| |
| |
| |
| Functions | |
| |
| |
| |
| Functions and Their Graphs | |
| |
| |
| |
| Combining Functions; Shifting and Scaling Graphs | |
| |
| |
| |
| Trigonometric Functions | |
| |
| |
| |
| Graphing with Calculators and Computers | |
| |
| |
| |
| Limits and Continuity | |
| |
| |
| |
| Rates of Change and Tangents to Curves | |
| |
| |
| |
| Limit of a Function and Limit Laws | |
| |
| |
| |
| The Precise Definition of a Limit | |
| |
| |
| |
| One-Sided Limits and Limits at Infinity | |
| |
| |
| |
| Infinite Limits and Vertical Asymptotes | |
| |
| |
| |
| Continuity | |
| |
| |
| |
| Tangents and Derivatives at a Point | |
| |
| |
| |
| Differentiation | |
| |
| |
| |
| The Derivative as a Function | |
| |
| |
| |
| Differentiation Rules | |
| |
| |
| |
| The Derivative as a Rate of Change | |
| |
| |
| |
| Derivatives of Trigonometric Functions | |
| |
| |
| |
| The Chain Rule | |
| |
| |
| |
| Implicit Differentiation | |
| |
| |
| |
| Related Rates | |
| |
| |
| |
| Linearization and Differentials | |
| |
| |
| |
| Parametrizations of Plane Curves | |
| |
| |
| |
| Applications of Derivatives | |
| |
| |
| |
| Extreme Values of Functions | |
| |
| |
| |
| The Mean Value Theorem | |
| |
| |
| |
| Monotonic Functions and the First Derivative Test | |
| |
| |
| |
| Concavity and Curve Sketching | |
| |
| |
| |
| Applied Optimization | |
| |
| |
| |
| Newton's Method | |
| |
| |
| |
| Antiderivatives | |
| |
| |
| |
| Integration | |
| |
| |
| |
| Area and Estimating with Finite Sums | |
| |
| |
| |
| Sigma Notation and Limits of Finite Sums | |
| |
| |
| |
| The Definite Integral | |
| |
| |
| |
| The Fundamental Theorem of Calculus | |
| |
| |
| |
| Indefinite Integrals and the Substitution Rule | |
| |
| |
| |
| Substitution and Area Between Curves | |
| |
| |
| |
| Applications of Definite Integrals | |
| |
| |
| |
| Volumes by Slicing and Rotation About an Axis | |
| |
| |
| |
| Volumes by Cylindrical Shells | |
| |
| |
| |
| Lengths of Plane Curves | |
| |
| |
| |
| Areas of Surfaces of Revolution | |
| |
| |
| |
| Work | |
| |
| |
| |
| Moments and Centers of Mass | |
| |
| |
| |
| Fluid Pressures and Forces | |
| |
| |
| |
| Transcendental Functions | |
| |
| |
| |
| Inverse Functions and Their Derivatives | |
| |
| |
| |
| Natural Logarithms | |
| |
| |
| |
| Exponential Functions | |
| |
| |
| |
| Inverse Trigonometric Functions | |
| |
| |
| |
| Exponential Change and Separable Differential Equations | |
| |
| |
| |
| Indeterminate Forms and L'Hopital's Rule | |
| |
| |
| |
| Hyperbolic Functions | |
| |
| |
| |
| Techniques of Integration | |
| |
| |
| |
| Integration by Parts | |
| |
| |
| |
| Trigonometric Integrals | |
| |
| |
| |
| Trigonometric Substitutions | |
| |
| |
| |
| Integration of Rational Functions by Partial Fractions | |
| |
| |
| |
| Integral Tables and Computer Algebra Systems | |
| |
| |
| |
| Numerical | |