Introduction to Mathematical Analysis 1st Edition by Igor Kriz, Ales Pultr ISBN 3034806353 9783034806350
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Product details:
ISBN 10: 3034806353
ISBN 13: 9783034806350
Author: Igor Kriz, Ales Pultr
The book begins at the level of an undergraduate student assuming only basic knowledge of calculus in one variable. It rigorously treats topics such as multivariable differential calculus, Lebesgue integral, vector calculus and differential equations. After having built on a solid foundation of topology and linear algebra, the text later expands into more advanced topics such as complex analysis, differential forms, calculus of variations, differential geometry and even functional analysis. Overall, this text provides a unique and well-rounded introduction to the highly developed and multi-faceted subject of mathematical analysis, as understood by a mathematician today.
Table of contents:
Part 1. A Rigorous Approach to Advanced Calculus
Chapter 1: Preliminaries
Chapter 2: Metric and Topological Spaces I
Chapter 3: Multivariable Differential Calculus
Chapter 4: Integration I: Multivariable Riemann Integral and Basic Ideas toward the Lebesgue Integral
Chapter 5: Integration II: Measurable Functions, Measure and the Techniques of Lebesgue Integration
Chapter 6: Systems of Ordinary Differential Equations
Chapter 7: System of Linear Differential Equations
Chapter 8: Line Integrals and Green’s Theorem
Part 2. Analysis and Geometry
Chapter 9: An Introduction to Complex Analysis
Chapter 10: Metric and Topological Spaces II
Chapter 11: Multilinear Algebra
Chapter 12: Smooth Manifolds, Differential Forms and Stokes’ Theorem
Chapter 13: Calculus of Variations and the Geodesic Equation
Chapter 14: Tensor Calculus and Riemannian Geometry
Chapter 15: Hilbert Spaces I: Definitions and Basic Properties
Chapter 16: Hilbert Spaces II: Examples and Applications
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Tags: Igor Kriz, Ales Pultr, Introduction, Mathematical, Analysis