University Calculus: Early Transcendentals

✍ Scribed by Joel Hass, Christopher Heil, Przemyslaw Bogacki, Maurice Weir, George Thomas

• Publisher: Pearson
• Year: 2019
• Tongue: English
• Leaves: 1210
• Edition: 4
• Category: Library

✦ Table of Contents

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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Geometry Formulas
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