Mathematical Analysis - 1st Edition - ISBN: 9780080107967, 9781483185378

Mathematical Analysis

1st Edition

A Special Course

Authors: G. Ye. Shilov
Editors: D. A. R. Wallace
eBook ISBN: 9781483185378
Imprint: Pergamon
Published Date: 1st January 1965
Page Count: 498
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Mathematical Analysis: A Special Course covers the fundamentals, principles, and theories that make up mathematical analysis. The title first provides an account of set theory, and then proceeds to detailing the elements of the theory of metric and normed linear spaces. Next, the selection covers the calculus of variations, along with the theory of Lebesgue integral. The text also tackles the geometry of Hilbert space and the relation between integration and differentiation. The last chapter of the title talks about the Fourier transform. The book will be of great use to individuals who want to expand and enhance their understanding of mathematical analysis.

Table of Contents

Foreword Chapter I. Sets

1. Sets, Subsets, Inclusions 2. Operations on Sets 3. Equivalence of Sets 4. Countable Sets 5. Sets of the Power of the Continuum 6. Sets of Higher Powers

Chapter II. Metric Spaces

1. Definition and Examples of Metric Spaces. Isometry 2. Open Sets 3. Convergent Sequences and Closed Sets 4. Complete Spaces 5. Theorem of the Fixed Point 6. Completion of a Metric Space 7. Continuous Functions and Compact Spaces 8. Normed Linear Spaces 9. Linear and Quadratic Functions on a Linear Space

Chapter III. The Calculus of Variations

1. Differentiable Functional 2. Extrema of Differentiable Functionals 3. Functionals of the Type b∫a f{x, y, y') dx 4. Functionals of the Type b∫a (x, y, y') dx (continued) 5. Functionals with Several Unknown Functions 6. Functionals with Several Independent Variables 7. Functionals with Higher Derivatives

Chapter IV. Theory of the Integral

1. Sets of Measure Zero and Measurable Functions 2. The Class C+ 3. Summable Functions 4. Measure of Sets and Theory of Lebesgue Integration 5. Generalisations

Chapter V. Geometry of Hilbert Space

1. Basic Definitions and Examples 2. Orthogonal Resolutions 3. Linear Operators 4. Integral Operators with Square-summable Kernels 5. The Sturm-Liouville Problem 6. Non-homogeneous Integral Equations with Symmetric Kernels 7. Non-homogeneous Integral Equations with Arbitrary Kernels 8. Applications to Potential Theory 9. Integral Equations with Complex Parameters

Chapter VI. Differentiation and Integration

1. Derivative of a Non-decreasing Function 2. Functions of Bounded Variation 3. Determination of a Function from its Derivative 4. Functions of Several Variables 5. The Stieltjes Integral 6. The S


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© Pergamon 1965
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About the Author

G. Ye. Shilov

About the Editor

D. A. R. Wallace

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