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Problem Solving

Problem Solving. Presentation of Engineering Solutions. As a pair, in the next 5 minutes review the contents of Supplement_3a.ppt (Note: This material was taken from Chapter 3.4 of Foundations of Engineering ). Engineers Solve Problems. Problem solving is a powerful human activity.

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Problem Solving

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  1. Problem Solving

  2. Presentation of Engineering Solutions • As a pair, in the next 5 minutes review the contents of Supplement_3a.ppt (Note: This material was taken from Chapter 3.4 of Foundations of Engineering)

  3. Engineers Solve Problems • Problem solving is a powerful human activity. • Computers are useful tools in problem solving, but it is the human who actually solves the problem. • It is impossible to teach specific facts that will always lead to a solution. • The ability to solve problem comes from doing it. • Many things must pull together to solve a problem.

  4. Methods for Problem Solving • If the problem is extremely well defined, use algorithms - A set of well-defined rules for the solution of a problem in a finite number of steps These may be implemented in computer programs e.g. Solve for x in ax2 + bx + c = 0

  5. Difficulties in Problem Solving • Most common difficulty: failure to use known information. • To avoid this problem: • Write the problem in primitive form and sketch an accurate picture of the setup (where applicable). • Transform the primitive statements to simpler language. • Translate verbal problems to more abstract mathematical statement(s) and figures, diagrams, charts, etc.

  6. Given: A student is in a stationary hot-air balloon that is momentarily fixed at 1325 ft above a piece of land. This pilot looks down 60o (from horizontal) and turns laterally 360o. Required: a) Sketch the problem b) How many acres of land are contained by the cone created by her line of site? c) How high would the balloon be if, using the same procedure, an area four times greater is encompassed? Pair Exercise (5 minutes) Note: 1 acre = 43,560 ft2

  7. Problem Solving • As a pair, in the next 10 minutes review the contents of • Supplement_3b.ppt • Supplement_3c.ppt (Note: This material was taken from Chapter 3 in Foundations of Engineering.)

  8. More Difficulties in Solving Problems • Imposing unnecessary constraints: • Association Constraints - unstated constraints based on previously learned associations. • Function Constraints - unstated constraints based on previously learned functions. • World View Constraints - unstated constraints imposed by individual's world view.

  9. Individual Exercise (3 minutes) • The nine dots shown are arranged in equally spaced rows and columns. Connect all nine points with four straight lines without lifting the pencil from the paper and without retracing any line.

  10. Team Exercise (3 minutes) • You are given six straws of equal length and asked to form four identical (equilateral) triangles with each side formed by one of the straws.

  11. Example: World-View Constraint A mathematics professor at Urban University was asked by his students to give the next member in the sequence 32, 38, 44, 48, 56, 60. The professor was told that the properties of the sequence were well known to him and the solution was simple. After a considerable effort trying to formulate a polynomial solution, the professor gave up. His students informed him that the answer was "Meadowlark" the elevated stop after the 60th street station on the city subway. The professor rode the subway daily and got off at Meadowlark.

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