| The Problem of Calculus | |
| Introduction | p. 1 |
| Mass and Line Density | p. 1 |
| Volume and Growth Rate | p. 4 |
| Measures of Rectilinear Motion | p. 6 |
| Force and Its Totals | p. 9 |
| Geometrical Quantities Associated with Curves | p. 18 |
| Numbers, Variables, and Functions | p. 28 |
| Integral and Derivative | |
| Introduction | p. 39 |
| Approximate Calculation of Mass | p. 40 |
| Description of Mass as an Integral | p. 46 |
| Other Integrals from Physics | p. 55 |
| Integrals and Graphs of Functions | p. 58 |
| Indefinite Integrals | p. 67 |
| Approximate Calculation of Line Density | p. 69 |
| Description of Line Density as a Derivative | p. 72 |
| Other Derivatives from Physics | p. 79 |
| Derivatives and Graphs of Functions | p. 81 |
| Signed Quantities and the Integral and Derivative in General | p. 90 |
| Differentiation and Integration: I | |
| Introduction | p. 100 |
| Limits and Continuity | p. 101 |
| Derivative of a Polynomial | p. 109 |
| Elementary Functions and their Derivatives | p. 115 |
| Rules for Differentiation Corresponding to Arithmetic Operations on Functions | p. 130 |
| The Fundamental Theorem of Calculus | p. 134 |
| The Evaluation of Integrals | p. 140 |
| The Fundamental Theorem and the Mean Value Theorems | p. 146 |
| Higher Derivatives and Linear Approximation | p. 162 |
| Behavior of Functions as Revealed by Derivatives | p. 171 |
| Differentiation and Integration: II | |
| Introduction | p. 183 |
| Composite Functions and their Derivatives | p. 183 |
| Applications of the Chain Rule | p. 193 |
| Inverse Functions and their Derivatives | p. 207 |
| Differentiation of the Trigonometric Functions and their Inverses | p. 215 |
| Differentiation of Functions of Several Variables | p. 225 |
| Methods of Integration | p. 237 |
| Improper Integrals | p. 249 |
| Integration in the Plane and in Space | p. 255 |
| Differential Equations of Rectilinear Motion | |
| Introduction | p. 269 |
| Uniform Gravitation | p. 270 |
| Simple Harmonic Motion | p. 275 |
| Energy | p. 283 |
| Inverse-Square Gravitation | p. 295 |
| The Differential Equation of Intrinsic Growth: The Exponential and Logarithmic Functions | |
| Introduction | p. 304 |
| Intrinsic Growth | p. 304 |
| The Exponential and Logarithmic Functions and their Applications | p. 312 |
| Length and Curvature of Plane Curves | |
| Introduction | p. 327 |
| Arc Length and Curvature | p. 328 |
| Length and Curvature of a Graph | p. 337 |
| Local Geometry | p. 350 |
| Parametric Representation | p. 358 |
| Line Integrals and Curvilinear Motion | p. 374 |
| Representation of Functions by Infinite Taylor Series | |
| Introduction | p. 389 |
| Polynomial Approximation and the Taylor Series | p. 389 |
| Taylor's Theorem and the Convergence of Taylor Series | p. 400 |
| Topical Summary | p. 419 |
| Conversion to CGS Units | p. 429 |
| The Epigraphs | p. 431 |
| Answers | p. 435 |
| Index | p. 505 |
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