Calculus: Early Transcendentals

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 Inverse Functions
• • 1.6 Exponential and Logarithmic Functions
• • 1.7 Technology: Calculators and Computers
• • Chapter Review Exercises

Chapter 2: Limits

• • 2.1 The Limit Idea: Instantaneous Velocity and Tangent Lines
• • 2.2 Investigating Limits
• • 2.3 Basic Limit Laws
• • 2.4 Limits and Continuity
• • 2.5 Indeterminate Forms
• • 2.6 The Squeeze Theorem and Trigonometric Limits
• • 2.7 Limits at Infinity
• • 2.8 The Intermediate Value Theorem
• • 2.9 The Formal Definition of a Limit
• • Chapter Review Exercises

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 Derivatives of General Exponential and Logarithmic Functions
• • 3.10 Related Rates
• • Chapter Review Exercises

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 Second Derivative and Concavity
• • 4.5 L’Hôpital’s Rule
• • 4.6 Analyzing and Sketching Graphs of Functions
• • 4.7 Applied Optimization
• • 4.8 Newton’s Method
• • Chapter Review Exercises

Chapter 5: Integration

• • 5.1 Approximating and Computing Area
• • 5.2 The Definite Integral
• • 5.3 The Indefinite Integral
• • 5.4 The Fundamental Theorem of Calculus, Part I
• • 5.5 The Fundamental Theorem of Calculus, Part II
• • 5.6 Net Change as the Integral of a Rate of Change
• • 5.7 The Substitution Method
• • 5.8 Further Integral Formulas
• • Chapter Review Exercises

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: Disks and Washers
• • 6.4 Volumes of Revolution: Cylindrical Shells
• • 6.5 Work and Energy
• • Chapter Review Exercises

Chapter 7: Techniques of Integration

• • 7.1 Integration by Parts
• • 7.2 Trigonometric Integrals
• • 7.3 Trigonometric Substitution
• • 7.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions
• • 7.5 The Method of Partial Fractions
• • 7.6 Strategies for Integration
• • 7.7 Improper Integrals
• • 7.8 Numerical Integration
• • Chapter Review Exercises

Chapter 8: Further Applications of the Integral

• • 8.1 Probability and Integration
• • 8.2 Arc Length and Surface Area
• • 8.3 Fluid Pressure and Force
• • 8.4 Center of Mass
• • Chapter Review Exercises

Chapter 9: Introduction to Differential Equations

• • 9.1 Solving Differential Equations
• • 9.2 Models Involving y'=k(y-b)
• • 9.3 Graphical and Numerical Methods
• • 9.4 The Logistic Equation
• • 9.5 First-Order Linear Equations
• • Chapter Review Exercises

Chapter 10: Infinite Series

• • 10.1 Sequences
• • 10.2 Summing an Infinite Series
• • 10.3 Convergence of Series with Positive Terms
• • 10.4 Absolute and Conditional Convergence
• • 10.5 The Ratio and Root Tests and Strategies for Choosing Tests
• • 10.6 Power Series
• • 10.7 Taylor Polynomials
• • 10.8 Taylor Series
• • Chapter Review Exercises

Chapter 11: Parametric Equations, Polar Coordinates, and Conic Sections

• • 11.1 Parametric Equations
• • 11.2 Arc Length and Speed
• • 11.3 Polar Coordinates
• • 11.4 Area and Arc Length in Polar Coordinates
• • 11.5 Conic Sections
• • Chapter Review Exercises

Chapter 12: Vector Geometry

• • 12.1 Vectors in the Plane
• • 12.2 Three-Dimensional Space: Surfaces, Vectors, and Curves
• • 12.3 Dot Product and the Angle Between Two Vectors
• • 12.4 The Cross Product
• • 12.5 Planes in 3-Space
• • 12.6 A Survey of Quadric Surfaces
• • 12.7 Cylindrical and Spherical Coordinates
• • Chapter Review Exercises

Chapter 13: Calculus of Vector-Valued Functions

• • 13.1 Vector-Valued Functions
• • 13.2 Calculus of Vector-Valued Functions
• • 13.3 Arc Length and Speed
• • 13.4 Curvature
• • 13.5 Motion in 3-Space
• • 13.6 Planetary Motion According to Kepler and Newton
• • Chapter Review Exercises

Chapter 14: Differentiation in Several Variables

• • 14.1 Functions of Two or More Variables
• • 14.2 Limits and Continuity in Several Variables
• • 14.3 Partial Derivatives
• • 14.4 Differentiability, Tangent Planes, and Linear Approximation
• • 14.5 The Gradient and Directional Derivatives
• • 14.6 The Chain Rule
• • 14.7 Optimization in Several Variables
• • 14.8 Lagrange Multipliers: Optimizing with a Constraint
• • Chapter Review Exercises

Chapter 15: Multiple Integration

• • 15.1 Integration in Two Variables
• • 15.2 Double Integrals Over More General Regions
• • 15.3 Triple Integrals
• • 15.4 Integration in Polar, Cylindrical, and Spherical Coordinates
• • 15.5 Applications of Multiple Integrals
• • 15.6 Change of Variables
• • Chapter Review Exercises

Chapter 16: Line and Surface Integrals

• • 16.1 Vector Fields
• • 16.2 Line Integrals
• • 16.3 Conservative Vector Fields
• • 16.4 Parametrized Surfaces and Surface Integrals
• • 16.5 Surface Integrals of Vector Fields
• • Chapter Review Exercises

Chapter 17: Fundamental Theorems of Vector Analysis

• • 17.1 Green’s Theorem
• • 17.2 Stokes’ Theorem
• • 17.3 Divergence Theorem
• • Chapter Review Exercises