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| Preliminaries | |
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| Graphs and Equations | |
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| Functions | |
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| The Straight Line and Linear Functions | |
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| The Trigonometric Functions | |
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| Calculus: A First Look | |
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| Introduction to Limits Part I | |
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| Limits | |
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| Introduction to Limits Part II | |
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| The Derivative: Two Problems With One Theme | |
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| Exponential Functions | |
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| Logarithms and the Logarithmic Function | |
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| Chapter Review | |
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| Numerical and Graphical Techniques | |
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| Calculator and Computer Graphs | |
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| Calculator and Computer Graphs | |
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| Calculator and Computer Tables | |
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| Parameters | |
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| The Damped Harmonic Oscillator | |
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| Zooming and Local Linearity | |
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| Roots and Slopes: When and How Fast? Solving Equations | |
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| Linear Curve Fitting | |
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| Nonlinear Curve Fitting | |
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| Chapter Review | |
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| Derivatives | |
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| The Derivative as a Function | |
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| The Derivative as a Function | |
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| Rules for Finding Derivatives | |
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| Derivatives of Sines, Cosines, Logs and Exponentials | |
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| The Chain Rule | |
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| Higher-Order Derivatives | |
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| Implicit Differentiation and Related Rates | |
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| Differentials and Approximations | |
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| Chapter Review | |
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| Applications of the Derivative | |
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| Maxima and Minima | |
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| Increasing, Decreasing, and the Derivative | |
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| Monotonicity and Concavity | |
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| Local Maxima and Minima | |
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| Ideal Gases and Real Gases | |
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| More Max-Min Problems | |
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| Applications from Economics | |
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| Graphing with Parameters | |
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| The Mean Value Theorem | |
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| Chapter Review | |
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| The Integral | |
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| Antiderivatives (Indefinite Integrals) | |
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| Introduction to Differential Equations | |
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| The Draining Can | |
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| Area and Reimann Sums | |
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| Area and Distance | |
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| The Definite Integral and Numerical Integration | |
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| Area Functions | |
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| The Fundamental Theorem of Calculus | |
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| More Properties of the Definite Integral | |
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| Substitution | |
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| Chapter Review | |
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| Applications of the Integral | |
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| The Area of a Plane Region | |
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| Volumes of Solids: Slabs, Disks, Washers | |
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| Length of a Plane Curve | |
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| Arc Length | |
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| Work | |
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| Moments, Center of Mass | |
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| Chapter Review | |
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| Transcendental Functions and Differential Equations | |
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| Inverse Functions and Their Derivatives | |
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| A Different Approach to Logarithmic and Exponential Functions | |
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| Falling Objects | |
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| General Exponential and Logarithmic Functions | |
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| Exponential Growth and Decay | |
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| Numerical and Graphical Approaches to Differential Equations | |
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| Planning Your Retirement | |
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| The Trigonometric Functions and Their Inverses | |
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| The Hyperbolic Functions and Their Inverses | |
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| Chapter Review | |
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| Techniques of Integration | |
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| Substitution and Tables of Integrals | |
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| Integration by Parts | |
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| Integration by Parts | |
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| Some Trigonometric Integrals | |
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| Integration of Rational Functions | |
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| Population Models | |
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| Indeterminate Forms | |
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| Improper Integrals | |
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| Probability and Improper Integrals | |
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| Chapter Review | |
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| Infinite Series | |
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| Infinite Sequences and Dynamical Systems | |
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| Discrete Population Models | |
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| Infinite Series | |
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| Bouncing Balls and Infinite Series | |
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| Altering Series, Absolute Convergence | |
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| Taylor's Approximation to Functions | |
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| Taylor Series and Fourier Series | |
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| The Error in Taylor's Approximation | |
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| Newton's Method | |
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| General Power Series | |
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| The Gamma Function and Taylor Series | |
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| Approximations | |
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| Operations on Power Series | |
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| Chapter Review | |
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| Conics, Polar Coordinates and Parametric Curves | |
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| Conic Sections | |
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| Translation of Axes | |
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| The Polar Coordinate System and Graphs | |
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| Technology and Graphs of Polar Equations | |
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| Graphs in Polor Coordinates | |
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| Calculus in Polar Coordinates | |
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| Orbits of the Planets | |
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| Plane Curves: Parametric Representation | |
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| Chapter Review | |