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| Functions, Graphs, and Limits | |
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| Functions | |
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| The Graph of a Function | |
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| Linear Functions | |
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| Functional Models | |
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| Limits | |
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| One-Sided Limits and Continuity | |
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| Differentiation: Basic Concepts | |
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| The Derivative | |
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| Techniques of Differentiation | |
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| Product and Quotient Rules; Higher-Order Derivatives | |
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| The Chain Rule | |
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| Marginal Analysis and Approximations Using Increments | |
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| Implicit Differentiation and Related Rates | |
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| Additional Applications of the Derivative | |
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| Increasing and Decreasing Functions; Relative Extrema | |
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| Concavity and Points of Inflection | |
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| Curve Sketching | |
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| Optimization; Elasticity of Demand | |
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| Additional Applied Optimization | |
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| Exponential and Logarithmic Functions | |
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| Exponential Functions: Continuous Compounding | |
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| Logarithmic Functions | |
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| Applications; Exponential Models | |
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| Integration | |
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| Antidifferentiation: The Indefinite Integral | |
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| Integration by Substitution | |
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| The Definite Integral and the Fundamental Theorem of Calculus | |
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| Applying Definite Integration: Area Between Curves and Average Value | |
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| Additional Applications to Business and Economics | |
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| Additional Applications to the Life and Social Sciences | |
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| Additional Topics in Integration | |
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| Integration by Parts; Integral Tables | |
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| Improper Integrals | |
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| Numerical Integration | |
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| Calculus of Several Variables | |
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| Functions of Several Variables | |
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| Partial Derivatives | |
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| Optimizing Functions of Two Variables | |
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| The Method of Least-Squares | |
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| Constrained Optimization: The Method of Lagrange Multipliers | |
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| Double Integrals | |
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| Differential Equations | |
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| Introduction to Differential Equations | |
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| First-Order Linear Differential Equations | |
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| Additional Applications of Differential Equations | |
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| Approximate Solutions of Differential Equations | |
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| Difference Equations; The Cobweb Model | |
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| Infinite Series and Taylor Series Approximations | |
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| Infinite Series; Geometric Series | |
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| Tests for Convergence | |
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| Functions as Power Series; Taylor Series | |
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| Probability and Calculus | |
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| Introduction to Probability; Discrete Random Variables | |
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| Continuous Random Variables | |
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| Expected Value and Variance of Continuous Random Variables | |
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| Normal and Poisson Probability Distributions | |
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| Trigonometric Functions | |
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| The Trigonometric Functions | |
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| Differentiation and Integration of Trigonometric Functions | |
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| Additional Applications Involving Trigonometric Function | |
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| Algebra Review | |
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| A Brief Review of Algebra | |
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| Factoring Polynomials and Solving Systems of Equations | |
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| Evaluating Limits with L’Hopital’s Rule | |
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| The Summation Notation | |