University Calculus: Early Transcendentals (4th Edition)

Contents
Preface
1. Functions
	1.1 Functions and Their Graphs
	1.2 Combining Functions; Shifting and Scaling Graphs
	1.3 Trigonometric Functions
	1.4 Graphing with Software
	1.5 Exponential Functions
	1.6 Inverse Functions and Logarithms
2. Limits and Continuity
	2.1 Rates of Change and Tangent Lines to Curves
	2.2 Limit of a Function and Limit Laws
	2.3 The Precise Definition of a Limit
	2.4 One-Sided Limits
	2.5 Continuity
	2.6 Limits Involving Infinity; Asymptotes of Graphs
	CHAPTER 2 Practice Exercises
3. Derivatives
	3.1 Tangent Lines and the Derivative at a Point
	3.2 The Derivative as a Function
	3.3 Differentiation Rules
	3.4 The Derivative as a Rate of Change
	3.5 Derivatives of Trigonometric Functions
	3.6 The Chain Rule
	3.7 Implicit Differentiation
	3.8 Derivatives of Inverse Functions and Logarithms
	3.9 Inverse Trigonometric Functions
	3.10 Related Rates
	3.11 Linearization and Differentials
	CHAPTER 3 Questions to Guide Your Review
	CHAPTER 3 Additional and Advanced Exercises
4. Applications of Derivatives
	4.1 Extreme Values of Functions on Closed Intervals
	4.2 The Mean Value Theorem
	4.3 Monotonic Functions and the First Derivative Test
	4.4 Concavity and Curve Sketching
	4.5 Indeterminate Forms and L’Hôpital’s Rule
	4.6 Applied Optimization
	4.7 Newton’s Method
	4.8 Antiderivatives
	CHAPTER 4 Questions to Guide Your Review
	CHAPTER 4 Practice Exercises
	CHAPTER 4 Additional and Advanced Exercises
5. Integrals
	5.1 Area and Estimating with Finite Sums
	5.2 Sigma Notation and Limits of Finite Sums
	5.3 The Definite Integral
	5.4 The Fundamental Theorem of Calculus
	5.5 Indefinite Integrals and the Substitution Method
	5.6 Definite Integral Substitutions and the Area Between Curves
	CHAPTER 5 Questions to Guide Your Review
	CHAPTER 5 Practice Exercises
	CHAPTER 5 Additional and Advanced Exercises
6. Applications of Definite Integrals
	6.1 Volumes Using Cross-Sections
	6.2 Volumes Using Cylindrical Shells
	6.3 Arc Length
	6.4 Areas of Surfaces of Revolution
	6.5 Work
	6.6 Moments and Centers of Mass
	CHAPTER 6 Questions to Guide Your Review
	CHAPTER 6 Practice Exercises
	CHAPTER 6 Additional and Advanced Exercises
7. Integrals and Transcendental Functions
	7.1 The Logarithm Defined as an Integral
	7.2 Exponential Change and Separable Differential Equations
	7.3 Hyperbolic Functions
	CHAPTER 7 Questions to Guide Your Review
	CHAPTER 7 Practice Exercises
	CHAPTER 7 Additional and Advanced Exercises
8. Techniques of Integration
	8.1 Integration by Parts
	8.2 Trigonometric Integrals
	8.3 Trigonometric Substitutions
	8.4 Integration of Rational Functions by Partial Fractions
	8.5 Integral Tables and Computer Algebra Systems
	8.6 Numerical Integration
	8.7 Improper Integrals
	CHAPTER 8 Questions to Guide Your Review
	CHAPTER 8 Practice Exercises
	CHAPTER 8 Additional and Advanced Exercises
9. Infinite Sequences and Series
	9.1 Sequences
	9.2 Infinite Series
	9.3 The Integral Test
	9.4 Comparison Tests
	9.5 Absolute Convergence; The Ratio and Root Tests
	9.6 Alternating Series and Conditional Convergence
	9.7 Power Series
	9.8 Taylor and Maclaurin Series
	9.9 Convergence of Taylor Series
	9.10 Applications of Taylor Series
	CHAPTER 9 Questions to Guide Your Review
	CHAPTER 9 Practice Exercises
	CHAPTER 9 Additional and Advanced Exercises
10. Parametric Equations and Polar Coordinates
	10.1 Parametrizations of Plane Curves
	10.2 Calculus with Parametric Curves
	10.3 Polar Coordinates
	10.4 Graphing Polar Coordinate Equations
	10.5 Areas and Lengths in Polar Coordinates
	CHAPTER 10 Questions to Guide Your Review
	CHAPTER 10 Practice Exercises
	CHAPTER 10 Additional and Advanced Exercises
11. Vectors and the Geometry of Space
	11.1 Three-Dimensional Coordinate Systems
	11.2 Vectors
	11.3 The Dot Product
	11.4 The Cross Product
	11.5 Lines and Planes in Space
	11.6 Cylinders and Quadric Surfaces
	CHAPTER 11 Questions to Guide Your Review
	CHAPTER 11 Practice Exercises
	CHAPTER 11 Additional and Advanced Exercises
12. Vector-Valued Functions and Motion in Space
	12.1 Curves in Space and Their Tangents
	12.2 Integrals of Vector Functions; Projectile Motion
	12.3 Arc Length in Space
	12.4 Curvature and Normal Vectors of a Curve
	12.5 Tangential and Normal Components of Acceleration
	12.6 Velocity and Acceleration in Polar Coordinates
	CHAPTER 12 Questions to Guide Your Review
	CHAPTER 12 Practice Exercises
	CHAPTER 12 Additional and Advanced Exercises
13. Partial Derivatives
	13.1 Functions of Several Variables
	13.2 Limits and Continuity in Higher Dimensions
	13.3 Partial Derivatives
	13.4 The Chain Rule
	13.5 Directional Derivatives and Gradient Vectors
	13.6 Tangent Planes and Differentials
	13.7 Extreme Values and Saddle Points
	13.8 Lagrange Multipliers
	CHAPTER 13 Questions to Guide Your Review
	CHAPTER 13 Practice Exercises
	CHAPTER 13 Additional and Advanced Exercises
14. Multiple Integrals
	14.1 Double and Iterated Integrals over Rectangles
	14.2 Double Integrals over General Regions
	14.3 Area by Double Integration
	14.4 Double Integrals in Polar Form
	14.5 Triple Integrals in Rectangular Coordinates
	14.6 Applications
	14.7 Triple Integrals in Cylindrical and Spherical Coordinates
	14.8 Substitutions in Multiple Integrals
	CHAPTER 14 Questions to Guide Your Review
	CHAPTER 14 Practice Exercises
	CHAPTER 14 Additional and Advanced Exercises
15. Integrals and VectorFields
	15.1 Line Integrals of Scalar Functions
	15.2 Vector Fields and Line Integrals: Work, Circulation, and Flux
	15.3 Path Independence, Conservative Fields, and Potential Functions
	15.4 Green’s Theorem in the Plane
	15.5 Surfaces and Area
	15.6 Surface Integrals
	15.7 Stokes’ Theorem
	15.8 The Divergence Theorem and a Unified Theory
	CHAPTER 15 Questions to Guide Your Review
	CHAPTER 15 Practice Exercises
	CHAPTER 15 Additional and Advanced Exercises
16. First-Order Differential Equations
	16.1 Solutions, Slope Fields, and Euler’s Method
	16.2 First-Order Linear Equations
	16.3 Applications
	16.4 Graphical Solutions of Autonomous Equations
	16.5 Systems of Equations and Phase Planes
	CHAPTER 16 Questions to Guide Your Review
	CHAPTER 16 Practice Exercises
	CHAPTER 16 Additional and Advanced Exercises
	ANSWERS TO ODD-NUMBERED EXERCISES
17. Second-Order Differential Equations
	17.1 Second-Order Linear Equations
	17.2 Nonhomogeneous Linear Equations
	17.3 Applications
	17.4 Euler Equations
	17.5 Power-Series Solutions
	ANSWERS TO ODD-NUMBERED EXERCISES
Appendix A
	A.1 Real Numbers and the Real Line
	A.2 Mathematical Induction
	A.3 Lines and Circles
	A.4 Conic Sections
	A.5 Proofs of Limit Theorems
	A.6 Commonly Occurring Limits
	A.7 Theory of the Real Numbers
	A.8 Complex Numbers
	A.9 The Distributive Law for Vector Cross Products
	A.10 The Mixed Derivative Theorem and the Increment Theorem
Appendix B
	B.1 Relative Rates of Growth
	B.2 Probability
	B.3 Conics in Polar Coordinates
	B.4 Taylor’s Formula for Two Variables
	B.5 Partial Derivatives with Constrained Variables
	ANSWERS TO ODD-NUMBERED EXERCISES
ANSWERS TO ODD-NUMBERED EXERCISES
	Chapter 1. SECTION 1.1, pp. 11–13
	SECTION 1.2, pp. 18–21
	SECTION 1.3, pp. 27–29
	SECTION 1.4, p. 33
	SECTION 1.5, pp. 37–38
	Chapter 2. SECTION 2.1, pp. 56–58
	SECTION 2.3, pp. 74–77
	PRACTICE EXERCISES, pp. 111–112
	ADDITIONAL AND ADVANCED EXERCISES, pp. 118–120
	SECTION 3.3, pp. 137–139
	SECTION 3.5, pp. 152–154
	SECTION 3.6, pp. 159–162
	SECTION 3.8, pp. 176–177
	SECTION 3.10, pp. 189–192
	ADDITIONAL AND ADVANCED EXERCISES, pp. 208–211
	SECTION 4.2, pp. 226–228
	SECTION 4.4, pp. 242–246
	SECTION 4.5, pp. 253–254
	SECTION 4.7, pp. 269–271
	PRACTICE EXERCISES, pp. 282–286
	ADDITIONAL AND ADVANCED EXERCISES, pp. 286–289
	Chapter 5. SECTION 5.1, pp. 298–300
	SECTION 5.5, pp. 338–339
	PRACTICE EXERCISES, pp. 350–353
	SECTION 6.3, pp. 379–381
	PRACTICE EXERCISES, pp. 402–403
	PRACTICE EXERCISES, pp. 433–434
	SECTION 8.3, pp. 454–455
	SECTION 8.6, pp. 476–478
	ADDITIONAL AND ADVANCED EXERCISES, pp. 492–494
	SECTION 9.2, pp. 515–517
	SECTION 9.4, pp. 528–529
	SECTION 9.7, pp. 551–554
	SECTION 9.10, pp. 572–574
	Chapter 10. SECTION 10.1, pp. 586–588
	SECTION 10.3, pp. 601–602
	SECTION 10.5, pp. 610–611
	ADDITIONAL AND ADVANCED EXERCISES, p. 613
	SECTION 11.3, pp. 634–636
	SECTION 11.5, pp. 649–651
	PRACTICE EXERCISES, pp. 657–659
	ADDITIONAL AND ADVANCED EXERCISES, pp. 659–661
	SECTION 12.2, pp. 675–677
	SECTION 12.5, p. 689–690
	Chapter 13. SECTION 13.1, pp. 812–814
	SECTION 13.2, pp. 820–823
	SECTION 13.4, pp. 842–844
	SECTION 13.6, pp. 860–863
	SECTION 13.8, pp. 879–882
	ADDITIONAL AND ADVANCED EXERCISES, pp. 894–896
	SECTION 14.2, pp. 784–793
	SECTION 14.3, p. 793–796
	SECTION 14.4, pp. 796–803
	SECTION 14.7, pp. 820–831
	SECTION 14.8, pp. 832–841
	PRACTICE EXERCISES, pp. 842–844
	SECTION 15.3, pp. 867–878
	SECTION 15.7, pp. 910–923
	APPENDIX A.4, PP. AP-22–AP-23
	APPENDIX A.8, PP. AP-37–AP-38
Applications Index
Subject Index
	A
	B, C
	D
	E
	F
	G, H, I
	J, K, L
	M
	N, O, P
	Q, R
	S
	T
	U, V
	W, X, Y, Z
A Brief Table of Integrals
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