| Description |
xviii, 517 pages : illustrations ; 23 cm |
|
regular print |
| Contents |
Ch. 1. The Problem of Calculus -- 1.1. Mass and Line Density -- 1.2. Volume and Growth Rate -- 1.3. Measures of Rectilinear Motion -- 1.4. Force and Its Totals -- 1.5. Geometrical Quantities Associated with Curves -- 1.6. Numbers, Variables, and Functions -- Ch. 2. Integral and Derivative -- 2.1. Approximate Calculation of Mass -- 2.2. Description of Mass as an Integral -- 2.3. Other Integrals from Physics -- 2.4. Integrals and Graphs of Functions -- 2.5. Indefinite Integrals -- 2.6. Approximate Calculation of Line Density -- 2.7. Description of Line Density as a Derivative -- 2.8. Other Derivatives from Physics -- 2.9. Derivatives and Graphs of Functions -- 2.10. Signed Quantities and the Integral and Derivative in General -- Ch. 3. Differentiation and Integration: I -- 3.1. Limits and Continuity -- 3.2. Derivative of a Polynomial -- 3.3. Elementary Functions and their Derivatives -- 3.4. Rules for Differentiation Corresponding to Arithmetic Operations on Functions -- 3.5. The Fundamental Theorem of Calculus -- 3.6. The Evaluation of Integrals -- 3.7. The Fundamental Theorem and the Mean Value Theorems -- 3.8. Higher Derivatives and Linear Approximation -- 3.9. Behavior of Functions as Revealed by Derivatives -- Ch. 4. Differentiation and Integration: II -- 4.1. Composite Functions and their Derivatives -- 4.2. Applications of the Chain Rule -- 4.3. Inverse Functions and their Derivatives -- 4.4. Differentiation of the Trigonometric Functions and their Inverses -- 4.5. Differentiation of Functions of Several Variables -- 4.6. Methods of Integration -- 4.7. Improper Integrals -- 4.8. Integration in the Plane and in Space -- Ch. 5. Differential Equations of Rectilinear Motion -- 5.1. Uniform Gravitation -- 5.2. Simple Harmonic Motion -- 5.3. Energy -- 5.4. Inverse-Square Gravitation -- Ch. 6. The Differential Equation of Intrinsic Growth: The Exponential and Logarithmic Functions -- 6.1. Intrinsic Growth -- 6.2. The Exponential and Logarithmic Functions and their Applications -- Ch. 7. Length and Curvature of Plane Curves -- 7.1. Arc Length and Curvature -- 7.2. Length and Curvature of a Graph -- 7.3. Local Geometry -- 7.4. Parametric Representation -- 7.5. Line Integrals and Curvilinear Motion -- Ch. 8. Representation of Functions by Infinite Taylor Series -- 8.1. Polynomial Approximation and the Taylor Series -- 8.2. Taylor's Theorem and the Convergence of Taylor Series -- App. 1. Conversion to CGS Units -- App. 2. The Epigraphs |
| Notes |
Includes index |
| Subject |
Calculus.
|
| LC no. |
2002069008 |
| ISBN |
9810249039 alkaline paper |
|
9810249047 paperback alkaline paper |
|
