近代應用數學基礎=Foundations of Modern Applied Mathematics-英文 978730
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物品所在地：中國大陸
原出版社：清華大學
物品所在地：中國大陸
原出版社：清華大學
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| *完成訂單後正常情形下約兩周可抵台。 *本賣場提供之資訊僅供參考，以到貨標的為正確資訊。 印行年月：202407*若逾兩年請先於私訊洽詢存貨情況，謝謝。 台灣(台北市)在地出版社，每筆交易均開具統一發票，祝您中獎最高1000萬元。 書名：近代應用數學基礎=Foundations of Modern Applied Mathematics-英文 ISBN：9787302620822 出版社：清華大學 著編譯者：蘇維宜 頁數：436 所在地：中國大陸 *此為代購商品 書號：1655901 可大量預訂，請先連絡。 【台灣高等教育出版社簡體書】 近代應用數學基礎=Foundations of Modern Applied Mathematics-英文 787302620822 蘇維宜 內容簡介 本書結合例題，系統地介紹集合論、近世代數、點集拓撲、泛函分析、分佈理論、微分幾何等近代應用數學的基本內容及其在自然科學研究中的應用。書中強調對近代數學概念的理解和對重要論證方法的思路分析，以幫助讀者掌握數學推理的基本思維方法，學會把近代應用數學中的重要定理和方法應用到本專業的具體問題中去。 本書可作為物理、天文、化學、地學、生物、計算機等專業學習相關課程的教材或參考書，也可供相關領域科研人員閱讀參考。目錄 PrefaceChapter 1 Set，Structure of Operation on Set 1 1 Sets，the Relations and Operations between Sets 1 1 1 Relations between sets 1 1 2 Operations between sets 1 1 3 Mappings between sets 1 2 Structures of Operations on Sets 1 2 1 Groups，rings，fields，and linear spaces 1 2 2 Group theory，some important groups 1 2 3 Subgroups，product groups，quotient groups Exercise 1 Chapter 2 Linear Spaces and Linear Transformations 2 1 Linear Spaces 2 1 1 Examples 2 1 2 Bases of linear spaces 2 1 3 Subspaces and product/directsum/quitient spaces 2 1 4 Inner product spaces 2 1 5 Dual spaces 2 1 6 Structures of linear spaces 2 2 Linear Transformations 2 2 1 Linear operator spaces 2 2 2 Conjugate operators of linear operators 2 2 3 Multilinear algebra Exercise 2 Chapter 3 Basic Knowledge of Point Set Topology 3 1 Metric Spaces，Normed Linear Spaces 3 1 1 Metric spaces 3 1 2 Normed linear spaces 3 2 Topological Spaces 3 2 1 Some definitions in topological spaces 3 2 2 Classification of topological spaces 3 3 Continuous Mappings on Topological Spaces 3 3 1 Mappings between topological spaces，continuity of mappings 3 3 2 Subspaces，product spaces，quotient spaces 3 4 Important Properties of Topological Spaces 3 4 1 Separation axioms of topological spaces 3 4 2 Connectivity of topological spaces 3 4 3 Compactness of topological spaces 3 4 4 Topological linear spaces Exercise 3 Chapter 4 Foundation of Functional Analysis 4 1 Metric Spaces 4 1 1 Completion of metric spaces 4 1 2 Compactness in metric spaces 4 1 3 Bases of Banach spaces 4 1 4 Orthgoonal systems in Hilbert spaces 4 2 Operator Theory 4 2 1 Linear operators on Banach spaces 4 2 2 Spectrum theory of bounded linear operators 4 3 Linear Functional Theory 4 3 1 Bounded linear functionals on normed linear spaces 4 3 2 Bounded linear functionals on Hilbert spaces Exercise 4 Chapter 5 Distribution Theory 5 1 Schwartz Space，Schwartz Distribution Space 5 1 1 Schwartz space 5 1 2 Schwartz distribution space 5 1 3 Spaces ERn，DRn and their distribution spaces 5 2 Fourier Transform on LpRn，1?p?2 5 2 1 Fourier transformations on L1Rn 5 2 2 Fourier transformations on L2Rn 5 2 3 Fourier transformations on LpRn，1 5 3 Fourier Transform on Schwartz Distribution Space 5 3 1 Fourier transformations of Schwartz functions 5 3 2 Fourier transformations of Schwartz distributions 5 3 3 Schwartz distributions with compact supports 5 3 4 Fourier transformations of convolutions of Schwartz distributions 5 4 Wavelet Analysis 5 4 1 Introduction 5 4 2 Continuous wavelet transformations 5 4 3 Discrete wavelet transformations 5 4 4 Applications of wavelet transformations Exercise 5 Chapter 6 Calculus on Manifolds 6 1 Basic Concepts 6 1 1 Structures of differential manifolds 6 1 2 Cotangent spaces，tangent spaces 6 1 3 Submanifolds 6 2 External Algebra 6 2 1 (r，s)type tensors，(r，s)type tensor spaces 6 2 2 Tensor algebra 6 2 3 Grassmann algebra (exterior algebra) 6 3 Exterior Differentiation of Exterior Differential Forms 6 3 1 Tensor bundles and vector bundles 6 3 2 Exterior differentiations of exterior differential form 6 4 Integration of Exterior Differential Forms 6 4 1 Directions of smooth manifolds 6 4 2 Integrations of exterior differential forms on directed manifold M 6 4 3 Stokes formula 6 5 Riemann Manifolds， Mathematics and Modern Physics 6 5 1 Riemann manifolds 6 5 2 Connections 6 5 3 Lie group and movingframe method 6 5 4 Mathematics and modern physics Exercise 6 Chapter 7 Complimentary Knowledge 7 1 Variational Calculus 詳細資料或其他書籍請至台灣高等教育出版社查詢，查後請於PChome商店街私訊告知ISBN或書號，我們即儘速上架。 |
