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Note: Each chapter concludes with Problem Solving | |
Prerequisites | |
Solving Equations Section Project: Projectile Motion | |
Solving Inequalities | |
Graphical Representation of Data | |
Graphs of Equations | |
Linear Equations in Two Variables | |
Functions and Their Graphs | |
Functions | |
Analyzing Graphs of Functions | |
Shifting, Reflecting, and Stretching Graphs | |
Combinations of Functions | |
Inverse Functions | |
Mathematical Modeling Section Project: Hooke's Law | |
Polynomial and Rational Functions | |
Quadratic Functions | |
Polynomial Functions of Higher Degree | |
Polynomial and Synthetic Division | |
Complex Numbers Section Project: The Mandelbrot Set | |
The Fundamental Theorem of Algebra | |
Rational Functions Section Project: Rational Functions | |
Limits and Their Properties | |
A Preview of Calculus | |
Finding Limits Graphically and Numerically | |
Evaluating Limits Analytically | |
Continuity and One-Sided Limits | |
Infinite Limits Section Project: Graphs and Limits of Functions Progressive Summary 1: Flowchart of Calculus | |
Differentiation | |
The Derivative and the Tangent Line Problem | |
Basic Differentiation Rules and Rates of Change | |
The Product and Quotient Rules and Higher-Order Derivatives | |
The Chain Rule | |
Implicit Differentiation Section Project: Optical Illusions | |
Related Rates | |
Applications of Differentiation | |
Extrema on an Interval | |
Rolle's Theorem and the Mean Value Theorem | |
Increasing and Decreasing Functions and the First Derivative Test | |
Concavity and the Second Derivative Test | |
Limits at Infinity | |
A Summary of Curve Sketching | |
Optimization Problems Section Project: Connecticut River | |
Differentials | |
Integration | |
Antiderivatives and Indefinite Integration | |
Area | |
Riemann Sums and Definite Integrals | |
The Fundamental Theorem of Calculus Section Project: Demonstrating the Fundamental Theorem | |
Integration by Substitution | |
Numerical Integration Progressive Summary 2: Flowchart of Calculus | |
Exponential and Logarithmic Functions | |
Exponential Functions and Their Graphs | |
Logarithmic Functions and Their Graphs | |
Using Properties of Logarithms | |
Exponential and Logarithmic Equations | |
Exponential and Logarithmic Models Section Project: Comparing Models | |
Exponential and Logarithmic Functions and Calculus | |
Exponential Functions: Differentiation and Integration | |
Logarithmic Functions and Differentiation Section Project: An Alternate Definition of ln x | |
Logarithmic Functions and Integration | |
Differential Equations: Growth and Decay Progressive Summary 3: Flowchart of Calculus | |
Trigonometric Functions | |
Radian and Degree Measure | |
Trigonometric Functions: The Unit Circle | |
Right Triangle Trigonometry | |
Trigonometric Functions of Any Angle | |
Graphs of Sine and Cosine Functions Section Project: Approximating Sine and Cosine Functions | |
Graphs of Other Trigonometric Functions | |
Inverse Trigonometric Functions | |
Applications and Models | |
Analytic Trigonometry | |
Using Fundamental Trigonometric Identities | |
Verifying Trigonometric Identities | |
Solving Trigonometric Equations Section Project: Modeling a Sound Wave | |
Sum and Difference Formulas | |
Multiple-Angle and Product-to-Sum Formulas | |
Trigonometric Functions and Calculus | |
Limits of Trigonometric Functions Section Project: Graphs and Limits of Trigonometric Functions | |
Trigonometric Functions: Differenti | |
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