Calculus Second Edition

✍ Scribed by Jon Rogawski

• Publisher: W.H. Freeman And Company
• Year: 2012
• Tongue: English
• Leaves: 1215
• Edition: 2
• Category: Library

✦ Synopsis

Book by Jon Rogawski

✦ Table of Contents

Cover Page
Half-Title Page
Copyright Page
Title-Page
Dedication Page
Table of Contents
ABOUT JON ROGAWSKI
PREFACE
CHAPTERS
Chapter 1: PRECALCULUS REVIEW
1.1: Real Numbers, Functions, and Graphs
1.2: Linear and Quadratic Functions
1.3: The Basic Classes of Functions
1.4: Trigonometric Functions
1.5: Technology: Calculators and Computers
Chapter 2: LIMITS
2.1: Limits, Rates of Change, and Tangent Lines
2.2: Limits: A Numerical and Graphical Approach
2.3: Basic Limit Laws
2.4: Limits and Continuity
2.5: Evaluating Limits Algebraically
2.6: Trigonometric Limits
2.7: Limits at Infinity
2.8: Intermediate Value Theorem
2.9: The Formal Definition of a Limit
Chapter 3: DIFFERENTIATION
3.1: Definition of the Derivative
3.2: The Derivative as a Function
3.3: Product and Quotient Rules
3.4: Rates of Change
3.5: Higher Derivatives
3.6: Trigonometric Functions
3.7: The Chain Rule
3.8: Implicit Differentiation
3.9: Related Rates
Chapter 4: APPLICATIONS OF THE DERIVATIVE
4.1: Linear Approximation and Applications
4.2: Extreme Values
4.3: The Mean Value Theorem and Monotonicity
4.4: The Shape of a Graph
4.5: Graph Sketching and Asymptotes
4.6: Applied Optimization
4.7: Newton’s Method
4.8: Antiderivatives
Chapter 5: THE INTEGRAL
5.1: Approximating and Computing Area
5.2: The Definite Integral
5.3: The Fundamental Theorem of Calculus, Part I
5.4: The Fundamental Theorem of Calculus, Part II
5.5: Net Change as the Integral of a Rate
5.6: Substitution Method
Chapter 6: APPLICATIONS OF THE INTEGRAL
6.1: Area Between Two Curves
6.2: Setting Up Integrals: Volume, Density, Average Value
6.3: Volumes of Revolution
6.4: The Method of Cylindrical Shells
6.5: Work and Energy
Chapter 7: EXPONENTIAL FUNCTIONS
7.1: Derivative of f (x) = bx and the Number e
7.2: Inverse Functions
7.3: Logarithms and Their Derivatives
7.4: Exponential Growth and Decay
7.5: Compound Interest and Present Value
7.6: Models Involving y' = k( y Š b)
7.7: L’Hôpital’s Rule
7.8: Inverse Trigonometric Functions
7.9: Hyperbolic Functions
Chapter 8: TECHNIQUES OF INTEGRATION
8.1: Integration by Parts
8.2: Trigonometric Integrals
8.3: Trigonometric Substitution
8.4: Integrals Involving Hyperbolic and Inverse Hyperbolic Functions
8.5: The Method of Partial Fractions
8.6: Improper Integrals
8.7: Probability and Integration
8.8: Numerical Integration
Chapter 9: FURTHER APPLICATIONS OF THEINTEGRAL AND TAYLOR POLYNOMIALS
9.1: Arc Length and Surface Area
9.2: Fluid Pressure and Force
9.3: Center of Mass
9.4: Taylor Polynomials
Chapter 10: INTRODUCTION TO DIFFERENTIAL EQUATIONS
10.1: Solving Differential Equations
10.2: Graphical and Numerical Methods
10.3: The Logistic Equation
10.4: First-Order Linear Equations
Chapter 11: INFINITE SERIES
11.1: Sequences
11.2: Summing an Infinite Series
11.3: Convergence of Series with Positive Terms
11.4: Absolute and Conditional Convergence
11.5: The Ratio and Root Tests
11.6: Power Series
11.7: Taylor Series
Chapter 12: PARAMETRIC EQUATIONS, POLAR COORDINATES, AND CONIC SECTIONS
12.1: Parametric Equations
12.2: Arc Length and Speed
12.3: Polar Coordinates
12.4: Area and Arc Length in Polar Coordinates
12.5: Conic Sections
Chapter 13: VECTOR GEOMETRY
13.1: Vectors in the Plane
13.2: Vectors in Three Dimensions
13.3: Dot Product and the Angle between Two Vectors
13.4: The Cross Product
13.5: Planes in Three-Space
13.6: A Survey of Quadric Surfaces
13.7: Cylindrical and Spherical Coordinates
Chapter 14: CALCULUS OF VECTOR-VALUED FUNCTIONS
14.1: Vector-Valued Functions
14.2: Calculus of Vector-Valued Functions
14.3: Arc Length and Speed
14.4 Curvature
14.5: Motion in Three-Space
14.6: Planetary Motion According to Kepler and Newton
Chapter 15: DIFFERENTIATION IN SEVERAL VARIABLES
15.1: Functions of Two or More Variables
15.2: Limits and Continuity in Several Variables
15.3: Partial Derivatives
15.4: Differentiability and Tangent Planes
15.5: The Gradient and Directional Derivatives
15.6: The Chain Rule
15.7: Optimization in Several Variables
15.8: Lagrange Multipliers: Optimizing with a Constraint
Chapter 16: MULTIPLE INTEGRATION
16.1: Integration in Two Variables
16.2: Double Integrals over More General Regions
16.3: Triple Integrals
16.4: Integration in Polar, Cylindrical, and Spherical Coordinates
16.5: Applications of Multiple Integrals
16.6: Change of Variables
Chapter 17: LINE AND SURFACE INTEGRALS
17.1: Vector Fields
17.2: Line Integrals
17.3: Conservative Vector Fields
17.4: Parametrized Surfaces and Surface Integrals
17.5: Surface Integrals of Vector Fields
Chapter 18: FUNDAMENTAL THEOREMS OF VECTOR ANALYSIS
18.1: Green’s Theorem
18.2: Stokes’ Theorem
18.3: Divergence Theorem
APPENDICES
A:
The Language of Mathematics
B: Properties of Real Numbers
C: Induction and the Binomial Theorem
D: Additional Proofs
ANSWERS TO ODD-NUMBERED EXERCISES
Chapter 1
Section 1.1 Preliminary Questions
Section 1.1 Exercises
Section 1.2 Preliminary Questions
Section 1.2 Exercises
Section 1.3 Preliminary Questions
Section 1.3 Exercises
Section 1.4 Preliminary Questions
Section 1.4 Exercises
Section 1.5 Preliminary Questions
Section 1.5 Exercises
Chapter 1 Review
Chapter 2
Section 2.1 Preliminary Questions
Section 2.1 Exercises
Section 2.2 Preliminary Questions
Section 2.2 Exercises
Section 2.3 Preliminary Questions
Section 2.3 Exercises
Section 2.4 Preliminary Questions
Section 2.4 Exercises
Section 2.5 Preliminary Questions
Section 2.5 Exercises
Section 2.6 Preliminary Questions
Section 2.6 Exercises
Section 2.7 Preliminary Questions
Section 2.7 Exercises
Section 2.8 Preliminary Questions
Section 2.8 Exercises
Section 2.9 Preliminary Questions
Section 2.9 Exercises
Chapter 2 Review
Chapter 3
Section 3.1 Preliminary Questions
Section 3.1 Exercises
Section 3.2 Preliminary Questions
Section 3.2 Exercises
Section 3.3 Preliminary Questions
Section 3.3 Exercises
Section 3.4 Preliminary Questions
Section 3.4 Exercises
Section 3.5 Preliminary Questions
Section 3.5 Exercises
Section 3.6 Preliminary Questions
Section 3.6 Exercises
Section 3.7 Preliminary Questions
Section 3.7 Exercises
Section 3.8 Preliminary Questions
Section 3.8 Exercises
Section 3.9 Preliminary Questions
Section 3.9 Exercises
Chapter 3 Review
Chapter 4
Section 4.1 Preliminary Questions
Section 4.1 Exercises
Section 4.2 Preliminary Questions
Section 4.2 Exercises
Section 4.3 Preliminary Questions
Section 4.3 Exercises
Section 4.4 Preliminary Questions
Section 4.4 Exercises
Section 4.5 Preliminary Questions
Section 4.5 Exercises
Section 4.6 Preliminary Questions
Section 4.6 Exercises
Section 4.7 Preliminary Questions
Section 4.7 Exercises
Section 4.8 Preliminary Questions
Section 4.8 Exercises
Chapter 4 Review
Chapter 5
Section 5.1 Preliminary Questions
Section 5.1 Exercises
Section 5.2 Preliminary Questions
Section 5.2 Exercises
Section 5.3 Preliminary Questions
Section 5.3 Exercises
Section 5.4 Preliminary Questions
Section 5.4 Exercises
Section 5.5 Preliminary Questions
Section 5.5 Exercises
Section 5.6 Preliminary Questions
Section 5.6 Exercises
Chapter 5 Review
Chapter 6
Section 6.1 Preliminary Questions
Section 6.1 Exercises
Section 6.2 Preliminary Questions
Section 6.2 Exercises
Section 6.3 Preliminary Questions
Section 6.3 Exercises
Section 6.4 Preliminary Questions
Section 6.4 Exercises
Section 6.5 Preliminary Questions
Section 6.5 Exercises
Chapter 6 Review
Chapter 7
Section 7.1 Preliminary Questions
Section 7.1 Exercises
Section 7.2 Preliminary Questions
Section 7.2 Exercises
Section 7.3 Preliminary Questions
Section 7.3 Exercises
Section 7.4 Preliminary Questions
Section 7.4 Exercises
Section 7.5 Preliminary Questions
Section 7.5 Exercises
Section 7.6 Preliminary Questions
Section 7.6 Exercises
Section 7.7 Preliminary Questions
Section 7.7 Exercises
Section 7.8 Preliminary Questions
Section 7.8 Exercises
Section 7.9 Preliminary Questions
Section 7.9 Exercises
Chapter 7 Review
Chapter 8
Section 8.1 Preliminary Questions
Section 8.1 Exercises
Section 8.2 Preliminary Questions
Section 8.2 Exercises
Section 8.3 Preliminary Questions
Section 8.3 Exercises
Section 8.4 Preliminary Questions
Section 8.4 Exercises
Section 8.5 Preliminary Questions
Section 8.5 Exercises
Section 8.6 Preliminary Questions
Section 8.6 Exercises
Section 8.7 Preliminary Questions
Section 8.7 Exercises
Section 8.8 Preliminary Questions
Section 8.8 Exercises
Chapter 8 Review
Chapter 9
Section 9.1 Preliminary Questions
Section 9.1 Exercises
Section 9.2 Preliminary Questions
Section 9.2 Exercises
Section 9.3 Preliminary Questions
Section 9.3 Exercises
Section 9.4 Preliminary Questions
Section 9.4 Exercises
Chapter 9 Review
Chapter 10
Section 10.1 Preliminary Questions
Section 10.1 Exercises
Section 10.2 Preliminary Questions
Section 10.2 Exercises
Section 10.3 Preliminary Questions
Section 10.3 Exercises
Section 10.4 Preliminary Questions
Section 10.4 Exercises
Chapter 10 Review
Chapter 11
Section 11.1 Preliminary Questions
Section 11.1 Exercises
Section 11.2 Preliminary Questions
Section 11.2 Exercises
Section 11.3 Preliminary Questions
Section 11.3 Exercises
Section 11.4 Preliminary Questions
Section 11.4 Exercises
Section 11.5 Preliminary Questions
Section 11.5 Exercises
Section 11.6 Preliminary Questions
Section 11.6 Exercises
Section 11.7 Preliminary Questions
Section 11.7 Exercises
Chapter 11 Review
Chapter 12
Section 12.1 Preliminary Questions
Section 12.1 Exercises
Section 12.2 Preliminary Questions
Section 12.2 Exercises
Section 12.3 Preliminary Questions
Section 12.3 Exercises
Section 12.4 Preliminary Questions
Section 12.4 Exercises
Section 12.5 Preliminary Questions
Section 12.5 Exercises Questions
Chapter 12 Review
CHAPTER 13
Section 13.1 Preliminary Questions
Section 13.1 Exercises
Section 13.2 Preliminary Questions
Section 13.2 Exercises
Section 13.3 Preliminary Questions
Section 13.3 Exercises
Section 13.4 Preliminary Questions
Section 13.4 Exercises
Section 13.5 Preliminary Questions
Section 13.5 Exercises
Section 13.6 Preliminary Questions
Section 13.6 Exercises
Section 13.7 Preliminary Questions
Section 13.7 Exercises
Chapter 13 Review
CHAPTER 14
Section 14.1 Preliminary Questions
Section 14.1 Exercises
Section 14.2 Preliminary
Section 14.2 Exercises
Section 14.3 Preliminary Questions
Section 14.3 Exercises
Section 14.4 Preliminary Questions
Section 14.4 Exercises
Section 14.5 Preliminary Questions
Section 14.5 Exercises
Section 14.6 Preliminary Questions
Section 14.6 Exercises
Chapter 14 Review
Chapter 15
Section 15.1 Preliminary Questions
Section 15.1 Exercises
Section 15.2 Preliminary Questions
Section 15.2 Exercises
Section 15.3 Preliminary Questions
Section 15.3 Exercises
Section 15.4 Preliminary Questions
Section 15.4 Exercises
Section 15.5 Preliminary Questions
Section 15.5 Exercises
Section 15.6 Preliminary Questions
Section 15.6 Exercises
Section 15.7 Preliminary Questions
Section 15.7 Exercises
Section 15.8 Preliminary Questions
Section 15.8 Exercises
Chapter 15 Review
Chapter 16
Section 16.1 Preliminary Questions
Section 16.1 Exercises
Section 16.2 Preliminary Questions
Section 16.2 Exercises
Section 16.3 Preliminary Questions
Section 16.3 Exercises
Section 16.4 Preliminary Questions
Section 16.4 Exercises Questions
Section 16.5 Preliminary Questions
Section 16.5 Exercises
Section 16.6 Preliminary Questions
Section 16.6 Exercises
Chapter 16 Review
Chapter 17
Section 17.1 Preliminary Questions
Section 17.1 Exercises
Section 17.2 Preliminary Questions
Section 17.2 Exercises
Section 17.3 Preliminary Questions
Section 17.3 Exercises
Section 17.4 Preliminary Questions
Section 17.4 Exercises
Section 17.5 Preliminary Questions
Section 17.5 Exercises
Chapter 17 Review
Chapter 18
Section 18.1 Preliminary Questions
Section 18.1 Exercises
Section 18.2 Preliminary Questions
Section 18.2 Exercises
Section 18.3 Preliminary Questions
Section 18.3 Exercises
Chapter 18 Review
REFERENCES
Section 1.1
Section 1.2
Section 1.5
Section 2.2
Section 2.3
Chapter 2 Review
Section 3.1
Section 3.2
Section 3.4
Section 3.5
Section 3.9
Chapter 3 Review
Section 4.2
Section 4.5
Section 4.6
Section 4.7
Chapter 4 Review
Section 5.1
Section 5.2
Section 5.4
Section 5.5
Section 5.6
Section 6.1
Section 6.3
Section 7.7
Section 8.1
Section 8.3
Section 8.6
Section 8.8
Section 9.1
Section 10.1
Section 11.1
Section 11.2
Section 11.4
Section 12.2
Section 12.3
Section 13.4
Section 14.3
Section 14.4
Section 14.5
Section 15.8
Section 16.3
Section 16.6
Section 17.2
Section 17.3
Appendix D
PHOTO CREDITS
INDEX