偏微分方程（第2捲）（第2版） [Partial Differential Equations II: Qualitative Studies of Linear Equations（2nd Edit pdf epub mobi txt 電子書 下載 2025

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[美] 泰勒（M．E．Taylor） 著

齣版社： 世界圖書齣版公司

ISBN：9787510068140

版次：2

商品編碼：11352191

包裝：平裝

外文名稱：Partial Differential Equations II: Qualitative Studies of Linear Equations（2nd Edition）

開本：24開

齣版時間：2014-01-01

用紙

內容簡介

　　This work is intended to provide a course of study of some of the major aspects of PDE. It is addressed to readers with a background in the basic introductory graduate mathematics courses in American universities: elementary real and complex analysis， differential geometry， and measure theory.

內頁插圖

目錄

Contents of Volumes I and III
Preface
7 Pseudo differential Operators
1 The Fourier integral representation and symbol classes
2 Schwartz kernels of pseudo differential operators
3 Adjoints and products
4 Elliptic operators and parametrices
5 L2 estimates
6 Garding's inequality
7 Hyperbolic evolution equations.
8 Egorov's theorem
9 Microlocal regularity
10 Operators on manifolds
11 The method of layer potentials
12 Parametrix for regular elliptic boundary problems
13 Parametrix for the heat equation
14 The Wey l calculus
15 Operators of harmonic oscillator type
Reference

8 Spectral Theory
1 The spectral theorem
2 Self-adjoint differential operators
3 Heat asymptotics and eigenvalue asymptotics
4 The Laplace operator on Sn
5 The Laplace operator on hyperbolic space
6 The harmonic oscillator
7 The quantum Coulomb problem
8 The Laplace operator on cones
References

9 Scattering by Obstacles
1 The scattering problem
2 Eigenfunction expansions
3 The scattering operator
4 Connections with the wave equatio
5 Wave operators
6 Translation representations and the Lax-Phillips semigroup Z（ t）
7 Integral equations and scattering poles
8 Trace formulas; the scattering phase
9 Scattering by a sphere
10 Inverse problems l
11 Inverse problems II
12 Scattering by rough obstacles
A Lidskii's trace theorem
References

10 Dirac Operators and Index Theory
1 Operators of Dirac type
2 Clifford algebras
3 Spinors
4 Weitzenbock formulas
5 Index of Dirac operators
6 Proof of the local index formula
7 The Chern-Gauss-Bonnet theorem
8 Spinc manifolds
9 The Riemann-Roch theorem
10 Direct attack in 2-D
11 Index of operators of harmonic oscillator type
References

11 Brownian Motion and Potential Theory
1 Brownian motion and Wiener measure
2 The Feynman-Kac formula
3 The Dirichlet problem and diffusion on domains with boundary
4 Martingales, stopping times, and the strong Markov property
5 First exit time and the Poisson integral
6 Newtonian capacity
7 Stochastic integrals
8 Stochastic integrals, II
9 Stochastic differential equations
10 Application to equations of diffusio
A The Trotter product formula
References
……

前言/序言

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從而使本書對於獨立自學也是非常適宜的。實數、有理數、整數，等等，在開始時就假設它無作為集閤的例子是熟知的代數係統來引入。從而實數正式被假定滿足一個域的公理。序和它的性質用其在“實直綫”上的位置來描述（大概作為公理，與域的性質有所不同，因而不把序的性質稱為公理）。自然數集N的“佩亞諾原理”由賦納法組成。完全性則未被定義，但在後麵被提及，它置於未經證明的“實連續函數的基本定理”之後，即一個閉區間的像是一個閉區間。極限的嚴格（ε. δ）定義被加以解釋，並伴以練習。較早——在微商前——就引入瞭一緻連續性。、總之，對於愛好數學嚴謹性的學生來說，本書作為初等微積分教程，無論是課堂教材還是自學書籍，都是一個良好的選擇。

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