W.H. Freeman and Company, 2012. - 810 pages.
Chapter 1 Precalculus review.
Real Numbers, Functions, and Graphs.
Linear and Quadratic Functions.
The Basic Classes of Functions.
Trigonometric Functions.
Technology: Calculators and Computers.
Chapter Review Exercises.
Chapter 2 Limits.
Limits, Rates of Change, and Tangent Lines.
Limits: A Numerical and Graphical Approach.
Basic Limit Laws.
Limits and Continuity.
Evaluating Limits Algebraically.
Trigonometric Limits.
Limits at Infinity.
Intermediate Value Theorem.
The Formal Definition of a Limit.
Chapter Review Exercises.
Chapter 3 Differentiation.
Definition of the Derivative.
The Derivative as a Function.
Product and Quotient Rules.
Rates of Change.
Higher Derivatives.
Trigonometric Functions.
The Chain Rule.
Implicit Differentiation.
Related Rates.
Chapter Review Exercises.
Chapter 4 Applications of the derivative.
Linear Approximation and Applications.
Extreme Values.
The Mean Value Theorem and Monotonicity.
The Shape of a Graph.
Graph Sketching and Asymptotes.
Applied Optimization.
Newton’s Method.
Antiderivatives.
Chapter Review Exercises.
Chapter 5 The integral.
Approximating and Computing Area.
The Definite Integral.
The Fundamental Theorem of Calculus, Part I.
The Fundamental Theorem of Calculus, Part II.
Net Change as the Integral of a Rate.
Substitution Method.
Chapter Review Exercises.
Chapter 6 Applications of the integral.
Area Between Two Curves.
Setting Up Integrals: Volume, Density, Average Value.
Volumes of Revolution.
The Method of Cylindrical Shells.
Work and Energy.
Chapter Review Exercises.
Chapter 7 Exponential functions.
Derivative of f (x) = bx and the Number e.
Inverse Functions.
Logarithms and Their Derivatives.
Exponential Growth and Decay.
Compound Interest and Present Value.
Models Involving.
L’H?pital’s Rule.
Inverse Trigonometric Functions.
Hyperbolic Functions.
Chapter Review Exercises.
Chapter 8 Techniques of integration.
Integration by Parts.
Trigonometric Integrals.
Trigonometric Substitution.
Integrals Involving Hyperbolic and Inverse Hyperbolic Functions.
The Method of Partial Fractions.
Improper Integrals.
Probability and Integration.
Numerical Integration.
Chapter Review Exercises.
Chapter 9 Further applications of the integrals and Taylor polynomials.
Arc Length and Surface Area.
Fluid Pressure and Force.
Center of Mass.
Taylor Polynomials.
Chapter Review Exercises.
Chapter 10 Introduction to differential equations.
Solving Differential Equations.
Graphical and Numerical Methods.
The Logistic Equation.
First-Order Linear Equations.
Chapter Review Exercises.
Chapter 11 Infinite series.
Sequences.
Summing an Infinite Series.
Convergence of Series with Positive Terms.
Absolute and Conditional Convergence.
The Ratio and Root Tests.
Power Series.
Taylor Series.
Chapter Review Exercises.
Chapter 12 Parametric equations, polar coordinates, and conic sections.
Parametric Equations.
Arc Length and Speed.
Polar Coordinates.
Area and Arc Length in Polar Coordinates.
Conic Sections.
Chapter Review Exercises.
Chapter 1 Precalculus review.
Real Numbers, Functions, and Graphs.
Linear and Quadratic Functions.
The Basic Classes of Functions.
Trigonometric Functions.
Technology: Calculators and Computers.
Chapter Review Exercises.
Chapter 2 Limits.
Limits, Rates of Change, and Tangent Lines.
Limits: A Numerical and Graphical Approach.
Basic Limit Laws.
Limits and Continuity.
Evaluating Limits Algebraically.
Trigonometric Limits.
Limits at Infinity.
Intermediate Value Theorem.
The Formal Definition of a Limit.
Chapter Review Exercises.
Chapter 3 Differentiation.
Definition of the Derivative.
The Derivative as a Function.
Product and Quotient Rules.
Rates of Change.
Higher Derivatives.
Trigonometric Functions.
The Chain Rule.
Implicit Differentiation.
Related Rates.
Chapter Review Exercises.
Chapter 4 Applications of the derivative.
Linear Approximation and Applications.
Extreme Values.
The Mean Value Theorem and Monotonicity.
The Shape of a Graph.
Graph Sketching and Asymptotes.
Applied Optimization.
Newton’s Method.
Antiderivatives.
Chapter Review Exercises.
Chapter 5 The integral.
Approximating and Computing Area.
The Definite Integral.
The Fundamental Theorem of Calculus, Part I.
The Fundamental Theorem of Calculus, Part II.
Net Change as the Integral of a Rate.
Substitution Method.
Chapter Review Exercises.
Chapter 6 Applications of the integral.
Area Between Two Curves.
Setting Up Integrals: Volume, Density, Average Value.
Volumes of Revolution.
The Method of Cylindrical Shells.
Work and Energy.
Chapter Review Exercises.
Chapter 7 Exponential functions.
Derivative of f (x) = bx and the Number e.
Inverse Functions.
Logarithms and Their Derivatives.
Exponential Growth and Decay.
Compound Interest and Present Value.
Models Involving.
L’H?pital’s Rule.
Inverse Trigonometric Functions.
Hyperbolic Functions.
Chapter Review Exercises.
Chapter 8 Techniques of integration.
Integration by Parts.
Trigonometric Integrals.
Trigonometric Substitution.
Integrals Involving Hyperbolic and Inverse Hyperbolic Functions.
The Method of Partial Fractions.
Improper Integrals.
Probability and Integration.
Numerical Integration.
Chapter Review Exercises.
Chapter 9 Further applications of the integrals and Taylor polynomials.
Arc Length and Surface Area.
Fluid Pressure and Force.
Center of Mass.
Taylor Polynomials.
Chapter Review Exercises.
Chapter 10 Introduction to differential equations.
Solving Differential Equations.
Graphical and Numerical Methods.
The Logistic Equation.
First-Order Linear Equations.
Chapter Review Exercises.
Chapter 11 Infinite series.
Sequences.
Summing an Infinite Series.
Convergence of Series with Positive Terms.
Absolute and Conditional Convergence.
The Ratio and Root Tests.
Power Series.
Taylor Series.
Chapter Review Exercises.
Chapter 12 Parametric equations, polar coordinates, and conic sections.
Parametric Equations.
Arc Length and Speed.
Polar Coordinates.
Area and Arc Length in Polar Coordinates.
Conic Sections.
Chapter Review Exercises.