分析（第2捲） pdf epub mobi txt 電子書 下載 2025

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☆☆☆☆☆

[德] 阿莫恩 著

齣版社： 世界圖書齣版公司

ISBN：9787510047992

版次：1

商品編碼：11181636

包裝：平裝

開本：16開

齣版時間：2012-09-01

頁數：400

內容簡介

　　As with the first, the second volume contains substantially more material than can be covered in a one-semester course. Such courses may omit many beautiful and well-grounded applications which connect broadly to many areas of mathematics.We of course hope that students will pursue this material independently; teachers may find it useful for undergraduate seminars.

目錄

Foreword
Chapter Ⅵ Integral calculus in one variable
1 Jump continuous functions
Staircase and jump continuous functions
A characterization of jump continuous functions
The Banach space of jump continuous functions
2 Continuous extensions
The extension of uniformly continuous functions
Bounded linear operators
The continuous extension of bounded linear operators
3 The Cauchy-Riemann Integral
The integral of staircase functions
The integral of jump continuous functions
Riemann sums
4 Properties of integrals
Integration of sequences of functions
The oriented integral
Positivity and monotony of integrals
Componentwise integration
The first fundamental theorem of calculus
The indefinite integral
The mean value theorem for integrals
5 The technique of integration
Variable substitution
Integration by parts
The integrals of rational functions
6 Sums and integrals
The Bernoulli numbers
Recursion formulas
The Bernoulli polynomials
The Euler-Maclaurin sum formula
Power sums
Asymptotic equivalence
The Biemann ζ function
The trapezoid rule
7 Fourier series
The L2 scalar product
Approximating in the quadratic mean
Orthonormal systems
Integrating periodic functions
Fourier coefficients
Classical Fourier series
Bessel's inequality
Complete orthonormal systems
Piecewise continuously differentiable functions
Uniform convergence
8 Improper integrals
Admissible functions
Improper integrals
The integral comparison test for series
Absolutely convergent integrals
The majorant criterion
9 The gamma function
Euler's integral representation
The gamma function on C（-N）
Gauss's representation formula
The reflection formula
The logarithmic convexity of the gamma function
Stirling's formula
The Euler beta integral
Chapter Ⅶ Multivariable differential calculus
1 Continuous linear maps
The completeness of/L（E, F）
Finite-dimensional Banach spaces
Matrix representations
The exponential map
Linear differential equations
Gronwall's lemma
The variation of constants formula
Determinants and eigenvalues
Fundamental matrices
Second order linear differential equations
Differentiability
The definition
The derivative
Directional derivatives
Partial derivatives
The Jacobi matrix
A differentiability criterion
The Riesz representation theorem
The gradient
Complex differentiability
Multivariable differentiation rules
Linearity
The chain rule
The product rule
The mean value theorem
The differentiability of limits of sequences of functions
Necessary condition for local extrema
Multilinear maps
Continuous multilinear maps
The canonical isomorphism
Symmetric multilinear maps
The derivative of multilinear maps
Higher derivatives
Definitions
Higher order partial derivatives
The chain rule
Taylor's formula
Functions of m variables
Sufficient criterion for local extrema
6 Nemytskii operators and the calculus of variations
Nemytskii operators
The continuity of Nemytskii operators
The differentiability of Nemytskii operators
The differentiability of parameter-dependent integrals
Variational problems
The Euler-Lagrange equation
Classical mechanics
7 Inverse maps
The derivative of the inverse of linear maps
The inverse function theorem
Diffeomorphisms
The solvability of nonlinear systems of equations
8 Implicit functions
Differentiable maps on product spaces
The implicit function theorem
Regular values
Ordinary differential equations
Separation of variables
Lipschitz continuity and uniqueness
The Picard-Lindelof theorem
9 Manifolds
Submanifolds of Rn
Graphs
The regular value theorem
The immersion theorem
Embeddings
Local charts and parametrizations
Change of charts
10 Tangents and normals
The tangential in Rn
The tangential space
Characterization of the tangential space
Differentiable maps
The differential and the gradient
Normals
Constrained extrema
Applications of Lagrange multipliers
Chapter Ⅷ Line integrals
1 Curves and their lengths
The total variation
Rectifiable paths
Differentiable curves
Rectifiable curves
2 Curves in Rn
Unit tangent vectors
Paramctrization by arc length
Oriented bases
The Frenet n-frame
Curvature of plane curves
Identifying lines and circles
Instantaneous circles along curves
The vector product
The curvature and torsion of space curves
3 Pfaff forms
Vector fields and Pfaff forms
The canonical basis
Exact forms and gradient fields
The Poincare lemma
Dual operators
Transformation rules
Modules
4 Line integrals
The definition
Elementary properties
The fundamental theorem of line integrals
Simply connected sets
The homotopy invariance of line integrals
5 Holomorphic functions
Complex line integrals
Holomorphism
The Cauchy integral theorem
The orientation of circles
The Cauchy integral formula
Analytic functions
Liouville's theorem
The Fresnel integral
The maximum principle
Harmonic functions
Goursat's theorem
The Weierstrass convergence theorem
6 Meromorphie functions
The Laurent expansion
Removable singularities
Isolated singularities
Simple poles
The winding number
The continuity of the winding number
The generalized Cauchy integral theorem
The residue theorem
Fourier integrals
References
Index

前言/序言

評分☆☆☆☆☆

書中有些證明需要構造算子或代數結構，但由於書中沒有給齣wff的相關邏輯規則，實際上，這些算子和代數結構不應該要求讀者去構造。因為這本書並沒有告訴讀者如何去檢驗自己的構造是否閤理。

評分☆☆☆☆☆

構造函數p^2-2，然後麯綫較好的切x軸的值值更靠近根號2 ，下麵因該是p+p但是為瞭2式且不違提設可以任意取值，這個算是有跡可循的… 後麵1.21構造齣來式子纔是天馬行空數學就是這樣子，想想那些世界級的數學難題，消耗幾代人幾十年幾百年的生命去計算思考那些復雜的數學題，就顯得微不足道瞭，數學-人類精神虐待! 大傢幫我看下那道數學題怎麼做其實我建議不要刷吉米，找一本卓裏奇或者魯丁，如果覺得這些難，找一本科大版的數分都可以，個人覺得還是要有一點數學品味的吉米的很多題還是可以，我主要是想練下多偏計算的。科大的數分我看瞭一下，更難，謝謝你的建議。都差不多吧。另外，劉玉漣的鋪墊解說比較多，使初學者不感到突兀;張築生的簡潔清晰，把其他人書裏的某些分開的東西融為一體，又把某些東西拆開講，先體係後細節。因為本人理解能力並不是很強。。所以想找一本比較簡單的。。不知是華師大版的數分比較簡單呢，還是陳紀修版的簡單，或者有更好的推薦嘛？

評分☆☆☆☆☆

導數不齣現,直到301頁,但當它介紹,它定義在條款的這東西到底是什麼:一個綫性近似。在大多數文本,這個觀點並不是討論直到“多元”分析覆蓋。

評分☆☆☆☆☆

書中有些證明需要構造算子或代數結構，但由於書中沒有給齣wff的相關邏輯規則，實際上，這些算子和代數結構不應該要求讀者去構造。因為這本書並沒有告訴讀者如何去檢驗自己的構造是否閤理。

評分☆☆☆☆☆

構造函數p^2-2，然後麯綫較好的切x軸的值值更靠近根號2 ，下麵因該是p+p但是為瞭2式且不違提設可以任意取值，這個算是有跡可循的… 後麵1.21構造齣來式子纔是天馬行空數學就是這樣子，想想那些世界級的數學難題，消耗幾代人幾十年幾百年的生命去計算思考那些復雜的數學題，就顯得微不足道瞭，數學-人類精神虐待! 大傢幫我看下那道數學題怎麼做其實我建議不要刷吉米，找一本卓裏奇或者魯丁，如果覺得這些難，找一本科大版的數分都可以，個人覺得還是要有一點數學品味的吉米的很多題還是可以，我主要是想練下多偏計算的。科大的數分我看瞭一下，更難，謝謝你的建議。都差不多吧。另外，劉玉漣的鋪墊解說比較多，使初學者不感到突兀;張築生的簡潔清晰，把其他人書裏的某些分開的東西融為一體，又把某些東西拆開講，先體係後細節。因為本人理解能力並不是很強。。所以想找一本比較簡單的。。不知是華師大版的數分比較簡單呢，還是陳紀修版的簡單，或者有更好的推薦嘛？

評分☆☆☆☆☆

拓撲結構的基本概念如連通性、密實度和介紹瞭homeomorphisms早期使用作為一個基礎,證明將遠不及優雅的(和不直接)否則。例如,介值定理,證明瞭結果的連接的一個空間。一旦這是結果確定下來的普遍性,它討論瞭R。　　

評分☆☆☆☆☆

這套書給人的感覺有點不上不下。具體來說，作者（基本上是）打算避開集閤論公理和數理邏輯，但又花瞭十幾頁的功夫去描述這兩個東西，而且還是在避免使用符號語言的情況下，使用自然語言來說明的.......嘛，因為原文是德文，說明上應該會比這英譯本的要嚴格一些，但是這英譯本就......舉個例子來講，英譯本中一會兒用英語“and”來錶示邏輯符號裏的"AND"，一會兒又用“and”來錶示邏輯符號裏的"INCLUSIVE OR"。都無語瞭......

評分☆☆☆☆☆

阿曼和埃捨爾的分析，第一捲連同第二和第三捲,組成瞭一個令人難以置信的豐富、全麵、獨立的對於高等的分析基礎的處理。從集閤論和實數的構建,作者繼續引理、定理,定理證明的聲明和斯托剋的定理在最後一章的流形體積三世。

評分☆☆☆☆☆

這種方法最初要求更多的讀者和他的抽象能力,但在評審者的意見,是絕對的最好方法主體。我真的不知道什麼是真正的初學者在數學也能想齣來但替代方法是定義事物反復在越來越通用上下文最分析文本做。