Calculus, Early Transcendentals, International Metric Eighth Edition

Cover
Title
Statement
Copyright
Contents
Preface
To the Student
Calculators, Computers, and Other Graphing Devices
Diagnostic Tests
A Preview of Calculus
Ch 1: Functions and Models
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: Exponential Functions
1.5: Inverse Functions and Logarithms
Ch 1: Review
Ch 1: Principles Ofproblem Solving
Ch 2: Limits and Derivatives
2.1: The Tangent and Velocity Problems
2.2: The Limit of a Function
2.3: Calculating Limits Using the Limit Laws
2.4: The Precise Definition of a Limit
2.5: Continuity
2.6: Limits at Infinity; Horizontal Asymptotes
2.7: Derivatives and Rates of Change
2.8: The Derivative as a Function
Ch 2: Review
Ch 2: Problems Plus
Ch 3: Differentiation Rules
3.1: Derivatives of Polynomials and Exponential Functions
3.2: The Product and Quotient Rules
3.3: Derivatives of Trigonometric Functions
3.4: The Chain Rule
3.5: Implicit Differentiation
3.6: Derivatives of Logarithmic Functions
3.7: Rates of Change in the Natural and Social Sciences
3.8: Exponential Growth and Decay
3.9: Related Rates
3.10: Linear Approximations and Differentials
3.11: Hyperbolic Functions
Ch 3: Review
Ch 3: Problems Plus
Ch 4: Applications of Differentiation
4.1: Maximum and Minimum Values
4.2: The Mean Value Theorem
4.3: How Derivatives Affect the Shape of a Graph
4.4: Indeterminate Forms and L’Hospital’s Rule
4.5: Summary of Curve Sketching
4.6: Graphing with Calculus and Calculators
4.7: Optimization Problems
4.8: Newton’s Method
4.9: Antiderivatives
Ch 4: Review
Ch 4: Problems Plus
Ch 5: Integrals
5.1: Areas and Distances
5.2: The Definite Integral
5.3: The Fundamental Theorem of Calculus
5.4: Indefinite Integrals and the Net Change Theorem
5.5: The Substitution Rule
Ch 5: Review
Ch 5: Problems Plus
Ch 6: Applications of Integration
6.1: Areas Between Curves
6.2: Volumes
6.3: Volumes by Cylindrical Shells
6.4: Work
6.5: Average Value of a Function
Ch 6: Review
Ch 6: 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
Ch 7: Review
Ch 7: 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
Ch 8: Review
Ch 8: 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
Ch 9: Review
Ch 9: 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
Ch 10: Review
Ch 10: 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
Ch 11: Review
Ch 11: 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
Ch 12: Review
Ch 12: 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
Ch 13: Review
Ch 13: 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
Ch 14: Review
Ch 14: 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
Ch 15: Review
Ch 15: 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
Ch 16: Review
Ch 16: 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
Ch 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: the Logarithm Defined as an Integral
H: Complex Numbers
I: Answers to Odd-Numbered Exercises
Index