Real and Convex Analysis
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Author Description
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. The book contains detailed illustrations, examples and exercises. It lays the groundwork for the needs of classical fields as well as the important new fields of optimization and probability theory.
Menrva's Summary
THE THESIS
This book provides a foundational course in analysis tailored for scientists and engineers, exploring core concepts through the lens of metric spaces. It builds upon fundamental material in its initial chapters, covering convergence, completeness, compactness, and continuity. Subsequent sections apply these tools to introduce differential and integral equations, convex analysis, and measure theory, laying groundwork for fields like optimization and probability theory.
THE SCOPE MAP
- Introduction to metric spaces as the central framework.
- Detailed coverage of convergence, completeness, compactness, and continuity.
- Applications to differential equations.
- Applications to integral equations.
- Introduction to convex analysis.
- Introduction to measure theory.
- Exploration of connections to optimization.
- Exploration of connections to probability theory.
THE AUTHORITY PERSPECTIVE
This text is designed as an advanced undergraduate or graduate-level introduction to analysis for scientific and engineering disciplines. Its modern treatment, supported by detailed illustrations and examples, aims to provide a clear and aesthetically pleasing presentation of complex topics. The book's structure emphasizes the foundational 'four-C's' of analysis before moving into more specialized areas, ensuring a robust understanding for students.
Page Count:
161
Publication Date:
2013-01-01
ISBN-10:
1461452570
ISBN-13:
9781461452577
Science
Non-Fiction
Analysis
Metric Spaces
Probability Theory
Optimization
Measure Theory
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