Aspects of Calculus (Paperback, Softcover Repri)

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.