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Introduction to Mathematical Analysis

  • Igor Kriz
  • Aleš Pultr

Table of contents

  1. Front Matter
    Pages i-xx
  2. A Rigorous Approach to Advanced Calculus

    1. Front Matter
      Pages 1-1
    2. Igor Kriz, Aleš Pultr
      Pages 3-31
    3. Igor Kriz, Aleš Pultr
      Pages 33-63
    4. Igor Kriz, Aleš Pultr
      Pages 65-95
    5. Igor Kriz, Aleš Pultr
      Pages 145-173
    6. Igor Kriz, Aleš Pultr
      Pages 175-191
    7. Igor Kriz, Aleš Pultr
      Pages 193-210
  3. Analysis and Geometry

    1. Front Matter
      Pages 211-211
    2. Igor Kriz, Aleš Pultr
      Pages 213-235
    3. Igor Kriz, Aleš Pultr
      Pages 237-266
    4. Igor Kriz, Aleš Pultr
      Pages 267-285
    5. Igor Kriz, Aleš Pultr
      Pages 287-310
    6. Igor Kriz, Aleš Pultr
      Pages 311-348
    7. Igor Kriz, Aleš Pultr
      Pages 349-366
    8. Igor Kriz, Aleš Pultr
      Pages 367-392
    9. Igor Kriz, Aleš Pultr
      Pages 393-426
    10. Igor Kriz, Aleš Pultr
      Pages 427-449
  4. Back Matter
    Pages 451-510

About this book

Introduction

The book begins at an undergraduate student level, assuming only basic knowledge of calculus in one variable. It rigorously treats topics such as multivariable differential calculus, the Lebesgue integral, vector calculus and differential equations. After having created 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 mathematicians today.​

Keywords

geometry integration manifolds mathematical analysis multivariate calculus

Authors and affiliations

  • Igor Kriz
    • 1
  • Aleš Pultr
    • 2
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA
  2. 2.Department of Applied Mathematics (KAM)Charles University Faculty of Mathematics and PhysicsPrague 1Czech Republic

Bibliographic information

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