Techniques of functional analysis for differential and integral equations / (Record no. 216392)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 05068cam a2200493 i 4500 |
| 040 ## - CATALOGING SOURCE | |
| Transcribing agency | YDX |
| 019 ## - | |
| -- | 987790925 |
| -- | 988021904 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780128114575 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 0128114576 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| -- | https://id.oclc.org/worldcat/ddc/E3Wfyx8bCwkrQH6kwpPj7T4rk4 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Sacks, Paul. |
| 245 10 - TITLE STATEMENT | |
| Title | Techniques of functional analysis for differential and integral equations / |
| Statement of responsibility, etc. | Paul Sacks. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication, distribution, etc. | London : |
| Name of publisher, distributor, etc. | Academic Press, |
| Date of publication, distribution, etc. | 2017. |
| 300 ## - DESCRIPTION | |
| Extent | 1 online resource |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Front Cover; Techniques of Functional Analysis for Differential and Integral Equations; Copyright; Contents; Preface; Chapter 1: Some Basic Discussion of Differential and Integral Equations; 1.1 Ordinary Differential Equations; 1.1.1 Initial Value Problems; 1.1.2 Boundary Value Problems; 1.1.3 Some Exactly Solvable Cases; 1.2 Integral Equations; 1.3 Partial Differential Equations; 1.3.1 First Order PDEs and the Method of Characteristics; 1.3.2 Second Order Problems in R2; 1.3.3 Further Discussion of Model Problems; Wave Equation; Heat Equation; Laplace Equation. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 1.3.4 Standard Problems and Side Conditions1.4 Well-Posed and Ill-Posed Problems; 1.5 Exercises; Chapter 2: Vector Spaces; 2.1 Axioms of a Vector Space; 2.2 Linear Independence and Bases; 2.3 Linear Transformations of a Vector Space; 2.4 Exercises; Chapter 3: Metric Spaces; 3.1 Axioms of a Metric Space; 3.2 Topological Concepts; 3.3 Functions on Metric Spaces and Continuity; 3.4 Compactness and Optimization; 3.5 Contraction Mapping Theorem; 3.6 Exercises; Chapter 4: Banach Spaces; 4.1 Axioms of a Normed Linear Space; 4.2 Infinite Series; 4.3 Linear Operators and Functionals. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 4.4 Contraction Mappings in a Banach Space4.5 Exercises; Chapter 5: Hilbert Spaces; 5.1 Axioms of an Inner Product Space; 5.2 Norm in a Hilbert Space; 5.3 Orthogonality; 5.4 Projections; 5.5 Gram-Schmidt Method; 5.6 Bessel's Inequality and Infinite Orthogonal Sequences; 5.7 Characterization of a Basis of a Hilbert Space; 5.8 Isomorphisms of a Hilbert Space; 5.9 Exercises; Chapter 6: Distribution Spaces; 6.1 The Space of Test Functions; 6.2 The Space of Distributions; 6.3 Algebra and Calculus With Distributions; 6.3.1 Multiplication of Distributions; 6.3.2 Convergence of Distributions. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 6.3.3 Derivative of a Distribution6.4 Convolution and Distributions; 6.5 Exercises; Chapter 7: Fourier Analysis; 7.1 Fourier Series in One Space Dimension; 7.2 Alternative Forms of Fourier Series; 7.3 More About Convergence of Fourier Series; 7.4 The Fourier Transform on RN; 7.5 Further Properties of the Fourier Transform; 7.6 Fourier Series of Distributions; 7.7 Fourier Transforms of Distributions; 7.8 Exercises; Chapter 8: Distributions and Differential Equations; 8.1 Weak Derivatives and Sobolev Spaces; 8.2 Differential Equations in D'; 8.3 Fundamental Solutions. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 8.4 Fundamental Solutions and the Fourier Transform8.5 Fundamental Solutions for Some Important PDEs; Laplace Operator; Heat Operator; Wave Operator; Schr�odinger Operator; Helmholtz Operator; Klein-Gordon Operator; Biharmonic Operator; 8.6 Exercises; Chapter 9: Linear Operators; 9.1 Linear Mappings Between Banach Spaces; 9.2 Examples of Linear Operators; 9.3 Linear Operator Equations; 9.4 The Adjoint Operator; 9.5 Examples of Adjoints; 9.6 Conditions for Solvability of Linear Operator Equations; 9.7 Fredholm Operators and the Fredholm Alternative; 9.8 Convergence of Operators; 9.9 Exercises. |
| 650 #0 - SUBJECT | |
| Keyword | Functional analysis. |
| 650 #0 - SUBJECT | |
| Keyword | Differential equations. |
| 650 #0 - SUBJECT | |
| Keyword | Integral equations. |
| 856 40 - ONLINE RESOURCES | |
| url | https://www.sciencedirect.com/science/book/9780128114261 |
| 758 ## - | |
| -- | has work: |
| -- | Techniques of functional analysis for differential and integral equations (Text) |
| -- | https://id.oclc.org/worldcat/entity/E39PCGdbXKY6kyKctWdJRRyYpq |
| -- | https://id.oclc.org/worldcat/ontology/hasWork |
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