# Mathematical Methods in Science

Share this page
*George Pólya*

MAA Press: An Imprint of the American Mathematical Society

Mathematics, taught and learned appropriately, improves the mind and implants good habits of thought. This tenet underlies all of Professor Pólya's works on teaching and problem-solving. The distinctive feature of Mathematical Methods in Science is the stress on the history of certain elementary chapters of science; these can be a source of enjoyment and deeper understanding of mathematics even for beginners who have little, or perhaps no, knowledge of physics.

#### Reviews & Endorsements

The book is organized into four content-rich chapters separated by one single-page chapter marking what Pólya terms the “tidal flow” between mathematics and physics. … It is not an easy read—the reader has to do the mathematics along with Pólya—but his explanations are clear and his dry wit lightens the work along the way. Topics are arranged historically and one follows developments with a sense of a time traveler watching the concepts as they unfold. The volume will appeal to a broad audience. … the close link between physics and mathematics makes this text a tool that can be used by teachers in either discipline.

-- Katherine Safford-Ramus, MAA Reviews

# Table of Contents

## Mathematical Methods in Science

- Front Cover Cover11
- Mathematical Methods in Science iii4
- Copyright Page iv5
- Contents ix10
- INTRODUCTION 114
- CHAPTER 1. From the History of Astronomy: Measurement and Successive Approximation 316
- CHAPTER 2. From the History of Statics 4760
- CHAPTER 3. From the History of Dynamics 8295
- SECTION 1 GALILEO 8295
- SECTION 2 NEWTON 105118
- 1 Apples, Cannon Balls, and the Moon 106119
- 2 Never Smoke Without Fire 107120
- 3 That the Planets do Accelerate Towards the Sun 108121
- 4 What is the Law of Universal Gravitation? 111124
- 5 Uniform Circular Motion: Hamilton's Hodograph 112125
- 6 On Newton's Discovery of the Law of Universal Gravitation 115128
- 7 Scientific Attitude: Verification 117130
- 8 Hindsight and Foresight 122135

- SECTION 3 THE PENDULUM 125138
- SECTION 4 ESCAPE VELOCITY 138151

- CHAPTER 4. Physical Reasoning in Mathematics 159172
- CHAPTER 5. Differential Equations and Their Use in Science 160173