Thomas’ Calculus꞉ Early Transcendentals, 15ᵗʰ Edition (2022)

Cover
Title Page
Copyright Page
Contents
Preface
Acknowledgments
Pearson’s Commitment to Diversity, Equity,and Inclusion
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
	Questions to Guide Your Review
	Practice Exercises
	Additional and Advanced Exercises
	Technology Application Projects
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
	Questions to Guide Your Review
	Practice Exercises
	Additional and Advanced Exercises
	Technology Application Projects
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
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
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
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
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
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
	8.9 Probability
	Questions to Guide Your Review
	Practice Exercises
	Additional and Advanced Exercises
	Technology Application Projects
9 First-Order Differential Equations
	9.1 Solutions, Slope Fields, and Euler’s Method
	9.2 First-Order Linear Equations
	9.3 Applications
	9.4 Graphical Solutions of Autonomous Equations
	9.5 Systems of Equations and Phase Planes
	Questions to Guide Your Review
	Practice Exercises
	Additional and Advanced Exercises
	Technology Application Projects
10 Infinite Sequences and Series
	10.1 Sequences
	10.2 Infinite Series
	10.3 The Integral Test
	10.4 Comparison Tests
	10.5 Absolute Convergence; The Ratio and Root Tests
	10.6 Alternating Series and Conditional Convergence
	10.7 Power Series
	10.8 Taylor and Maclaurin Series
	10.9 Convergence of Taylor Series
	10.10 Applications of Taylor Series
	Questions to Guide Your Review
	Practice Exercises
	Additional and Advanced Exercises
	Technology Application Projects
11 Parametric Equations and Polar Coordinates
	11.1 Parametrizations of Plane Curves
	11.2 Calculus with Parametric Curves
	11.3 Polar Coordinates
	11.4 Graphing Polar Coordinate Equations
	11.5 Areas and Lengths in Polar Coordinates
	11.6 Conic Sections
	11.7 Conics in Polar Coordinates
	Questions to Guide Your Review
	Practice Exercises
	Additional and Advanced Exercises
	Technology Application Projects
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 Lines and Planes in Space
	12.6 Cylinders and Quadric Surfaces
	Questions to Guide Your Review
	Practice Exercises
	Additional and Advanced Exercises
	Technology Application Projects
13 Vector-Valued Functions and Motion in Space
	13.1 Curves in Space and Their Tangents
	13.2 Integrals of Vector Functions; Projectile Motion
	13.3 Arc Length in Space
	13.4 Curvature and Normal Vectors of a Curve
	13.5 Tangential and Normal Components of Acceleration
	13.6 Velocity and Acceleration in Polar Coordinates
	Questions to Guide Your Review
	Practice Exercises
	Additional and Advanced Exercises
	Technology Application Projects
14 Partial Derivatives
	14.1 Functions of Several Variables
	14.2 Limits and Continuity in Higher Dimensions
	14.3 Partial Derivatives
	14.4 The Chain Rule
	14.5 Directional Derivatives and Gradient Vectors
	14.6 Tangent Planes and Differentials
	14.7 Extreme Values and Saddle Points
	14.8 Lagrange Multipliers
	14.9 Taylor’s Formula for Two Variables
	14.10 Partial Derivatives with Constrained Variables
	Questions to Guide Your Review
	Practice Exercises
	Additional and Advanced Exercises
	Technology Application Projects
15 Multiple Integrals
	15.1 Double and Iterated Integrals over Rectangles
	15.2 Double Integrals over General Regions
	15.3 Area by Double Integration
	15.4 Double Integrals in Polar Form
	15.5 Triple Integrals in Rectangular Coordinates
	15.6 Applications
	15.7 Triple Integrals in Cylindrical and Spherical Coordinates
	15.8 Substitutions in Multiple Integrals
	Questions to Guide Your Review
	Practice Exercises
	Additional and Advanced Exercises
	Technology Application Projects
16 Integrals and Vector Fields
	16.1 Line Integrals of Scalar Functions
	16.2 Vector Fields and Line Integrals: Work, Circulation, and Flux
	16.3 Path Independence, Conservative Fields, and Potential Functions
	16.4 Green’s Theorem in the Plane
	16.5 Surfaces and Area
	16.6 Surface Integrals
	16.7 Stokes’ Theorem
	16.8 The Divergence Theorem and a Unified Theory
	Questions to Guide Your Review
	Practice Exercises
	Additional and Advanced Exercises
	Technology Application Projects
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
18 Complex Functions
	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
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
Appendix A
	A.1 Real Numbers and the Real Line
	A.2 Mathematical Induction
	A.3 Lines, Circles, and Parabolas
	A.4 Proofs of Limit Theorems
	A.5 Commonly Occurring Limits
	A.6 Theory of the Real Numbers
	A.7 The Distributive Law for Vector Cross Products
	A.8 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
Applications Index
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Subject Index
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A Brief Table of Integrals
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