ProblemSolving for engineering presentation.ppt
- 2. What Is Engineering? • Engineering is the application of science and mathematics to solve technical problems and create new systems, products, or devices to benefit civilization. • The end result of science is new knowledge. The end result of engineering is design. • ABET: Engineering is the profession in which a knowledge of the mathematical and natural sciences gained by study, experience, and practice is applied with judgment to develop ways to utilize, economically, the materials and forces of nature for the benefit of mankind.
- 3. The Technological Team Scientist Engineer Technologist Craftsperson Theory <---------------------------------------------->Practice
- 4. Problem Solving • ... is the foundation of all engineering activities. • ... is the process of determining the best possible action to take in a given situation.
- 5. Two Types of Problems: Analysis and Design • Analysis Problems - closed-ended problems which determine the properties of a given device or system, and generally have only a single correct solution. • Design Problems - open-ended problems to create a system or device that has given properties, and generally have multiple correct solutions. • A formal, systematic problem-solving methodology is necessary for both types of problems.
- 7. The Analysis Process - 5 Steps 1. Define problem - diagram or sketch is good. 2. Collect information - data, theories, assumptions, approximations. 3. Generate a solution - maybe several possible ways. 4. Refine and implement - use a tool: spreadsheet, MATLAB, or other computer program/language. 5. Verify and test - estimate, work another way, try other data input, compare with a plot, check dimensional consistency.
- 8. Problem-Solving Tools • Calculator, pencil, and paper • Electronic spreadsheet • Math software • Programming languages
- 9. Example: Typical math “word problem” 1. Define the problem: Bill is shopping for some carpet for his den, which is 12 x 18 feet. The carpet he likes is $20 per square yard. He has $500 to spend. After purchasing the carpet, will he be able to purchase a $5 Happy Meal with the money left over?
- 10. Word Problem (cont’d) 2. Collect information $500 available $20 per square yard 9 square feet per square yard 18 ft = 6 yds 12 ft = 4 yds
- 11. Word Problem (cont’d) 3. Generate a solution • Develop an algorithm: – Find dimensions of room in yards. – Find area of room in square yards. – Multiply by cost of the carpet per square yard to get total cost. – Subtract total cost from money available. – Is remainder enough for Happy Meal? • Draw a flow chart for this.
- 12. Word Problem (cont’d) 4. Refine and implement – Compute steps using a pencil and paper, or a calculator.
- 13. Word Problem (cont’d) 5. Verify and test – Rework problem in feet, rather than yards. – Estimate and compare: » 12 x 18 is close to 10 x 20 = 200 sq ft » 200 sq ft is close to 20 sq yds » 20 sq yds times $20 each is $400 » This is the same order of magnitude as our $480 answer. » Estimates are used simply to check whether your answer makes sense.
- 14. Example: Maximum Height of a Projectile 1. Define the problem: A snowball is tossed straight up in the air with an initial velocity of 100 ft/sec. The moment it leaves the thrower’s hand it is 6 ft above the ground. What is the maximum height reached by the snowball? 2. Collect information 3. Generate a solution 4. Refine and implement – pencil and paper (chalk and blackboard) – spreadsheet – MATLAB 5. Verify and test
- 15. Communicating Solutions • All solutions should be clearly labeled, documented, and commented. • Standards will be followed in this course for: – Spreadsheet solutions – MATLAB solutions
- 16. Spreadsheet Solutions • Provide standard labeled sections. • Use separate, labeled sheets to divide the work logically. • Label columns, rows, important cells. • Use (but don’t overuse) color to delimit ranges in a consistent way. • Use named ranges - carefully.
- 17. MATLAB Solutions • Provide standard labeled sections. • Insert comments or subsection headings liberally. • Choose meaningful, consistent variable names. • Entire program should execute correctly from the top.
- 18. Design Problems
- 19. The Design Process - 5 Steps 1. Define the problem. 2. Collect information. 3. Generate multiple solutions. 4. Analyze and select a solution. (Use a tool.) 5. Test and implement the solution. (Use a tool.) This is a contingent, iterative process.
- 20. Test & implement a solution Define the problem Gather information Generate multiple solutions Analyze & select a solution Engineering Design Process
- 21. Example: Creating a Report 1. Define the problem: Write and print out a professional-looking report that includes a table of data stored in a text file on the Engineering anonymous ftp server (UNIX), and a figure stored in a BMP file on the Windows NT server. 2. Collect information 3. Generate multiple solutions 4. Analyze and select best solution 5. Test and implement