1 The Logarithmic and Exponential Functions. - 1. An Area Problem. - 2. The Natural Logarithm. - 3. The Exponential Function. - 4. The Hyperbolic Functions. - 5. Miscellaneous Examples. - Exercises to Chapter 1. - 2 Limits and Continuity. - 1. Limits. - 2. Continuity. - 3. Monotonic Functions. - 4. Miscellaneous Examples. - Exercises to Chapter 2. - 3 Differentiation. - 1. Basic Rules of Differentiation. - 2. Derivatives of Basic Functions. - 3. Mechanics of Differentiation. - 4. Asymptotes. - 5. Tangent to a Conic Section. - Exercises to Chapter 3. - 4 Applications of Differentiation. - 1. Mean Value Theorems. - 2. Taylor's Theorem. - 3. Concave Functions. - 4. Newton's Method for Approximating Real Roots of Functions. - 5. Arithmetic and Geometric Means. - 6. Miscellaneous Examples. - Exercises to Chapter 4. - 5 Integration. - 1. Examples of Area Calculation. - 2. Area of a Planar Region. - 3. The Riemann Integral. - 4. Basic Propositions of Integral Calculus. - 5. Numerical Integration. - Exercises to Chapter 5. - 6 Additional Topics in Integration. - 1. The Indefinite Integral. - 2. Some Techniques of Integration. - 3. Integration of Rational Functions. - 4. Integration by Rationalization. - 5. Some Applications of Integration. - Exercises to Chapter 6. - 7 Infinite Series. - 1. Numerical Sequences. - 2. The Formulas of Wallis and Stirling. - 3. Numerical Series. - 4. Groupings and Rearrangements. - 5. Uniform Convergence. - 6. Power Series. - 7. Some Important Power Series. - 8. Miscellaneous Examples. - Exercises to Chapter 7. Language: English