**Graduate Studies in Mathematics**

Volume: 143;
2013;
250 pp;
Hardcover

MSC: Primary 46;
Secondary 35

Print ISBN: 978-0-8218-8771-4

Product Code: GSM/143

List Price: $64.00

Individual Member Price: $51.20

**Electronic ISBN: 978-0-8218-9406-4
Product Code: GSM/143.E**

List Price: $64.00

Individual Member Price: $51.20

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#### Supplemental Materials

# Lecture Notes on Functional Analysis: With Applications to Linear Partial Differential Equations

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*Alberto Bressan*

This textbook is addressed to graduate
students in mathematics or other disciplines who wish to understand
the essential concepts of functional analysis and their applications
to partial differential equations.

The book is intentionally concise, presenting all the fundamental
concepts and results but omitting the more specialized topics. Enough
of the theory of Sobolev spaces and semigroups of linear operators is
included as needed to develop significant applications to elliptic,
parabolic, and hyperbolic PDEs. Throughout the book, care has been
taken to explain the connections between theorems in functional
analysis and familiar results of finite-dimensional linear
algebra.

The main concepts and ideas used in the proofs are
illustrated with a large number of figures. A rich collection of
homework problems is included at the end of most chapters. The book is
suitable as a text for a one-semester graduate course.

#### Table of Contents

# Table of Contents

## Lecture Notes on Functional Analysis: With Applications to Linear Partial Differential Equations

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Preface xi12 free
- Chapter 1. Introduction 114 free
- Chapter 2. Banach spaces 1124 free
- Chapter 3. Spaces of continuous functions 4558
- Chapter 4. Bounded linear operators 6174
- Chapter 5. Hilbert spaces 7790
- Chapter 6. Compact operators on a Hilbert space 101114
- Chapter 7. Semigroups of linear operators 115128
- Chapter 8. Sobolev spaces 139152
- Chapter 9. Linear partial differential equations 185198
- Chapter 10. Background material 217230
- Summary of notation 241254
- Bibliography 245258
- Index 247260 free
- Back Cover Back Cover1265

#### Readership

Graduate students interested in functional analysis and partial differential equations.