Rogawski Jon, Adams Colin. Calculus

Rd edition. — W. H. Freeman and Company, 2015. — 1180 p. — ISBN13: 978-1-4641-9379-8; ISBN10: 1-4641-9379-7.Precalculus Review.
Real Numbers, Functions, and Graphs.
Linear and Quadratic Functions.
The Basic Classes of Functions.
Trigonometric Functions.
Technology: Calculators and Computers.
Review Exercises.
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.
Review Exercises.
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.
Review Exercises.
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.
Review Exercises.
The Integral.
Approximating and Computing Area.
The Definite Integral.
The Indefinite Integral.
The Fundamental Theorem of Calculus, Part I.
The Fundamental Theorem of Calculus, Part II.
Net Change as the Integral of a Rate of Change.
Substitution Method.
Review Exercises.
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.
Review Exercises.
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 y′ = k(y − b).
L’Hôpital’s Rule.
Inverse Trigonometric Functions.
Hyperbolic Functions.
Review Exercises.
Techniques of Integration.
Integration by Parts.
Trigonometric Integrals.
Trigonometric Substitution.
Integrals Involving Hyperbolic and Inverse Hyperbolic.
Functions.
The Method of Partial Fractions.
Strategies for Integration.
Improper Integrals.
Probability and Integration.
Numerical Integration.
Review Exercises.
Further Applications of the Integral and Taylor Polynomials.
Arc Length and Surface Area.
Fluid Pressure and Force.
Center of Mass.
Taylor Polynomials.
Review Exercises.
Introduction to Differential Equations.
Solving Differential Equations.
Graphical and Numerical Methods.
The Logistic Equation.
First-Order Linear Equations.
Review Exercises.
Infinite Series.
Sequences.
Summing an Infinite Series.
Convergence of Series with Positive Terms.
Absolute and Conditional Convergence.
The Ratio and Root Tests and Strategies for Choosing.
Tests.
Power Series.
Taylor Series.
Review Exercises.
Parametric Equations, Polar Coordinates, and Conic Sections.
Parametric Equations.
Arc Length and Speed.
Polar Coordinates.
Area and Arc Length in Polar Coordinates.
Conic Sections.
Review Exercises.
Vector Geometry.
Vectors in the Plane.
Vectors in Three Dimensions.
Dot Product and the Angle Between Two Vectors.
The Cross Product.
Planes in 3-Space.
A Survey of Quadric Surfaces.
Cylindrical and Spherical Coordinates.
Review Exercises.
Calculus of Vector-Valued Functions.
Vector-Valued Functions.
Calculus of Vector-Valued Functions.
Arc Length and Speed.
Curvature.
Motion in 3-Space.
Planetary Motion According to Kepler and Newton.
Review Exercises.
Differentiation in Serial Variables.
Functions of Two or More Variables.
Limits and Continuity in Several Variables.
ial Derivatives.
Differentiability and Tangent Planes.
The Gradient and Directional Derivatives.
The Chain Rule.
Optimization in Several Variables.
Lagrange Multipliers: Optimizing with a Constraint.
Review Exercises.
Multiple Integration.
Integration in Two Variables.
Double Integrals over More General Regions.
Triple Integrals.
Integration in Polar, Cylindrical, and Spherical Coordinates.
Applications of Multiple Integrals.
Change of Variables.
Review Exercises.
Line and Surface Integrals.
Vector Fields.
Line Integrals.
Conservative Vector Fields.
Parametrized Surfaces and Surface Integrals.
Surface Integrals of Vector Fields.
Review Exercises.
Fundamental Theorems of Vector Analysis.
Green’s Theorem.
Stokes’ Theorem.
Divergence Theorem.
Review Exercises.
Appendices
The Language of Mathematics.
Properties of Real Numbers.
Induction and the Binomial Theorem.
Additional Proofs.
Answers To Odd-Numbered Exercises.

Index.
Additional content can be accessed online via LaunchPad.
Additional Proofs.
L’Hôpital’s Rule.
Error Bounds for Numerical Integration.
Comparison Test for Improper Integrals.
Additional Content.
Second Order Differential Equations.
Complex Numbers.