Thomas' Calculus: Early Transcendentals in SI Units

Front Cover
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Title Page
Copyright Page
Contents
Preface
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
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
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
	Questions to Guide Your Review
	Practice Exercises
	Additional and Advanced Exercises
	Technology Application Projects
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
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
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
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
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
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
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
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
Appendices
	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 Complex Numbers
	A.9 Probability
	A.10 The Distributive Law for Vector Cross Products
	A.11 The Mixed Derivative Theorem and the Increment Theorem
Answers to Odd‐Numbered Exercises
Credits
Applications Index
Subject Index
A Brief Table of Integrals
Basic Algebra Formulas
Limits, Differentiation Rules, and Integration Rules
Back Cover