Chapter 1 PRECALCULUS REVIEW
1.1 Real Numbers, Functions, and Graphs
1.2 Linear and Quadratic Functions
1.3 The Basic Classes of Functions
1.4 Trigonometric Functions
1.5 Technology: Calculators and Computers
Chapter 2 LIMITS
2.1 Limits, Rates of Change, and Tangent Lines
2.2 Limits: A Numerical and Graphical Approach
2.3 Basic Limit Laws
2.4 Limits and Continuity
2.5 Evaluating Limits Algebraically
2.6 Trigonometric Limits
2.7 Intermediate Value Theorem
2.8 The Formal Definition of a Limit
Chapter 3 DIFFERENTIATION
3.1 Definition of the Derivative
3.2 The Derivative as a Function
3.3 Product and Quotient Rules
3.4 Rates of Change
3.5 Higher Derivatives
3.6 Trigonometric Functions
3.7 The Chain Rule
3.8 Implicit Differentiation
3.9 Related Rates
Chapter 4 APPLICATIONS OF THE DERIVATIVE
4.1 Linear Approximation and Applications
4.2 Extreme Values
4.3 The Mean Value Theorem and Monotonicity
4.4 The Shape of a Graph
4.5 Graph Sketching and Asymptotes
4.6 Applied Optimization
4.7 Newton’s Method
4.8 Antiderivatives
Chapter 5 THE INTEGRAL
5.1 Approximating and Computing Area
5.2 The Definite Integral
5.3 The Fundamental Theorem of Calculus, Part I
5.4 The Fundamental Theorem of Calculus, Part II
5.5 Net or Total Change as the Integral of a Rate
5.6 Substitution Method
Chapter 6 APPLICATIONS OF THE INTEGRAL
6.1 Area Between Two Curves
6.2 Setting Up Integrals: Volume, Density, Average Value
6.3 Volumes of Revolution
6.4 The Method of Cylindrical Shells
6.5 Work and Energy
Chapter 7 EXPONENTIAL FUNCTIONS
7.1 Derivative of f(x)=b^x and the Number e
7.2 Inverse Functions
7.3 Logarithms and their Derivatives
7.4 Exponential Growth and Decay
7.5 Compound Interest and Present Value
7.6 Models Involving y’= k(y-b)
7.7 L’Hoˆpital’s Rule
7.8 Inverse Trigonometric Functions
7.9 Hyperbolic Functions
Chapter 8 TECHNIQUES OF INTEGRATION
8.1 Numerical Integration
8.2 Integration by Parts
8.3 Trigonometric Integrals
8.4 Trigonometric Substitution
8.5 The Method of Partial Fractions
8.6 Improper Integrals
Chapter 9 FURTHER APPLICATIONS OF THE INTEGRAGAL TAYLOR POLYNOMIALS
9.1 Arc Length and Surface Area
9.2 Fluid Pressure and Force
9.3 Center of Mass
9.4 Taylor Polynomials
Chapter 10 INTRODUCTION TO DIFFERENTIAL EQUATIONS
10.1 Solving Differential Equations
10.2 Graphical and Numerical Methods
10.3 The Logistic Equation
10.4 First-Order Linear Equations
Chapter 11 INFINITE SERIES
11.1 Sequences
11.2 Summing an Infinite Series
11.3 Convergence of Series with Positive Terms
11.4 Absolute and Conditional Convergence
11.5 The Ratio and Root Tests
11.6 Power Series
11.7 Taylor Series
Chapter 12 PARAMETRIC EQUATIONS, POLAR COORDINATES, AND CONIC SECTIONS
12.1 Parametric Equations
12.2 Arc Length and Speed
12.3 Polar Coordinates
12.4 Area and Arc Length in Polar Coordinates
12.5 Conic Sections