Differential and Integral Equations (Paperback)

Peter Collins

  • 出版商: Oxford University
  • 出版日期: 2006-10-05
  • 售價: $1,150
  • 貴賓價: 9.8$1,127
  • 語言: 英文
  • 頁數: 392
  • 裝訂: Paperback
  • ISBN: 0199297894
  • ISBN-13: 9780199297894
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Differential and integral equations involve important mathematical techniques, and as such will be encountered by mathematicians, and physical and social scientists, in their undergraduate courses. This text provides a clear, comprehensive guide to first- and second-order ordinary and partial differential equations, whilst introducing important and useful basic material on integral equations. Readers will encounter detailed discussion of the wave, heat and Laplace equations, of Green's functions and their application to the Sturm-Liouville equation, and how to use series solutions, transform methods and phase-plane analysis. The calculus of variations will take them further into the world of applied analysis.

Providing a wealth of techniques, but yet satisfying the needs of the pure mathematician, and with numerous carefully worked examples and exercises, the text is ideal for any undergraduate with basic calculus to gain a thorough grounding in 'analysis for applications'.


Table of Contents

How to use this book
1. Integral equations and Picard's method
2. Existence and uniqueness
3. The homogeneous linear equation and Wronskians
4. The non-homogeneous linear equation: Variations of parameters and Green's functions
5. First-order partial differential equations
6. Second-order partial differential equations
7. The diffusion and wave equations and the equation of Laplace
8. The Fredholm alternative
9. Hilbert-Schmidt theory
10. Iterative methods and Neumann series
11. The calculus of variations
12. The Sturm-Liouville equation
13. Series solutions
14. Transform methods
15. Phase-plane analysis
Appendix: The solution of some elementary ordinary differential equations






1. 積分方程和皮卡法
2. 存在性和唯一性
3. 齊次線性方程和朗斯基行列式
4. 非齊次線性方程:參數變化和格林函數
5. 一階偏微分方程
6. 二階偏微分方程
7. 扩散方程、波動方程和拉普拉斯方程
8. 弗雷德霍姆交替定理
9. 分部積分和格林函數
10. 線性方程組和矩陣
11. 矩陣特徵值問題
12. 矩陣特徵值問題的應用
13. 矩陣特徵值問題的數值方法
14. 矩陣特徵值問題的非線性問題
15. 矩陣特徵值問題的非線性問題的數值方法
16. 矩陣特徵值問題的非線性問題的應用
附錄 A: 微分方程的基本定理
附錄 B: 矩陣特徵值問題的基本定理
附錄 C: 矩陣特徵值問題的數值方法
附錄 D: 矩陣特徵值問題的非線性問題的數值方法
附錄 E: 矩陣特徵值問題的非線性問題的應用