Now in its third edition, Mathematical Concepts in the Physical Sciences, 3rd Edition provides a comprehensive introduction to the areas of mathematical physics. It combines all the essential math concepts into one compact, clearly written reference.
This book is intended for students who have had a two-semester or three-semester introductory calculus course. Its purpose is to help students develop, in a short time, a basic competence in each of the many areas of mathematics needed in advanced courses in physics, chemistry, and engineering. Students are given sufficient depth to gain a solid foundation (this is not a recipe book). At the same time, they are not overwhelmed with detailed proofs that are more appropriate for students of mathematics. The emphasis is on mathematical methods rather than applications, but students are given some idea of how the methods will be used along with some simple applications.
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Preface
To the Student
Contents
CHAPTER 1 Infinite Series, Power Series
1. THE GEOMETRIC SERIES
2. DEFINITIONS AND NOTATION
3. APPLICATIONS OF SERIES
4. CONVERGENT AND DIVERGENT SERIES
5. TESTING SERIES FOR CONVERGENCE; THE PRELIMINARY TEST
6. CONVERGENCE TESTS FOR SERIES OF POSITIVE TERMS; ABSOLUTE CONVERGENCE
A. The Comparison Test
B. The Integral Test
C. The Ratio Test
D. A Special Comparison Test
7. ALTERNATING SERIES
8. CONDITIONALLY CONVERGENT SERIES
9. USEFUL FACTS ABOUT SERIES
10. POWER SERIES; INTERVAL OF CONVERGENCE
11. THEOREMS ABOUT POWER SERIES
12. EXPANDING FUNCTIONS IN POWER SERIES
13. TECHNIQUES FOR OBTAINING POWER SERIES EXPANSIONS
A. Multiplying a Series by a Polynomial or by Another Series
B. Division of Two Series or of a Series by a Polynomial