5
Translate the algorithm to lines of code
Verify Results

8. Scientific Problem-Solving Method
Problem Statement
Diagram
Theory
Assumptions
Solution Steps
Identify Results & Verify Accuracy
Computerize the solution
Deduce the algorithm from step 5
Translate the algorithm to lines of code
Verify Results
“coding” is very late in the process.
NEVER create a program to “solve” a problem.
=> Create a program to re-use the solution for other sets of givens.

9. Scientific Problem-Solving Method
Problem Statement
Summarize the given information
Must contain all essential information, units included!
GET RID OF useless information!
State what is to be determined
Diagram
Theory
Assumptions
Solution Steps
Identify Results & Verify Accuracy
Computerize the solution

10. Example – Aerospace Engineering
Pb: ideal gas law
Givens
Temperature (Kelvin)
Volume (meters cubed)
n : chemical amount of gas (moles)
R : gas constant R = Joules/(moles*Kelvin)
Solve for
The pressure (Pascals)

11. Example – Mechanical Engineering
R2 = 60lb
R3 = 20lb
Pb: Stress on a beam
Givens
Load 1: R1 = 10lb
Load 2: R2 = 60lb
Load 3: R3 = 20lb
Load 4: R4 = 50lb
Distances from start of beam to load2: 5ft
Distance between load2 and 3: 15ft
Distance between load3 and end of beam: 7ft
Solve for
shear diagram
moment diagram
5ft
15ft
7ft
square beam
R1 = 10lb
R4 = 50lb

12. Example – Civil Engineering
Pb: Elongation of rod
Givens
diameter of rod: 0.5in
length of rod: 6ft
weight of load: 2000lbs
material: steel
Solve for
normal stress in rod (psi)
strain (elongation for 1 unit) in the rod (in./in)
elongation of rod (inches)
6ft
2000 lbs

13. Scientific Problem-Solving Method
Problem Statement
Diagram
Sketch
Diagrams
Indicate all dimensions
Theory
Assumptions
Solution Steps
Identify Results & Verify Accuracy
Computerize the solution

14. Example – Aerospace Engineering

15. Example – Civil Engineering

16. Example – Electrical Engineering

17. Scientific Problem-Solving Method
Problem Statement
Diagram
Theory
State/List all equations that will be used
Explain all variables
This step will be simple as a Freshmen, but may get to pages and pages of derivations in Senior year!
Assumptions
Solution Steps
Identify Results & Verify Accuracy
Computerize the solution

18. Example – General Equations
Volume of a sphere
Equation of a line
V = 4/3*∏*R^3
y = m*x + b
Volume of a cube
Slope
V = L^3
m = Δy/Δx = (y2-y1)/(x2-x1)
Newton’s second law of motion
Weight
W = mass * g
F = m*a

19. Example – ME/AE Engineering
If the system is in equilibrium,
ΣF = 0 (“sum of all forces equals zero”)
Bernoulli’s Principle (fluid dynamic)

20. Example – Electrical/Civil Engineering
Ohm’s law
V = R*I (V=voltage (V), R=resistance (Ω), I=current (A))
Electrical Power (i.e. Work)
P = V * I (P = power, in Watts)
Potential Energy
Penergy = w * h (W=weight (Newtons), h=height (m), P (Joules))
Kinetic Energy
Kenergy = ½*m * v2

21. Scientific Problem-Solving Method
Problem Statement
Diagram
Theory
Assumptions
List any assumptions (physical, mathematical, …)
Make them clear to the reader
Solution Steps
Identify Results & Verify Accuracy
Computerize the solution

22. For example… Assume no friction Assume wall thickness is negligible
Assume initial speed is zero
Assume mass of object is negligible
Aerodynamics: Assume laminar flow
(i.e. no turbulence)
Thermodynamics: Assume geometry of a turkey is that of an American football
Solids: assume system is in equilibrium

23. Scientific Problem-Solving Method
Problem Statement
Diagram
Theory
Assumptions
Solution Steps
Show all complete steps and equations
Number the equations if it helps you
Detail each step precisely, even those that seem trivial to you
Choose actual numerical values if needed
The READER is the one who needs to understand
Identify Results & Verify Accuracy
Computerize the solution

24. Examples
Number the equations
© FrigginPhysics.com

25. Scientific Problem-Solving Method
Problem Statement
Diagram
Theory
Assumptions
Solution Steps
Identify Results & Verify Accuracy
Circle your answer(s), draw a square around it, underline
Make sure they have units
VERIFY that the answer is plausible, realistic
Computerize the solution

26. Identify Results Make sure the solutions are clearly identified
example: boxed, circled, colored, underlined, centered…
© FrigginPhysics.com

27. Verify Do the values match/verify the diagram? Common sense Visually
Time cannot be negative
Distance cannot be negative
Visually
If you drew a scaled diagram, verify that the results match the drawing?
Is it realistic?
Drive Time = 394,242,305,932seconds?
Vrunner = miles/hr
When turning in homework, always work on fixing errors, but if you fail, at least indicate “something wrong, this is unrealistic”… before turning it in..

28. Last but not least!!! Presenting the data
Paper, or machine
Either way:
Clearly present the information
Words and sentences must explain what’s going on each step
Skip lines, space things out!
not everything has to fit on the top left corner!!!!

29. Bad Presentations
inadequate paper size, incomplete (missing data, and units), change of orientation, no breathing room…
where are the results?!
Semester 2012 Fall

30. Scientific Problem-Solving Method
Problem Statement
Diagram
Theory
Assumptions
Solution Steps
Identify Results & Verify Accuracy
Computerize the solution
Deduce the algorithm from step 5
Translate the algorithm to lines of code
Verify Results
If all steps above were done thoroughly, this step 7 should not be mind-stressing.
b. and c. is what will be learned all this semester!

31. 7.a. Deduce the algorithm
In mathematics and computer science, an algorithm is a step-by-step procedure for calculation. (Wikipedia)
More precisely, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. (Wikipedia)
Algorithms
must not be complex!
should be detailed/organized
must be general enough for different values of inputs
Simple problem = simple algorithm
Complex problem = detailed algorithm

32. Example The problem The algorithm Define base and height
Calculate area
Display result OR
Define side1 and 2’s length
Define angle between the two sides
height=6m
base=3m
“detailed yet general”
side 1=25m
side 2 = 45m
angle = 26.5deg

33. Wrapping Up Determine what the problem is about: givens/solve for
Use diagrams to help, if possible to scale!
Careful with units
Solve step by step – DETAILED.
Make clear where are the results
VERIFY the 1)reality and 2)accuracy of your result
then code…
NEVER code immediately
Vocabulary:
user, programmer, algorithm

34. Try it yourself Apply steps 1 through 7a. for the following problem
You’re buying this odd shaped land. Cost of land is $100,000/acre. Given the following data (expressed in meters), how much do you expect to pay for this land?