Analysis of Functions of a Single Variable by Lawrence Baggett - HTML preview
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Analysis of Functions of a Single Variable
Table of Contents
- Preface to Analysis of Functions of a Single Variable: A Detailed Development
- Chapter 1. The Real and Complex Numbers
- Chapter 2. The Limit of a Sequence of Numbers
- Chapter 3. Functions and Continuity
- 3.1. Functions and Continuity Definition of the Number π
- 3.2. Functions
- 3.3. Polynomial Functions
- 3.4. Continuity
- 3.5. Continuity and Topology
- 3.6. Deeper Analytic Properties of Continuous Functions
- 3.7. Power Series Functions
- 3.8. The Elementary Transcendental Functions
- 3.9. Analytic Functions and Taylor Series
- 3.10. Uniform Convergence
- Chapter 4. Differentiation, Local Behavior
- 4.1. Differentiation, Local Behavior E^iπ = -1.
- 4.2. The Limit of a Function
- 4.3. The Derivative of a Function
- 4.4. Consequences of Differentiability, the Mean Value Theorem
- 4.5. The Exponential and Logarithm Functions
- 4.6. The Trigonometric and Hyperbolic Functions
- 4.7. L'Hopital's Rule
- 4.8. Higher Order Derivatives
- 4.9. Taylor Polynomials and Taylor's Remainder Theorem
- 4.10. The General Binomial Theorem
- 4.11. More on Partial Derivatives
- Chapter 5. Integration, Average Behavior
- Chapter 6. Integration over Smooth Curves in the Plane
- Chapter 7. The Fundamental Theorem of Algebra, and The Fundamental Theorem of Analysis
- 7.1. The Fundamental Theorem of Algebra, and the Fundamental Theorem of Analysis
- 7.2. Cauchy's Theorem
- 7.3. Basic Applications of the Cauchy Integral Formula
- 7.4. The Fundamental Theorem of Algebra
- 7.5. The Maximum Modulus Principle
- 7.6. The Open Mapping Theorem and the Inverse Function Theorem
- 7.7. Uniform Convergence of Analytic Functions
- 7.8. Isolated Singularities, and the Residue Theorem
- Appendix A. Appendix: Existence and Uniqueness of a Complete Ordered Field
- Index