2013

Introduction to Mathematical Analysis

Authors:

ISBN: 978-3-0348-0635-0 (Print) 978-3-0348-0636-7 (Online)

Table of contents (17 chapters)

  1. Front Matter

    Pages i-xx

  2. A Rigorous Approach to Advanced Calculus

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 3-31

      Preliminaries

    3. No Access

      Book Chapter

      Pages 33-63

      Metric and Topological Spaces I

    4. No Access

      Book Chapter

      Pages 65-95

      Multivariable Differential Calculus

    5. No Access

      Book Chapter

      Pages 97-116

      Integration I: Multivariable Riemann Integral and Basic Ideas Toward the Lebesgue Integral

    6. No Access

      Book Chapter

      Pages 117-143

      Integration II: Measurable Functions, Measure and the Techniques of Lebesgue Integration

    7. No Access

      Book Chapter

      Pages 145-173

      Systems of Ordinary Differential Equations

    8. No Access

      Book Chapter

      Pages 175-191

      Systems of Linear Differential Equations

    9. No Access

      Book Chapter

      Pages 193-210

      Line Integrals and Green’s Theorem

  3. Analysis and Geometry

    1. Front Matter

      Pages 211-211

    2. No Access

      Book Chapter

      Pages 213-235

      Metric and Topological Spaces II

    3. No Access

      Book Chapter

      Pages 237-266

      Complex Analysis I: Basic Concepts

    4. No Access

      Book Chapter

      Pages 267-285

      Multilinear Algebra

    5. No Access

      Book Chapter

      Pages 287-310

      Smooth Manifolds, Differential Forms and Stokes’ Theorem

    6. No Access

      Book Chapter

      Pages 311-348

      Complex Analysis II: Further Topics

    7. No Access

      Book Chapter

      Pages 349-366

      Calculus of Variations and the Geodesic Equation

    8. No Access

      Book Chapter

      Pages 367-392

      Tensor Calculus and Riemannian Geometry

    9. No Access

      Book Chapter

      Pages 393-426

      Banach and Hilbert Spaces: Elements of Functional Analysis

    10. No Access

      Book Chapter

      Pages 427-449

      A Few Applications of Hilbert Spaces

  4. Back Matter

    Pages 451-510