Thomas' Calculus: Early Transcendentals

Cover
Digital Resoures for Students
Title Page
Copyright
Contents
Preface
Pearson’s Commitment to Diversity, Equity, and Inclusion
Chapter 1. Functions
1.1 Functions and Their Graphs
1.2 Combining Functions; Shifting and Scaling Graphs
1.3 Trigonometric Functions
1.4 Exponential Functions
1.5 Inverse Functions and Logarithms
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
Technology Application Projects
Chapter 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 Limits Involving Infinity; Asymptotes of Graphs
2.6 Continuity
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
Technology Application Projects
Chapter 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
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
Technology Application Projects
Chapter 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
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
Technology Application Projects
Chapter 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
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
Technology Application Projects
Chapter 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 and Fluid Forces
6.6 Moments and Centers of Mass
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
Technology Application Projects
Chapter 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
7.4 Relative Rates of Growth
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
Chapter 8. Techniques of Integration
8.1 Using Basic Integration Formulas
8.2 Integration by Parts
8.3 Trigonometric Integrals
8.4 Trigonometric Substitutions
8.5 Integration of Rational Functions by Partial Fractions
8.6 Integral Tables and Computer Algebra Systems
8.7 Numerical Integration
8.8 Improper Integrals
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
Technology Application Projects
Chapter 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
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
Technology Application Projects
Chapter 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
10.6 Conic Sections
10.7 Conics in Polar Coordinates
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
Technology Application Projects
Chapter 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
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
Technology Application Projects
Chapter 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
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
Technology Application Projects
Chapter 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
13.9 Taylor’s Formula for Two Variables
13.10 Partial Derivatives with Constrained Variables
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
Technology Application Projects
Chapter 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
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
Technology Application Projects
Chapter 15. Integrals and Vector Fields
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
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
Technology Application Projects
Chapter 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
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
Technology Application Projects
Chapter 17. Second-Order Differential Equations
Overview
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-Numberd Exercises
Chapter 18. Complex Functions
Introduction
18.1 Complex Numbers
18.2 Functions of a Complex Variable
18.3 Derivatives
18.4 The Cauchy-Riemann Equations
18.5 Complex Power Series
18.6 Some Complex Functions
18.7 Conformal Maps
Questions to Guide Your Review
Additional and Advanced Exercises
Answers To Odd-Numbered Exercises
Chapter 19. Fourier Series and Wavelets
19.1 Periodic Functions
19.2 Summing Sines and Cosines
19.3 Vectors and Approximation in Three and More Dimensions
19.4 Approximation of Functions
19.5 Advanced Topic: The Haar System and Wavelets
Questions to Guide Your Review
Additional and Advanced Exercises
Answers To Odd-Numbered Exercises
Appendix A
A.1 Real Numbers and the Real Line
A.2 Graphing with Software
A.3 Mathematical Induction
A.4 Lines, Circles, and Parabolas
A.5 Proofs of Limit Theorems
A.6 Commonly Occurring Limits
A.7 Theory of the Real Numbers
A.8 Probability
A.9 The Distributive Law for Vector Cross Products
A.10 The Mixed Derivative Theorem and the Increment Theorem
Appendix B
B.1 Determinants
B.2 Extreme Values and Saddle Points for Functions of More than Two Variables
B.3 The Method of Gradient Descent
Answers To Odd-Numbered Exercises
Answere To Odd-Numberd Exercises
Applications Index
Subject Index
Credits
A Brief Table of Integrals
Formulas and Rules