1. Problem Solving: Practice & Approaches 1.Practice solving a variety of problems 2.Strategies for solving problems 3.More Practice 1

2. General Idea of This Lesson Programming is like learning a language – You need to learn the vocabulary (keywords), grammar (syntax), and how to use punctuation (symbols) Problem solving is like learning to cook – A novice chef has a recipe – An master chef can create their own recipe Both tasks require practice! 2

3. Review: Scientific Problem-Solving Method 1.Problem Statement 2.Diagram 3.Theory 4.Assumptions 5.Solution Steps 6.Identify Results & Verify Accuracy 7.Computerize the solution a.Deduce the algorithm from step 5 b.Translate the algorithm to lines of code c.Verify Results 3

4. Example #1: Balancing a fulcrum A 30-kg child and a 20-kg child sit on a 5.00-m long teeter-totter. Where should the fulcrum be placed so the two children balance? (Note: an object is in static equilibrium when all moments balance.) Using the supplied worksheet, solve the problem with the people sitting next to you. 4

5. Example #1: Balancing a fulcrum 5 1.Problem Statement: a)Givens: a)Find: 2.Diagram

6. Example #1: Balancing a fulcrum 6 3.Theory 4.Assumptions 1 2 3

7. Example #1: Balancing a fulcrum 7 5.Solution Steps

8. Example #1: Balancing a fulcrum 8 6.Identify results and verify Does this make sense? – Units? – Overall Dimension? – Easy to imagine! – Can you rerun the analyses with other givens using Step 5? This is the key to Computer Programming!!

9. Problem Solving Strategies The trouble with Step 5: “Solution Steps” There can be many approaches to solving the same problem Creativity is an important component on how we view and approach problems: 9

10. Creativity Connect the following 9 dots with four continuous lines without lifting your pencil Sometimes you will need to think outside the box 10

11. Problem Solving Strategies (Polya, 1945) Utilize analogies – Flow through a piping system can be modeled with electronics Resistors – Fluid Friction Capacitors – Holdup tanks Batteries – Pumps Work Auxiliary Problems – Remove some constraints Generalize the problem Ex: L 1 = m 2 * L / (m 1 + m 2 ) 11

12. Problem Solving Strategies (Polya, 1945) Decompose & Recombine problems – Break the problem into individual components Calculate Cost of Area 12 Prove the following equation 2 x 2 x 2 x 2 = 16

13. Problem Solving Strategies (Polya, 1945) Work backwards from the solution Ex: Measure exactly 7 oz. of liquid from a large container using only a 5 oz. container and an 8 oz. Container Solution: 13 8 5 7?

14. Example #2: Fuel tank design A fuel tank is to be constructed that will hold 5 x 10 5 L. The shape is cylindrical with a hemisphere top and a cylindrical midsection. Costs to construct the cylindrical portion will be $300/m 2 of surface area and $400/m 2 of surface area of the hemispheres. What is the tank dimension that will result in the lowest dollar cost? 14

15. 1.Problem Statement: a)Givens: b)Find: 2.Diagram Example #2: Fuel tank design 15 R H

16. Example #2: Fuel tank design 16 3.Theory 4.Assumptions 1 2 3 4

17. Example #2: Fuel tank design 17 5.Solution Steps

18. Example #2: Fuel tank design 18 5.Solution Steps

19. Example #2: Fuel tank design 19 5.Solution Steps R

20. Example #2: Fuel tank design 20 6.Identify results and Verify Does this make sense? – Units? – Overall Dimension? – Can you rerun the analyses with other givens using Step 5?

21. Wrapping Up Utilize the 7 step process before you begin programming Be clear about your approach Think creatively Use a couple of strategies when understanding a problem Practice! Use Matlab to make your life easier 21

22. Try it yourself What if the fuel tank had two hemispheres? 22 R H A fuel tank is to be constructed that will hold 5 x 10 5 L. The shape is cylindrical with a hemisphere top, a hemisphere base and, and a cylindrical midsection. Costs to construct the cylindrical portion will be $250/m 2 of surface area and $300/m 2 of surface area of the hemispheres. What is the tank dimension that will result in the lowest dollar cost?