How to Solve Problems: For Success in Freshman Physics, Engineering, and Beyond

✍ Scribed by Donald Scarl

• Publisher: Dosoris Press
• Year: 1998
• Tongue: English
• Leaves: 132
• Edition: 5
• Category: Library

✦ Synopsis

Teaches problem-solving style by explaining the methods that experienced scientist and engineers use to define a problem, to solve it, and to present their solution to others.

✦ Table of Contents

Cover
Back Cover
Title
Contents
Preface
1. Why Solve Problems?
Lifetime learning
Workmanship
Previously solved problems
Reflexes
Presenting work to others
Barriers
Creativity and disorganization
2. School
Science and engineering texts
Learning equations
An equation’s importance
Classifying equations
Special conditions for each equation
Definitions of symbols
Example: How to classify equations
Homework
Exams
Efficiency
Teachers
Working in a group
Professional qualities
Exercise
3. Methods
Example 1: World Trade Center elevator
Solution for Example 1
Divide into parts
Do the parts separately
Label each part
Work down the page
Write clearly
Make everything explicit
Use symbols
Zero
Do one step at a time
Use ratios
Example 2: Surface area of a sphere
Solution for Example 2
Do the assigned problem
Example 3: Oscillating car
Solution for Example 3
Exercises
4. Describing the Problem
Example 4: Ultralight plane takeoff
Solution for Example 4
Define the problem
Write a heading
Title
Name and date
Draw a diagram
Diagram or picture
Axes
Scale
Three-dimensional drawings
Labels
Drawing vectors
Name the variables
Symbol definitions
Data equations
Check
Write preliminary equations
Units
Constants
Trigonometry and vector components
Exercises
5. Finding the Solution
Science equations
Choosing the right equation
General equations
Particular equations
Algebra
Use a small number of known operations
Get unknowns on left hand side alone
Copy symbols exactly
Checks
Check algebra
Check units
Make a variational check
Check test cases
Check by approximation
Check the size of the result
Reread the problem
Mistakes
Exercises
6. Presenting the Results
Numerical results
Put in known numbers
Use significant figures to indicate accuracy
Include units
Use engineering prefixes
Put the result in a sentence
Decorate your results
Graphs
Title
Axis labels
Scale divisions
Points and lines
Straight lines
Logarithmic axes
Rewriting
Reports and Publications
Exercises
7. Can't Solve It
Use thinking where it counts
Look for a similar problem
Simplify
Generalize
Put in numbers
Look for unused data
Try a ratio
Put it aside
Go for a little help
How to ask for help
8. Spreadsheets
Calculating a single value
Example 5: Solar rocks
Solution for Example 5
Inputs
Constants
Unit conversion
Calculation
Results
Plotting data and calculating functions
Example 6; Optical detector power
Solution for Example 6
Graphing data
Graphing a function
Fitting a function to data
Numerical differentiation
Numerical integration
Other operations
Organizing a spreadsheet
Avoid numbers
Giving cells names
Editing a spreadsheet
Choosing a type of graph
Exercises
Problems
Further Reading
Problem Solutions
Index