Calculus

Contents
Preface
To the Student
Calculators, Computers, and Other Graphing Devices
Diagnostic Tests
A Preview of Calculus
Ch 1: Functions and Limits
	1.1: Four Ways to Represent a Function
	1.2: Mathematical Models: A Catalog of Essential Functions
	1.3: New Functions from Old Functions
	1.4: The Tangent and Velocity Problems
	1.5: The Limit of a Function
	1.6: Calculating Limits Using the Limit Laws
	1.7: The Precise Definition of a Limit
	1.8: Continuity
	1: Review
	Principles of Problem Solving
Ch 2: Derivatives
	2.1: Derivatives and Rates of Change
	2.2: The Derivative as a Function
	2.3: Differentiation Formulas
	2.4: Derivatives of Trigonometric Functions
	2.5: The Chain Rule
	2.6: Implicit Differentiation
	2.7: Rates of Change in the Natural and Social Sciences
	2.8: Related Rates
	2.9: Linear Approximations and Differentials
	2: Review
	Problems Plus
Ch 3: Applications of Differentiation
	3.1: Maximum and Minimum Values
	3.2: The Mean Value Theorem
	3.3: How Derivatives Affect the Shape of a Graph
	3.4: Limits at Infinity; Horizontal Asymptotes
	3.5: Summary of Curve Sketching
	3.6: Graphing with Calculus and Calculators
	3.7: Optimization Problems
	3.8: Newton\'s Method
	3.9: Antiderivatives
	3: Review
	Problems Plus
Ch 4: Integrals
	4.1: Areas and Distances
	4.2: The Definite Integral
	4.3: The Fundamental Theorem of Calculus
	4.4: Indefinite Integrals and the Net Change Theorem
	4.5: The Substitution Rule
	4: Review
	Problems Plus
Ch 5: Applications of Integration
	5.1: Areas between Curves
	5.2: Volumes
	5.3: Volumes by Cylindrical Shells
	5.4: Work
	5.5: Average Value of a Function
	5: Review
	Problems Plus
Ch 6: Inverse Functions
	6.1: Inverse Functions
	6.2: Exponential Functions and Their Derivatives
	6.3: Logarithmic Functions
	6.4: Derivatives of Logarithmic Functions
	6.5: Exponential Growth and Decay
	6.6: Inverse Trigonometric Functions
	6.7: Hyperbolic Functions
	6.8: Indeterminate Forms and l\'Hospital\'s Rule
	6: Review
	Problems Plus
Ch 7: Techniques of Integration
	7.1: Integration by Parts
	7.2: Trigonometric Integrals
	7.3: Trigonometric Substitution
	7.4: Integration of Rational Functions by Partial Fractions
	7.5: Strategy for Integration
	7.6: Integration Using Tables and Computer Algebra Systems
	7.7: Approximate Integration
	7.8: Improper Integrals
	7: Review
	Problems Plus
Ch 8: Further Applications of Integration
	8.1: Arc Length
	8.2: Area of a Surface of Revolution
	8.3: Applications to Physics and Engineering
	8.4: Applications to Economics and Biology
	8.5: Probability
	8: Review
	Problems Plus
Ch 9: Differential Equations
	9.1: Modeling with Differential Equations
	9.2: Direction Fields and Euler\'s Method
	9.3: Separable Equations
	9.4: Models for Population Growth
	9.5: Linear Equations
	9.6: Predator-Prey Systems
	9: Review
	Problems Plus
Ch 10: Parametric Equations and Polar Coordinates
	10.1: Curves Defined by Parametric Equations
	10.2: Calculus with Parametric Curves
	10.3: Polar Coordinates
	10.4: Areas and Lengths in Polar Coordinates
	10.5: Conic Sections
	10.6: Conic Sections in Polar Coordinates
	10: Review
	Problems Plus
Ch 11: Infinite Sequences and Series
	11.1: Sequences
	11.2: Series
	11.3: The Integral Test and Estimates of Sums
	11.4: The Comparison Tests
	11.5: Alternating Series
	11.6: Absolute Convergence and the Ratio and Root Tests
	11.7: Strategy for Testing Series
	11.8: Power Series
	11.9: Representations of Functions as Power Series
	11.10: Taylor and Maclaurin Series
	11.11: Applications of Taylor Polynomials
	11: Review
	Problems Plus
Ch 12: Vectors and the Geometry of Space
	12.1: Three-Dimensional Coordinate Systems
	12.2: Vectors
	12.3: The Dot Product
	12.4: The Cross Product
	12.5: Equations of Lines and Planes
	12.6: Cylinders and Quadric Surfaces
	12: Review
	Problems Plus
Ch 13: Vector Functions
	13.1: Vector Functions and Space Curves
	13.2: Derivatives and Integrals of Vector Functions
	13.3: Arc Length and Curvature
	13.4: Motion in Space: Velocity and Acceleration
	13: Review
	Problems Plus
Ch 14: Partial Derivatives
	14.1: Functions of Several Variables
	14.2: Limits and Continuity
	14.3: Partial Derivatives
	14.4: Tangent Planes and Linear Approximations
	14.5: The Chain Rule
	14.6: Directional Derivatives and the Gradient Vector
	14.7: Maximum and Minimum Values
	14.8: Lagrange Multipliers
	14: Review
	Problems Plus
Ch 15: Multiple Integrals
	15.1: Double Integrals over Rectangles
	15.2: Double Integrals over General Regions
	15.3: Double Integrals in Polar Coordinates
	15.4: Applications of Double Integrals
	15.5: Surface Area
	15.6: Triple Integrals
	15.7: Triple Integrals in Cylindrical Coordinates
	15.8: Triple Integrals in Spherical Coordinates
	15.9: Change of Variables in Multiple Integrals
	15: Review
	Problems Plus
Ch 16: Vector Calculus
	16.1: Vector Fields
	16.2: Line Integrals
	16.3: The Fundamental Theorem for Line Integrals
	16.4: Green\'s Theorem
	16.5: Curl and Divergence
	16.6: Parametric Surfaces and Their Areas
	16.7: Surface Integrals
	16.8: Stokes\' Theorem
	16.9: The Divergence Theorem
	16.10: Summary
	16: Review
	Problems Plus
Ch 17: Second-Order Differential Equations
	17.1: Second-Order Linear Equations
	17.2: Nonhomogeneous Linear Equations
	17.3: Applications of Second-Order Differential Equations
	17.4: Series Solutions
	17: Review
Appendixes
	A: Numbers, Inequalities, and Absolute Values
	B: Coordinate Geometry and Lines
	C: Graphs of Second-Degree Equations
	D: Trigonometry
	E: Sigma Notation
	F: Proofs of Theorems
	G: Complex Numbers
	H: Answers to Odd-Numbered Exercises
Index
Reference
Concept Check Answers