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: Sears Tower elevator
- Solution for Example 1
- Divide into parts
- 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
