Cover; Copyright Page; Contents; Acknowledgments; Preface; Chapter I. The Real Number System; 1. Familiar Number Systems; 2. Intervals; 3. Suprema and Infima; 4. Exact Arithmetic in R; 5. Topics for Further Study; Chapter II. Continuous Functions; 1. Functions in Mathematics; 2. Continuity of Numerical Functions; 3. The Intermediate Value Theorem; 4. More Ways to Form Continuous Functions; 5. Extreme Values; Chapter III. Limits; 1. Sequences and Limits; 2. Limits and Removing Discontinuities; 3. Limits Involving infinity; Chapter IV. The Derivative; 1. Differentiability

2. Combining Differentiable Functions3. Mean Values; 4. Second Derivatives and Approximations; 5. Higher Derivatives; 6. Inverse Functions; 7. Implicit Functions and Implicit Differentiation; Chapter V. The Riemann Integral; 1. Areas and Riemann Sums; 2. Simplifying the Conditions for Integrability; 3. Recognizing Integrability; 4. Functions Defined by Integrals; 5. The Fundamental Theorem of Calculus; 6. Topics for Further Study; Chapter VI. Exponential and Logarithmic Functions; 1. Exponents and Logarithms; 2. Algebraic Laws as Definitions; 3. The Natural Logarithm

4. The Natural Exponential Function5. An Important Limit; Chapter VII. Curves and Arc Length; 1. The Concept of Arc Length; 2. Arc Length and Integration; 3. Arc Length as a Parameter; 4. The Arctangent and Arcsine Functions; 5. The Fundamental Trigonometric Limit; Chapter VIII. Sequences and Series of Functions; 1. Functions Defined by Limits; 2. Continuity and Uniform Convergence; 3. Integrals and Derivatives; 4. Taylor's Theorem; 5. Power Series; 6. Topics for Further Study; Chapter IX. Additional Computational Methods; 1. L'Hôpital's Rule; 2. Newton's Method; 3. Simpson's Rule

4. The Substitution Rule for IntegralsReferences; Index