Enhanced descriptions from Syndetics:

Intended for the three semester calculus course, this sixth edition includes precise statements of theorems, use of geometric reasoning in applied problems, and the diverse range of applications across the sciences. It features a separate chapter on differential equations and numerous Maple examples.

Table of contents provided by Syndetics

• Preface
• To the Student
• To the Instructor
• Acknowledgments
• What Is Calculus?
• Preliminaries
• P.1 Real Numbers and the Real Line
• P.2 Cartesian Coordinates in the Plane
• P.3 Graphs of Quadratic Equations
• P.4 Functions and Their Graphs
• P.5 Combining Functions to Make New Functions
• P.6 Polynomials and Rational Functions
• P.7 The Trigonometric Functions
• 1 Limits and Continuity
• 1.1 Examples of Velocity, Growth Rate, and Area
• 1.2 Limits of Functions
• 1.3 Limits at Infinity and Infinite Limits
• 1.4 Continuity
• 1.5 The Formal Definition of Limit
• Chapter Review
• 2 Differentiation
• 2.1 Tangent Lines and Their Slopes
• 2.2 The Derivative
• 2.3 Differentiation Rules
• 2.4 The Chain Rule
• 2.5 Derivatives of Trigonometric Functions
• 2.6 The Mean-Value Theorem
• 2.7 Using Derivatives
• 2.8 Higher-Order Derivatives
• 2.9 Implicit Differentiation
• 2.10 Antiderivatives and Initial-Value Problems
• 2.11 Velocity and Acceleration
• Chapter Review
• 3 Transcendental Functions
• 3.1 Inverse Functions
• 3.2 Exponential and Logarithmic Functions
• 3.3 The Natural Logarithm and Exponential
• 3.4 Growth and Decay
• 3.5 The Inverse Trigonometric Functions
• 3.6 Hyperbolic Functions
• 3.7 Second-Order Linear DEs with Constant Coefficients
• Chapter Review
• 4 Some Applications of Derivatives
• 4.1 Related Rates
• 4.2 Extreme Values
• 4.3 Concavity and Inflections
• 4.4 Sketching the Graph of a Function
• 4.5 Extreme-Value Problems
• 4.6 Finding Roots of Equations
• 4.7 Linear Approximations
• 4.8 Taylor Polynomials
• 4.9 Indeterminate Forms
• Chapter Review
• 5 Integration
• 5.1 Sums and Sigma Notation
• 5.2 Areas as Limits of Sums
• 5.3 The Definite Integral
• 5.4 Properties of the Definite Integral
• 5.5 The Fundamental Theorem of Calculus
• 5.6 The Method of Substitution
• 5.7 Areas of Plane Regions
• Chapter Review
• 6 Techniques of Integration
• 6.1 Integration by Parts
• 6.2 Inverse Substitutions
• 6.3 Integrals of Rational Functions
• 6.4 Integration Using Computer Algebra or Tables
• 6.5 Improper Integrals
• 6.6 The Trapezoid and Midpoint Rules
• 6.7 Simpson's Rule
• 6.8 Other Aspects of Approximate Integration
• Chapter Review
• 7 Applications of Integration
• 7.1 Volumes by Slicing-Solids of Revolution
• 7.2 More Volumes by Slicing
• 7.3 Arc Length and Surface Area
• 7.4 Mass, Moments, and Centres of Mass
• 7.5 Centroids
• 7.6 Other Physical Applications
• 7.7 Applications in Business, Finance, and Ecology
• 7.8 Probability
• 7.9 First-Order Differential Equations
• Chapter Review
• 8 Conics, Parametric Curves, and Polar Curves
• 8.1 Conics
• 8.2 Parametric Curves
• 8.3 Smooth Parametric Curves and Their Slopes
• 8.4 Arc Lengths and Areas for Parametric Curves
• 8.5 Polar Coordinates and Polar Curves
• 8.6 Slopes, Areas, and Arc Lengths for Polar Curves
• Chapter Review
• 9 Sequences, Series, and Power Series
• 9.1 Sequences and Convergence
• 9.2 Infinite Series
• 9.3 Convergence Tests for Positive Series
• 9.4 Absolute and Conditional Convergence
• 9.5 Power Series
• 9.6 Taylor and Maclaurin Series
• 9.7 Applications of Taylor and Maclaurin Series
• 9.8 The Binomial Theorem and Binomial Series
• 9.9 Fourier Series
• Chapter Review
• 10 Vectors and Coordinate Geometry in 3-Space
• 10.1 Analytic Geometry in Three Dimensions
• 10.2 Vectors
• 10.3 The Cross Product in 3-Space
• 10.4 Planes and Lines
• 10.5 Quadric Surfaces
• 10.6 A Little Linear Algebra
• 10.7 Using Maple for Vector and Matrix Calculations
• Chapter Review
• 11 Vector Functions and Curves
• 11.1 Vector Functions of One Variable
• 11.2 Some Applications of Vector Differentiation
• 11.3 Curves and Parametrizations
• 11.4 Curvature, Torsion, and the Frenet Frame
• 11.5 Curvature and Torsion for General Parametrizations
• 11.6 Kepler's Laws of Planetary Motion
• Chapter Review
• 12 Partial Differentiation
• 12.1 Functions of Several Variables
• 12.2 Limits and Continuity
• 12.3 Partial Derivatives
• 12.4 Higher-Order Derivatives
• 12.5 The Chain Rule
• 12.6 Linear Approximations, Differentiability, and Differentials
• 12.7 Gradients and Directional Derivatives
• 12.8 Implicit Functions
• 12.9 Taylor Series and Approximations
• Chapter Review
• 13 Applications of Partial Derivatives
• 13.1 Extreme Values
• 13.2 Extreme Values of Functions Defined on Restricted Domains
• 13.3 Lagrange Multipliers
• 13.4 The Method of Least Squares
• 13.5 Parametric Problems
• 13.6 Newton's Method
• 13.7 Calculations with Maple
• Chapter Review
• 14 Multiple Integration
• 14.1 Double Integrals
• 14.2 Iteration of Double Integrals in Cartesian Coordinates
• 14.3 Improper Integrals and a Mean-Value Theorem
• 14.4 Double Integrals in Polar Coordinates
• 14.5 Triple Integrals
• 14.6 Change of Variables in Triple Integrals
• 14.7 Applications of Multiple Integrals
• Chapter Review
• 15 Vector Fields
• 15.1 Vector and Scalar Fields
• 15.2 Conservative Fields
• 15.3 Line Integrals
• 15.4 Line Integrals of Vector Fields
• 15.5 Surfaces and Surface Integrals
• 15.6 Oriented Surfaces and Flux Integrals
• Chapter Review
• 16 Vector Calculus
• 16.1 Gradient, Divergence, and Curl
• 16.2 Some Identities Involving Grad, Div, and Curl
• 16.3 Green's Theorem in the Plane
• 16.4 The Divergence Theorem in 3-Space
• 16.5 Stokes's Theorem
• 16.6 Some Physical Applications of Vector Calculus
• 16.7 Orthogonal Curvilinear Coordinates
• Chapter Review
• 17 Ordinary Differential Equations
• 17.1 Classifying Differential Equations
• 17.2 Solving First-Order Equations
• 17.3 Existence, Uniqueness, and Numerical Methods
• 17.4 Differential Equations of Second Order
• 17.5 Linear Differential Equations with Constant Coefficients
• 17.6 Nonhomogeneous Linear Equations
• 17.7 Series Solutions of Differential Equations
• Chapter Review
• Appendix I Complex Numbers
• Appendix II Complex Functions
• Appendix III Continuous Functions
• Appendix IV The Riemann
• Appendix V Doing Calculus with Maple
• Answers to Odd-Numbered Exercises
• Index