Advanced Calculus is intended as a text for courses that furnish the backbone of the student's undergraduate education in mathematical analysis. The goal is to rigorously present the fundamental concepts within the context of illuminating examples and stimulating exercises. This book is self-contained and starts with the creation of basic tools using the completeness axiom. The continuity, differentiability, integrability, and power series representation properties of functions of a single variable are established. The next few chapters describe the topological and metric properties of Euclidean space. These are the basis of a rigorous treatment of differential calculus (including the Implicit Function Theorem and Lagrange Multipliers) for mappings between Euclidean spaces and integration for functions of several real variables. Special attention has been paid to the motivation for proofs. Selected topics, such as the Picard Existence Theorem for differential equations, have been included in such a way that selections may be made while preserving a fluid presentation of the essential material. Supplemented with numerous exercises, Advanced Calculus is a perfect book for undergraduate students of analysis.
- 610 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
About this book
Table of contents
- Cover
- Preface
- Tools for Analysis
- Convergent Sequences
- Continuous Functions
- Differentiation
- Elementary Functions as Solutions of Differential Equations
- Integration: Two Fundamental Theorems
- Integration: Further Topics
- Approximation By Taylor Polynomials
- Sequences And Series Of Functions
- The Euclidean Space
- Continuity, Compactness, And Connectedness
- Metric Spaces
- Differentiating Functions Of Several Variables
- Local Approximation Of Real-Valued Functions
- Approximating Nonlinear Mappings By Linear Mappings
- Images And Inverses: The Inverse Function Theorem
- The Implicit Function Theorem And Its Applications
- Integrating Functions Of Several Variables
- Iterated Integration And Changes Of Variables
- Line And Surface Integrals
- Appendix A Consequences Of The Field And Positivity Axioms
- Appendix B Linear Algebra
- Index
- Back Cover
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Information
Publisher
American Mathematical SocietyYear
2009Topic
MathematicsSubtopic
Mathematics GeneraleBook ISBN
9781470411183
Index
MathematicsFrequently asked questions
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Yes, you can access Advanced Calculus by Patrick M. Fitzpatrick in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over 1.5 million books available in our catalogue for you to explore.