Problem Solving: Practice & Approaches

Problem Solving: Practice & Approaches Practice solving a variety of problems Strategies for solving problems More Practice

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!

Review: 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

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.

Example #1: Balancing a fulcrum • Problem Statement: • Givens: • Find: • Diagram

Example #1: Balancing a fulcrum • Theory • Assumptions 1 2 3

Example #1: Balancing a fulcrum • Solution Steps

Example #1: Balancing a fulcrum • 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!!

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:

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

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: L1= m2* L / (m1 + m2)

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

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: 8 7? 5

Example #2: Fuel tank design A fuel tank is to be constructed that will hold 5 x 105 L. The shape is cylindrical with a hemisphere top and a cylindrical midsection. Costs to construct the cylindrical portion will be $300/m2 of surface area and $400/m2 of surface area of the hemispheres. What is the tank dimension that will result in the lowest dollar cost?

Example #2: Fuel tank design • Problem Statement: • Givens: • Find: • Diagram R H

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

Example #2: Fuel tank design • Solution Steps

Example #2: Fuel tank design • Solution Steps R

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

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

Try it yourself • What if the fuel tank had two hemispheres? A fuel tank is to be constructed that will hold 5 x 105 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/m2 of surface area and $300/m2 of surface area of the hemispheres. What is the tank dimension that will result in the lowest dollar cost? R H

Problem Solving: Practice & Approaches