本书通过大量丰富的实例,帮助读者实现从基本的常微分方程向更多**概念(偏微分方程、傅里叶级数和边界值问题等)的顺利过渡。作者轻松的语言风格使得书中的材料通俗易懂,尤其适合那些渴望了解更多和更深微积分知识的读者。
本书在第1版的基础上增加了偏微分方程在工程和物理学方面的应用,并且提供了更多数学证明和偏微分方程的原理。此外,本书的每一小节后都配备了大量的习题,并在页边提供了注释、国标或重要的公式等,突出了书中的**与难点,方便读者自学。
本书提供读者利用计算机辅助学习,旨在使读者更直观、更清晰地理解和掌握书中所讲述的题材。读者可以利用从作者网站上下载的Mathematica文件进行上机实践。

1 A Preview of Applications and Techniques
2 Fourier Series
3 Partial Differential Equations in Rectangular Coordinates
4 Partial Differential Equations in Polar and Cylindrical Coordinates
5 Partial Differential Equations in Spherical Coordinates
6 Sturm-Liouville Theory with Engineering Applications
7 The Fourier Transform and Its Applications
8 The Laplace and Hankel Transforms with Applications
9 Finite Difference Numerical Methods
10 Sampling and Discrete Fourier Analysis with Applications to Partial Differential Equations
11 An Introduction to Quantum Mechanics
12 Green's Functions and Conformal Mappings
Appendix A: Ordinary Differential Equations: Review of Concepts and Methods
Appendix B: Tables of Transforms
References
Answers to Selected Exercises
Index