Elements of Problem Solving


paperback or hardcover, 116 p.  published 2013.

Become an expert problem solver with this imperishable volume.  Capable of being enjoyed in one or two sittings, this concise volume offers valuable tips, strategies, and habits for anyone learning calculus, physics, or engineering.

SKU: 9780985062743 Category:

Product Description

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About This Book

This concise volume seeks to address the silent void that university students embarking on mathematical coursework inevitably face:  How does one apply ideas, concepts, and theory to story problems that at first seem intractable?  We pay equal attention to the abstract aspects of problem solving as well as the practical.  We discuss common misperceptions of ability and pay close attention to the attitudes and habits employed by successful problem solvers.  We reveal problem solving as both achievable and fun, and illustrate these themes with specific examples and stories throughout the text.  We also enumerate simple, executable steps that can be implemented when faced with virtually any new problem:  understand the problem; draw a picture; define variables; be consistent; utilize principles.  Far from trivial, these steps often lead novice problem solvers to error.  In sum, we hope you find this charming work to be an indispensable guide on your journey and an effective means to improving and maturing your problem-solving capabilities.

Table of Contents

Part I.  A Few Notes on Style

  1. Mathematics as a Language
  2. Nouns and Verbs
  3. Equations and Mathematical Sentences
  4. Run-ons:  the Good, the Bad, and the Ugly
  5. Equations as Balances
  6. Learning Language

Part II.  Working Problems

  1. The Triune Brain
  2. Problem Solving as a Creative Process
  3. Follow Your Leads
  4. All Roads Lead to Rome
  5. Mathematics is not a Spectator Sport
  6. Make it Yours
  7. Make it Fun
  8. Make it a Habit

Part III.  Solving Problems

  1. Read the Problem–Twice
  2. Write the Problem
  3. Draw a Picture
  4. Define Variables
  5. Be Consistent
  6. Build a Logical Bridge
  7. Determine the Equations
  8. Seek out Alternate Solutions
  9. Perform a Reality Check
  10. Be all on, or all off

Part IV.  Utilizing Assumptions

  1. What are Assumptions?
  2. Scaffolding Assumptions
  3. When Assumptions Go Bad

Part V.  Some Fundamental Principles

  1. Conservation Laws and Control Volume Analysis
  2. Nodal Analysis
  3. Dimensional Analysis

Part VI.  A Few Common Hints and Tricks

  1. Precalculus
  2. Calculus I
  3. Calculus II

Appendix A.  SI Units

Appendix B.  Fermi Problems

Additional Information

Weight 0.5 lbs
Dimensions 5.5 x 8.5 x 0.29 in



March, 2013




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