Mathematical Methods - 1st Edition - ISBN: 9781483228136, 9781483270746

Mathematical Methods

1st Edition

Linear Algebra / Normed Spaces / Distributions / Integration

Authors: Jacob Korevaar
eBook ISBN: 9781483270746
Imprint: Academic Press
Published Date: 1st January 1968
Page Count: 518
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Description

Mathematical Methods, Volume I: Linear Algebra, Normed Spaces, Distributions, Integration focuses on advanced mathematical tools used in applications and the basic concepts of algebra, normed spaces, integration, and distributions.

The publication first offers information on algebraic theory of vector spaces and introduction to functional analysis. Discussions focus on linear transformations and functionals, rectangular matrices, systems of linear equations, eigenvalue problems, use of eigenvectors and generalized eigenvectors in the representation of linear operators, metric and normed vector spaces, and delta sequences and convergence and approximation. The text then examines the Lebesgue integral, including approximation of integrable functions and applications, integration of sequences and series, functions of bounded variation and the Stieltjes integral, and multiple integrals. Curves and integrals, holomorphic functions and integrals in the complex plane, and multiple integrals are also discussed.

The book is a valuable reference for students in the physical sciences, mathematics students interested in applications, and mathematically oriented engineering students.

Table of Contents


Preface

Chapter One. Algebraic Theory of Vector Spaces

1. Vector Spaces

2. Generating Sets, Linearly Independent Sets, and Bases

3. Dimension of a Vector Space

4. Linear Transformations

5. Linear Functionals

6. Rectangular Matrices

7. Square Matrices

8. Determinants

9. Systems of Linear Equations

10. Eigenvalue Problems

11. Use of Eigenvectors and Generalized Eigenvectors in the Representation of Linear Operators

12. Further Representation Theorems for Linear Operators and Applications

13. Algebraic Theory of Tensors

Bibliography

Chapter Two. Introduction to Functional Analysis. Distributions

1. Various Kinds of Convergence

2. Metric Spaces

3. Normed Vector Spaces

4. Completeness and Completion

5. The Banach Spaces L, LP, and C

6. Continuous Linear Functionals

7. Distributions or Generalized Functions (Part 1)

8. Distributions or Generalized Functions (Part 2)

9. Delta Sequences and Convergence and Approximation

10. Spanning Sets and Schauder Bases

Bibliography

Chapter Three. The Lebesgue Integral and Related Topics

1. Definition of the Lebesgue Integral

2. Approximation of Integrable Functions and Applications

3. Integration of Sequences and Series

4. Lebesgue Measure

5. Functions of Bounded Variation and the Stieltjes Integral

6. Rules Based on the Use of Indefinite Integrals

7. Multiple Integrals

8. Curves and Line Integrals

9. Holomorphic Functions and Integrals in the Complex Plane

Bibliography

Subject and Author Index

Index of Notation

Details

No. of pages:
518
Language:
English
Copyright:
© Academic Press 1968
Published:
Imprint:
Academic Press
eBook ISBN:
9781483270746

About the Author

Jacob Korevaar