Ebook: Real and Convex Analysis
Author: Erhan Çinlar Robert J Vanderbei
- Genre: Mathematics // Analysis
- Series: Undergraduate Texts in Mathematics
- Year: 2013
- Publisher: Springer
- Edition: 2013
- Language: English
- pdf
This book offers a first course in analysis for scientists and engineers. It can be used at the advanced undergraduate level or as part of the curriculum in a graduate program. The book is built around metric spaces. In the first three chapters, the authors lay the foundational material and cover the all-important “four-C’s”: convergence, completeness, compactness, and continuity. In subsequent chapters, the basic tools of analysis are used to give brief introductions to differential and integral equations, convex analysis, and measure theory. The treatment is modern and aesthetically pleasing. It lays the groundwork for the needs of classical fields as well as the important new fields of optimization and probability theory.
Table of Contents
Cover
Real and Convex Analysis
ISBN 9781461452560 ISBN 9781461452577
Preface
Contents
Notation and Usage
Chapter 1. Sets and Functions
A. Sets
B. Functions and Sequences
C. Countability
D. On the Real Line
E. Series
Chapter 2. Metric Spaces
A. Euclidean Spaces
B. Metrics
C. Open and Closed Sets
D. Convergence
E. Completeness
F. Compactness
Chapter 3. Functions on Metric Spaces
A. Continuous Mappings
B. Compactness and Uniform Continuity
C. Sequences of Functions
D. Spaces of Continuous Functions
Chapter 4. Differential and Integral Equations
A. Contraction Mappings
B. Systems of Linear Equations
C. Integral Equations
D. Differential Equations
Chapter 5. Convexity
A. Convex Sets and Convex Functions
B. Projections
C. Supporting Hyperplane Theorem
D. Legendre Transform
E. Infimal Convolution
Chapter 6. Convex Optimization
A. Primal and Dual Problems
B. Linear Programming and Polyhedra
C. Lagrangians
D. Saddle Points
Chapter 7. Measure and Integration
A. Algebras
B. Measurable Spaces and Functions
C. Measures
D. Integration
E. Transforms and Indefinite Integrals
F. Kernels and Product Spaces
Further Reading
Bibliography
Index
Table of Contents
Cover
Real and Convex Analysis
ISBN 9781461452560 ISBN 9781461452577
Preface
Contents
Notation and Usage
Chapter 1. Sets and Functions
A. Sets
B. Functions and Sequences
C. Countability
D. On the Real Line
E. Series
Chapter 2. Metric Spaces
A. Euclidean Spaces
B. Metrics
C. Open and Closed Sets
D. Convergence
E. Completeness
F. Compactness
Chapter 3. Functions on Metric Spaces
A. Continuous Mappings
B. Compactness and Uniform Continuity
C. Sequences of Functions
D. Spaces of Continuous Functions
Chapter 4. Differential and Integral Equations
A. Contraction Mappings
B. Systems of Linear Equations
C. Integral Equations
D. Differential Equations
Chapter 5. Convexity
A. Convex Sets and Convex Functions
B. Projections
C. Supporting Hyperplane Theorem
D. Legendre Transform
E. Infimal Convolution
Chapter 6. Convex Optimization
A. Primal and Dual Problems
B. Linear Programming and Polyhedra
C. Lagrangians
D. Saddle Points
Chapter 7. Measure and Integration
A. Algebras
B. Measurable Spaces and Functions
C. Measures
D. Integration
E. Transforms and Indefinite Integrals
F. Kernels and Product Spaces
Further Reading
Bibliography
Index
Download the book Real and Convex Analysis for free or read online
Continue reading on any device:
Last viewed books
Related books
{related-news}
Comments (0)