Author | Klambauer, Gabriel. author |
---|---|
Title | Aspects of Calculus [electronic resource] / by Gabriel Klambauer |
Imprint | New York, NY : Springer New York, 1986 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-9561-4 |
Descript | X, 516 p. online resource |
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. Taylorโs Theorem -- 3. Concave Functions -- 4. Newtonโs 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