Mathematical Methods: Linear Algebra, Normed Spaces, Distributions, Integration
Rigorous but not abstract, this intensive introductory treatment provides many of the advanced mathematical tools used in applications. It also supplies the theoretical background that makes most other parts of modern mathematical analysis accessible. Geared toward advanced undergraduates and graduate students in the physical sciences and applied mathematics. 1968 edition.
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Rigorous but not abstract, this intensive introductory treatment provides many advanced mathematical tools used in applications, plus theoretical background that makes most other parts of modern mathematical analysis accessible. 1968 edition.
Preface vAlgebraic Theory of Vector Spaces 1Vector Spaces 3Generating Sets, Linearly Independent Sets, and Bases 12Dimension of a Vector Space 21Linear Transformations 30Linear Functionals 39Rectangular Matrices 50Square Matrices 64Determinants 73Systems of Linear Equations 81Eigenvalue Problems 94Use of Eigenvectors and Generalized Eigenvectors in the Representation of Linear Operators 108Further Representation Theorems for Linear Operators and Applications 121Algebraic Theory of Tensors 144Bibliography 157Introduction to Functional Analysis. Distributions 160Various Kinds of Convergence 162Metric Spaces 177Normed Vector Spaces 190Completeness and Completion 206The Banach Spaces L, L[superscript p], and C 226Continuous Linear Functionals 249Distributions or Generalized Functions (Part 1) 263Distributions or Generalized Functions (Part 2) 288Delta Sequences and Convergence andApproximation 318Spanning Sets and Schauder Bases 344Bibliography 353The Lebesgue Integral and Related Topics 356Definition of the Lebesgue Integral 359Approximation of Integrable Functions and Applications 373Integration of Sequences and Series 381Lebesgue Measure 395Functions of Bounded Variation and the Stieltjes Integral 400Rules Based on the Use of Indefinite Integrals 413Multiple Integrals 426Curves and Line Integrals 450Holomorphic Functions and Integrals in the Complex Plane 465Bibliography 486Subject and Author Index 489Index of Notation 503
