Principles of Mathematical Analysis 3/e 2023 Edition (3版)

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Principles of Mathematical Analysis 3/e 2023 Edition 作者：Walter Rudin ISBN：9786269708116 版次：3 年份：2023 出版商：McGraw-Hill 頁數/規格：342頁/平裝單色 Description This book is intended to serve as a text for the course in analysis that is usually taken by advanced undergraduates or by first-year students who study mathematics. NEW to This Edition The material on functions of several variables in Chapter 9 is significantly rewritten, with many details filled in, and with more examples and more motivation. The proof of the inverse function theorem is simplified by means of the fixed point theorem about contraction mappings. Differential forms are discussed in much greater detail. Several applications of Stokes' theorem are included. The Riemann-Stieltjes integral in Chapter 6 has been trimmed a bit. A short do-it-yourself section on the gamma function has been added to Chapter 8. There is a large number of new exercises throughout the book, most of them with fairly detailed hints. Several references to articles appearing in the American Mathematical Monthly and in Mathematics Magazine are included for students to develop the habit of looking into the journal literature. 目錄 Table of Contents Chapter 1: The Real and Complex Number Systems  Chapter 2: Basic Topology  Chapter 3: Numerical Sequences and Series  Chapter 4: Continuity  Chapter 5: Differentiation  Chapter 6: The Riemann-Stieltjes Integral  Chapter 7: Sequences and Series of Functions  Chapter 8: Some Special Functions  Chapter 9: Functions of Several Variables  Chapter 10: Integration of Differential Forms  Chapter 11: The Lebesgue Theory

LINEAR ALGEBRA (4版)

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書名：Linear Algebra 4/E 作者：Friedberg / Insel / Spence 出版社：Pearson 出版日期：2013/00/00 ISBN：9781292026503

(特價書 85折)Partial differential equations : methods and applications 2/E IE 2003 <PH> 978-986-154-578-3 (2版)

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書名：(特價書 85折)Partial differential equations : methods and applications 2/E IE 2003 <PH> 978-986-154-578-3 作者：Robert McOwen 出版社：PEARSON 出版日期：2003-12 ISBN：9789861545783

研究所講重點【線性代數及其應用習題詳解】 (5版)

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書名：研究所分章題庫：線性代數及其應用習題詳解(五版) 作者：黃子嘉 出版社：大碩 出版日期：2019/08/00 ISBN：9789863456476 內容簡介 1.內容完整兼具深度及廣度以深入淺出的方式來表達。 2.相關試題收集最完整。 3.以最有效且最詳實的方式來解題。 4.適合研究所入學考試及自修用的參考書。

研究所講重點【線性代數及其應用(上)】 (5版)

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書名: 研究所講重點：線性代數及其應用(上) ISBN: 9789863456445 作者: 黃子嘉 出版社: 大碩 出版日期: 2019-09 書名: 研究所講重點：線性代數及其應用(下) ISBN: 9789863456452 作者: 黃子嘉 出版社: 大碩 出版日期: 2019-08 內容簡介 　　★內容完整兼具深度及廣度以深入淺出的方式來表達 　　★相關試題收集最完整 　　★以最有效且最詳實的方式來解題 　　★適合研究所入學考試及自修用的參考書 上冊目錄 第零章 基礎數學 0-1 集合 0-2 證明的方法 0-3 關係與函數 0-4 體 0-5 複數 0-6 多項式 第一章 矩陣與線性方程組 1-1 矩陣及矩陣運算 1-2 反矩陣 1-3 基本列運算 1-4 線性方程組 1-5 可逆矩陣的充要條件 1-6 LU分解 1-7 基本行運算 第二章 行列式 2-1 二階行列式 2-2 高階行列式 2-3 行列式的性質 2-4 古典伴隨矩陣 第三章 向量空間 3-1 向量空間 3-2 子空間 3-3 生成與線性獨立 3-4 基底與維度 3-5 直和 3-6* Lagrange內插法 第四章 線性映射 4-1 線性映射 4-2 座標化 4-3 矩陣表示法與換底公式 4-4 核空間與像集 4-5 矩陣的秩 4-6 線性映射的合成與可逆 4-7* 對偶空間與零化集 下冊目錄 第五章 對角化及其應用 5-1 相似性 5-2 不變子空間 5-3 特徵根及特徵向量 5-4 對角化 5-5 冪等算子與矩陣 5-6 對角化的應用 5-7 特徵根的近似解法 5-8 Markov鏈 第六章 Jordan型及其應用 6-1 冪零算子 6-2 循環子空間及循環分解 6-3 Jordan 型 6-4 Cayley-Hamilton 定理及其應用 6-5 Jordan 型的應用 6-6 極小多項式 第七章 內積空間 7-1 內積 7-2 Gram-Schmidt正交化及QR分解 7-3 正交投影 7-4 正交補空間 第八章 內積上的算子及其應用 8-1 伴隨算子 8-2 正規算子與矩陣 8-3 么正及正交算子的特性 8-4 雙線性型式與半雙線性型式 8-5 正定及正半定算子與矩陣 8-6 么正及正交對角化 8-7 正定及正半定矩陣的特性 8-8 二次式的應用 8-9 矩陣的長度及條件數 8-10 Householder轉換 8-11 奇異值分解

研究所講重點【線性代數及其應用(下)】 (5版)

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書名: 研究所講重點：線性代數及其應用(上) ISBN: 9789863456445 作者: 黃子嘉 出版社: 大碩 出版日期: 2019-09 書名: 研究所講重點：線性代數及其應用(下) ISBN: 9789863456452 作者: 黃子嘉 出版社: 大碩 出版日期: 2019-08 內容簡介 　　★內容完整兼具深度及廣度以深入淺出的方式來表達 　　★相關試題收集最完整 　　★以最有效且最詳實的方式來解題 　　★適合研究所入學考試及自修用的參考書 上冊目錄 第零章 基礎數學 0-1 集合 0-2 證明的方法 0-3 關係與函數 0-4 體 0-5 複數 0-6 多項式 第一章 矩陣與線性方程組 1-1 矩陣及矩陣運算 1-2 反矩陣 1-3 基本列運算 1-4 線性方程組 1-5 可逆矩陣的充要條件 1-6 LU分解 1-7 基本行運算 第二章 行列式 2-1 二階行列式 2-2 高階行列式 2-3 行列式的性質 2-4 古典伴隨矩陣 第三章 向量空間 3-1 向量空間 3-2 子空間 3-3 生成與線性獨立 3-4 基底與維度 3-5 直和 3-6* Lagrange內插法 第四章 線性映射 4-1 線性映射 4-2 座標化 4-3 矩陣表示法與換底公式 4-4 核空間與像集 4-5 矩陣的秩 4-6 線性映射的合成與可逆 4-7* 對偶空間與零化集 下冊目錄 第五章 對角化及其應用 5-1 相似性 5-2 不變子空間 5-3 特徵根及特徵向量 5-4 對角化 5-5 冪等算子與矩陣 5-6 對角化的應用 5-7 特徵根的近似解法 5-8 Markov鏈 第六章 Jordan型及其應用 6-1 冪零算子 6-2 循環子空間及循環分解 6-3 Jordan 型 6-4 Cayley-Hamilton 定理及其應用 6-5 Jordan 型的應用 6-6 極小多項式 第七章 內積空間 7-1 內積 7-2 Gram-Schmidt正交化及QR分解 7-3 正交投影 7-4 正交補空間 第八章 內積上的算子及其應用 8-1 伴隨算子 8-2 正規算子與矩陣 8-3 么正及正交算子的特性 8-4 雙線性型式與半雙線性型式 8-5 正定及正半定算子與矩陣 8-6 么正及正交對角化 8-7 正定及正半定矩陣的特性 8-8 二次式的應用 8-9 矩陣的長度及條件數 8-10 Householder轉換 8-11 奇異值分解

PRINCETON LECTURES IN ANALYSIS II COMPLEX ANALYSIS (1版)

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【原文書】 書名：Complex Analysis (Princeton Lectures in Analysis, No. 2) 作者：STEIN 出版社：PRINCETON 出版日期：2003/04/07 ISBN：9780691113852

Probability, Random Variables & Stochastic Processes (4版)

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【原文書】 書名 : Probability, Random Variables & Stochastic Processes 4/E(IE) 作者 : Athanasios Papoulis, S. Unnikrishna Pillai 出版社 : McGrasHill 出版日期 : 2002/01 ISBN : 9780071226615 Synopsis The fourth edition of "Probability, Random Variables and Stochastic Processes" has been updated significantly from the previous edition, and it now includes co-author S. Unnikrishna Pillai of Polytechnic University. The book is intended for a senior/graduate level course in probability and is aimed at students in electrical engineering, math, and physics departments. The authors' approach is to develop the subject of probability theory and stochastic processes as a deductive discipline and to illustrate the theory with basic applications of engineering interest. Approximately 1/3 of the text is new material - this material maintains the style and spirit of previous editions. In order to bridge the gap between concepts and applications, a number of additional examples have been added for further clarity, as well as several new topics. Table of contents Part 1 Probability and Random Variables 1 The Meaning of Probability 2 The Axioms of Probability 3 Repeated Trials 4 The Concept of a Random Variable 5 Functions of One Random Variable 6 Two Random Variables 7 Sequences of Random Variables 8 Statistics Part 2 Stochastic Processes 9 General Concepts 10 Random Walk and Other Applications 11 Spectral Representation 12 Spectral Estimation 13 Mean Square Estimation 14 Entropy 15 Markov Chains 16 Markov Processes and Queueing Theory

Introduction to Linear Algebra 6/e (6版)

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Introduction to Linear Algebra 6/e 作者：Gilbert Strang ISBN：9786269708109 年份：2023 出版商：New Moon Education 頁數/規格：440頁/平裝單色 Description Linear algebra now rivals or surpasses calculus in importance for people working in quantitative fields of all kinds: engineers, scientists, economists and business people. Gilbert Strang has taught linear algebra at MIT for more than 50 years and the course he developed has become a model for teaching around the world. His video lectures on MIT OpenCourseWare have been viewed over ten million times and his twelve textbooks are popular with readers worldwide. This sixth edition of Professor Strang's most popular book, Introduction to Linear Algebra, introduces the ideas of independent columns and the rank and column space of a matrix early on for a more active start. Then the book moves directly to the classical topics of linear equations, fundamental subspaces, least squares, eigenvalues and singular values – in each case expressing the key idea as a matrix factorization. The final chapters of this edition treat optimization and learning from data: the most active application of linear algebra today. Everything is explained thoroughly in Professor Strang's characteristic clear style. It is sure to delight and inspire the delight and inspire the next generation of learners. Table of Contents 1 Vectors and Matrices 2 Solving Linear Equations Ax = b 3 The Four Fundamental Subspaces 4 Orthogonality 5 Determinants 6 Eigenvalues and Eigenvectors 7 The Singular Value Decomposition (SVD) 8 Linear Transformations 9 Linear Algebra in Optimization 10 Learning from Data

ELEMENTS OF DISCRETE MATHEMATICS (2版)

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書名：Elements of Discrete Mathematics 2/e 作者：LIU 出版社：McGraw-Hill 出版日期：1985/00/00 ISBN：9780071005449 內容簡介 This book presents a selection of topics from set theory, combinatorics, graph theory, and algebra which were been considered as basic and useful to students in Applied Mathematics, Computer Seience, and Engineering. It's intended to be a textbook for a course in Discrete Mathematics at the sophomore-junior level, although it can also be used in a freshman-level course since the presentation does not assume any background beyond high-school mathematics. 目錄 1. Sets and Propositions 2. Computability and Formal Languages 3. Permutations, Combinations, and Discrete Probability 4. Relations and Functions 5. Graphs and Planar Graphs 6. Trees and Cut-Sets 7. Finite State Machines 8. Analysis of Algorithms 9. Discrete Numberic Functions and Generating Functions 10. Recurrence Relations and Recursive Algorithms 11. Groups and Rings 12. Boolean Algebras

Real and complex analysis (3版)

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【簡介】 Description This is an advanced text for the one- or two-semester course in analysis taught primarily to math, science, computer science, and electrical engineering majors at the junior, senior or graduate level. The basic techniques and theorems of analysis are presented in such a way that the intimate connections between its various branches are strongly emphasized. The traditionally separate subjects of 'real analysis' and 'complex analysis' are thus united in one volume. Some of the basic ideas from functional analysis are also included. This is the only book to take this unique approach. The third edition includes a new chapter on differentiation. Proofs of theorems presented in the book are concise and complete and many challenging exercises appear at the end of each chapter. The book is arranged so that each chapter builds upon the other, giving students a gradual understanding of the subject. 【目錄】 Table of Contents Chapter 1: Abstract Integration Chapter 2: Positive Borel Measures Chapter 3: Lp-Spaces Chapter 4: Elementary Hilbert Space Theory Chapter 5: Examples of Banach Space Techniques Chapter 6: Complex Measures Chapter 7: Differentiation Chapter 8: Integration on Product Spaces Chapter 9: Fourier Transforms Chapter 10: Elementary Properties of Holomorphic Functions Chapter 11: Harmonic Functions Chapter 12: The Maximum Modulus Principle Chapter 13: Approximation by Rational Functions Chapter 14: Conformal Mapping Chapter 15: Zeros of Holomorphic Functions Chapter 16: Analytic Continuation Chapter 17: Hp-Spaces Chapter 18: Elementary Theory of Banach Algebras Chapter 19: Holomorphic Fourier Transforms Chapter 20: Uniform Approximation by Polynomials

The Classical Fields Structural Features of the Real and Relational Numbers

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The classical fields are the real, rational, complex and p-adic numbers. Each of these fields comprises several intimately interwoven algebraical and topological structures. This comprehensive volume analyzes the interaction and interdependencies of these different aspects. The real and rational numbers are examined additionally with respect to their orderings, and these fields are compared to their non-standard counterparts. Typical substructures and quotients, relevant automorphism groups and many counterexamples are described. Also discussed are completion procedures of chains and of ordered and topological groups, with applications to classical fields. The p-adic numbers are placed in the context of general topological fields: absolute values, valuations and the corresponding topologies are studied, and the classification of all locally compact fields and skew fields is presented. Exercises are provided with hints and solutions at the end of the book. An appendix reviews ordinals and cardinals, duality theory of locally compact Abelian groups and various constructions of fields.

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