| Functions, Limits, and Derivatives | |
| The Basics | |
| Numbers and Sets | |
| Equations | |
| Inequalities | |
| Logic | |
| Proofs | |
| Functions | |
| What Is a Function? | |
| Graphs of Functions | |
| Linear Functions | |
| A Basic Library of Functions | |
| Combinations of Functions | |
| Transformations and Symmetry | |
| Inverse Functions | |
| Limits | |
| Intuitive Notion of Limit | |
| Formal Definition of limit | |
| Delta-Epsilon Proofs | |
| Limit Rules | |
| Calculating Limits | |
| Continuity | |
| Two Theorems About Continuous Functions | |
| Appendix: Proofs of Selected Limit Rules | |
| Derivatives | |
| Tangent Lines and the Derivative at a Point | |
| The Derivative as an Instantaneous Rate of Change | |
| Differentiability | |
| The Derivative as a Function | |
| Basic Differentiation Rules | |
| Three Theorems about Tangent Lines | |
| The First Derivative and Function Behavior | |
| The Second Derivative and Function Behavior | |
| Algebraic Functions | |
| Power Functions | |
| The Algebra of Power Functions | |
| Limits of Power Functions | |
| Derivatives of Power Functions | |
| Graphs of Power Functions with Integer Powers | |
| Graphs of Power Functions with Rational Powers | |
| Polynomial Functions | |
| The Algebra of Polynomial Functions | |
| Limits and Derivatives of Polynomial Functions | |
| Graphing Polynomial Functions | |
| Optimization with Polynomial Functions | |
| Rational Functions | |
| The Algebra of Rational Functions | |
| Limits and Asymptotes of Rational Functions | |
| Derivatives of Rational Functions | |
| Graphs of Rational Functions | |
| General Algebraic Functions | |
| Working with Algebraic Functions | |
| The Product Rule and the Chain Rule | |
| Implicit Differentiation | |
| Related Rates | |
| Optimization and Curve Sketching | |
| Transcendental Functions | |
| Exponential Functions | |
| The Algebra of Exponential Functions | |
| The Natural Exponential Function | |
| Limits of Exponential Functions | |
| Derivatives of Exponential Functions | |
| Graphs of Exponential Functions | |
| Applications of Exponential Functions | |
| L' Hocirc;pital's Rule | |
| Logarithmic Functions | |
| The Algebra of Logarithmic Functions | |
| Limits and Derivatives of Logarithmic Functions | |
| Using Logarithms as a Calculational Tool | |
| Trigonometric Functions | |
| Right Triangle Trigonometry | |
| Unit Circle Trigonometry | |
| The Algebra of Trigonometric Functions | |
| Limits of Trigonometric Functions | |
| Derivatives of Trigonometric Functions | |
| Graphs of Trigonometric Functions | |
| Inverse Trigonometric Functions | |
| Defining the Inverse Trigonometric Functions | |
| Derivatives of Inverse Trigonometric Functions | |
| Integration | |
| Definite Integrals | |
| Geometric Approximation and Sigma Notation | |
| Approximating Area with Riemann Sums | |
| The Definite Integral | |
| Area and Average Value | |
| The Fundamental Theorem of Calculus | |
| Indefinite Integrals | |
| The Fundamental Theorem of Calculus | |
| Functions Defined by Integrals | |
| Basic Integration Techniques | |
| Integration by Substitution | |
| Integration by Parts | |
| Trigonometric Integrals | |
| Trigonometric Substitution | |
| Applications of Integration | |
| Arc Length | |
| Volumes by Slicing | |
| Volumes by Shells | |
| Practical Applications | |
| Selected Answers | |
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