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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商品描述

Description

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

Preface
How to use this book
Prerequisites
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
Bibliography
Index

商品描述(中文翻譯)

描述

微分和積分方程涉及重要的數學技巧,因此在大學課程中,數學家、物理學家和社會科學家都會遇到這些方程。本書提供了對一階和二階常微分方程和偏微分方程的清晰、全面的指南,同時介紹了關於積分方程的重要且有用的基礎材料。讀者將會遇到對波動方程、熱方程和拉普拉斯方程的詳細討論,以及對格林函數及其在斯圖姆-李維爾方程中的應用、使用級數解法、變換方法和相平面分析的介紹。變分法將使他們更深入地了解應用分析的世界。

本書提供了豐富的技巧,滿足純數學家的需求,並附有許多精心解釋的例題和練習題,非常適合具備基礎微積分知識的本科生全面掌握「應用分析」。

目錄

前言
如何使用本書
先備知識
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