Problem Solving - Introduction to Engineering - Lecture Slides, Slides of Engineering Mathematics

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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. of Foundations of Engineering )

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 ax 2 + bx + c = 0

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.

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. )

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.

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.

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.