Calculus: Early Transcendentals - 9th edition

Chapter 0 Before Calculus
0.1 Functions
0.2 New Functions from Old
0.4 Families of Functions
0.5 Inverse Functions; Inverse Trigonometric Functions
0.6 Exponential and Logarithmic Functions

Chapter 1 Limits and Continuity
1.1 Limits (An Intuitive Approach)
1.2 Computing Limits
1.3 Limits at Infinity; End Behavior of a Function
1.4 Limits (Discussed More Rigorously)
1.5 Continuity
1.6 Continuity of Trigonometric, Exponential, and Inverse Functions

Chapter 2 The Derivative
2.1 Tangent Lines and Rates of Change
2.2 The Derivative Function
2.3 Introduction to Techniques of Differentiation
2.4 The Product and Quotient Rules
2.5 Derivatives of Trigonometric Functions
2.6 The Chain Rule

Chapter 3 Topics in Differentiation
3.1 Implicit Differentiation
3.2 Derivatives of Logarithmic Functions
3.3 Derivatives of Exponential and Inverse Trigonometric Functions
3.4 Related Rates
3.5 Local Linear Approximation; Differentials

Chapter 4 The Derivative in Graphing and Applications
4.1 Analysis of Functions I: Increase, Decrease, and Concavity
4.2 Analysis of Functions II: Relative Extrema; Graphing Polynomials
4.3 Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents
4.4 Absolute Maxima and Minima
4.5 Applied Maximum and Minimum Problems
4.6 Rectilinear Motion
4.7 Newton's Method
4.8 Rolle's Theorem; Mean-Value Theorem

Chapter 5 Integration
5.1 An Overview of the Area Problem
5.2 The Indefinite Integral
5.3 Integration by Substitution
5.4 The Definition of Area as a Limit; Sigma Notation
5.5 The Definite Integral
5.6 The Fundamental Theorem of Calculus
5.7 Rectilinear Motion Revisited Using Integration
5.8 Average Value of a Function and its Applications
5.9 Evaluating Definite Integrals by Substitution
5.10 Logarithmic and Other Functions Defined by Integrals

Chapter 6 Applications of the Definite Integral in Geometry, Science, and Engineering
6.1 Area Between Two Curves
6.2 Volumes by Slicing; Disks and Washers
6.3 Volumes by Cylindrical Shells
6.4 Length of a Plane Curve
6.5 Area of a Surface of Revolution
6.6 Work
6.7 Moments, Centers of Gravity, and Centroids
6.8 Fluid Pressure and Force
6.9 Hyperbolic Functions and Hanging Cables

Chapter 7 Principles of Integral Evaluation
7.1 An Overview of Integration Methods
7.2 Integration by Parts
7.3 Integrating Trigonometric Functions
7.4 Trigonometric Substitutions
7.5 Integrating Rational Functions by Partial Fractions
7.6 Using Computer Algebra Systems and Tables of Integrals
7.7 Numerical Integration; Simpson's Rule
7.8 Improper Integrals

Chapter 8 Mathematical Modeling with Differential Equations
8.1 Modeling with Differential Equations
8.2 Separation of Variables
8.3 Slope Fields; Euler's Method
8.4 First-Order Differential Equations and Applications

Chapter 9 Infinite Series
9.1 Sequences
9.2 Monotone Sequences
9.3 Infinite Series 9.4 Convergence Tests
9.5 The Comparison, Ratio, and Root Tests
9.6 Alternating Series; Absolute and Conditional Convergence
9.7 Maclaurin and Taylor Polynomials
9.8 Maclaurin and Taylor Series; Power Series
9.9 Convergence of Taylor Series
9.10 Differentiating and Integrating Power Series; Modeling with Taylor Series

Chapter 10 Parametric and Polar Curves; Conic Sections
10.1 Parametric Equations; Tangent Lines and Arc Length for Parametric Curves
10.2 Polar Coordinates
10.3 Tangent Lines, Arc Length, and Area for Polar Curves
10.4 Conic Sections
10.5 Rotation of Axes; Second-Degree Equations
10.6 Conic Sections in Polar Coordinates

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