| |
| |
| |
| Functions, Graphs, and Limits | |
| |
| |
| |
| Functions | |
| |
| |
| |
| The Graph of a Function | |
| |
| |
| |
| Linear Functions | |
| |
| |
| |
| Functional Models | |
| |
| |
| |
| Limits | |
| |
| |
| |
| One-Sided Limits and Continuity | |
| |
| |
| |
| Differentiation: Basic Concepts | |
| |
| |
| |
| The Derivative | |
| |
| |
| |
| Techniques of Differentiation | |
| |
| |
| |
| Product and Quotient Rules; Higher-Order Derivatives | |
| |
| |
| |
| The Chain Rule | |
| |
| |
| |
| Marginal Analysis and Approximations Using Increments | |
| |
| |
| |
| Implicit Differentiation and Related Rates | |
| |
| |
| |
| Additional Applications of the Derivative | |
| |
| |
| |
| Increasing and Decreasing Functions; Relative Extrema | |
| |
| |
| |
| Concavity and Points of Inflection | |
| |
| |
| |
| Curve Sketching | |
| |
| |
| |
| Optimization; Elasticity of Demand | |
| |
| |
| |
| Additional Applied Optimization | |
| |
| |
| |
| Exponential and Logarithmic Functions | |
| |
| |
| |
| Exponential Functions: Continuous Compounding | |
| |
| |
| |
| Logarithmic Functions | |
| |
| |
| |
| Applications; Exponential Models | |
| |
| |
| |
| Integration | |
| |
| |
| |
| Antidifferentiation: The Indefinite Integral | |
| |
| |
| |
| Integration by Substitution | |
| |
| |
| |
| The Definite Integral and the Fundamental Theorem of Calculus | |
| |
| |
| |
| Applying Definite Integration: Area Between Curves and Average Value | |
| |
| |
| |
| Additional Applications to Business and Economics | |
| |
| |
| |
| Additional Applications to the Life and Social Sciences | |
| |
| |
| |
| Additional Topics in Integration | |
| |
| |
| |
| Integration by Parts; Integral Tables | |
| |
| |
| |
| Introduction to Differential Equations | |
| |
| |
| |
| Improper Integrals; Continuous Probability | |
| |
| |
| |
| Numerical Integration | |
| |
| |
| |
| Calculus of Several Variables | |
| |
| |
| |
| Functions of Several Variables | |
| |
| |
| |
| Partial Derivatives | |
| |
| |
| |
| Optimizing Functions of Two Variables | |
| |
| |
| |
| The Method of Least-Squares | |
| |
| |
| |
| Constrained Optimization: The Method of Lagrange Multipliers | |
| |
| |
| |
| Double Integrals | |
| |
| |
| |
| Algebra Review | |
| |
| |
| |
| A Brief Review of Algebra | |
| |
| |
| |
| Factoring Polynomials and Solving Systems of Equations | |
| |
| |
| |
| Evaluating Limits with LG++HopitalG++s Rule | |
| |
| |
| |
| The Summation Notation | |