University Calculus: Early Transcendentals in SI Units

Cover
MyLab Math forUniversity Calculus, 4e in SI Units
Tilte 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 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
	Questions to Guide Your Review
	Practice Exercises
	Additional and Advanced 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
	Questions to Guide Your Review
	Practice Exercises
	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’Hopital’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
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
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
	Questions to Guide Your Review
	Practice Exercises
	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
	Questions to Guide Your Review
	Practice Exercises
	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
	Questions to Guide Your Review
	Practice Exercises
	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
	Questions to Guide Your Review
	Practice Exercises
	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
	Questions to Guide Your Review
	Practice Exercises
	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
	Questions to Guide Your Review
	Practice Exercises
	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
	Questions to Guide Your Review
	Practice Exercises
	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
	Questions to Guide Your Review
	Practice Exercises
	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
	Questions to Guide Your Review
	Practice Exercises
	Additional and Advanced Exercises
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
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
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
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
Applications Index
Subject Index
Credits
A Brief Table of Integrals
Copyright
Title Page
Dedication
Contents
Chapter 1: ‘I’m thinking’ – Oh, but are you?
Chapter 2: Renegade perception
Chapter 3: The Pushbacker sting
Chapter 4: ‘Covid’: The calculated catastrophe
Chapter 5: There is no ‘virus’
Chapter 6: Sequence of deceit
Chapter 7: War on your mind
Chapter 8: ‘Reframing’ insanity
Chapter 9: We must have it? So what is it?
Chapter 10: Human 2.0
Chapter 11: Who controls the Cult?
Chapter 12: Escaping Wetiko
Postscript
Appendix: Cowan-Kaufman-Morell Statement on Virus Isolation
Bibliography
Index
Book Cover
Diagnostic Tests
	A: Diagnostic Test: Algebra
	B: Diagnostic Test: Analytic Geometry
	C: Diagnostic Test: Functions
	D: Diagnostic Test: Trigonometry
Chapter 1- Functions and Models
	1.1: Four Ways to Represent a Function
	1.2: Mathematical Models: A Catalog of Essential Functions
	1.3: New Functions from Old Functions
	1.4: Exponential Functions
	1.5: Inverse Functions and Logarithms
	Review
	Principles of Problem Solving
Chapter 2- Limits and Derivatives
	2.1: The Tangent and Velocity Problems
	2.2: The Limit of a Function
	2.3: Calculating Limits Using the Limit Laws
	2.4: The Precise Definition of a Limit
	2.5: Continuity
	2.6: Limits at Infinity; Horizontal Asymptotes
	2.7: Derivatives and Rates of Change
	2.8: The Derivative as a Function
	Review
	Problems Plus
Chapter 3- Differentiation Rules
	3.1: Derivatives of Polynomials and Exponential Functions
	3.2: The Product and Quotient Rules
	3.3: Derivatives of Trigonometric Functions
	3.4: The Chain Rule
	3.5: Implicit Differentiation
	3.6: Derivatives of Logarithmic Functions
	3.7: Rates of Change in the Natural and Social Sciences
	3.8: Exponential Growth and Decay
	3.9: Related Rates
	3.10: Linear Approximations and Differentials
	3.11: Hyperbolic Functions
	Review
	Problems Plus
Chapter 4- Applications of Differentiation
	4.1: Maximum and Minimum Values
	4.2: The Mean Value Theorem
	4.3: How Derivatives Affect the Shape of a Graph
	4.4: Indeterminate Forms and L'Hospital's Rule
	4.5: Summary of Curve Sketching
	4.6: Graphing with Calculus and Calculators
	4.7: Optimization Problems
	4.8: Newton's Method
	4.9: Antiderivatives
	Review
	Problems Plus
Chapter 5- Integrals
	5.1: Areas and Distances
	5.2: The Definite Integral
	5.3: The Fundamental Theorem of Calculus
	5.4: Indefinite Integrals and the Net Change Theorem
	5.5: The Substitution Rule
	Review
	Problems Plus
Chapter 6- Applications of Integration
	6.1: Areas between Curves
	6.2: Volumes
	6.3: Volumes by Cylindrical Shells
	6.4: Work
	6.5: Average Value of a Function
	Review
	Problems Plus
Chapter 7- Techniques of Integration
	7.1: Integration by Parts
	7.2: Trigonometric Integrals
	7.3: Trigonometric Substitution
	7.4: Integration of Rational Functions by Partial Fractions
	7.5: Strategy for Integration
	7.6: Integration Using Tables and Computer Algebra Systems
	7.7: Approximate Integration
	7.8: Improper Integrals
	Review
	Problems Plus
Chapter 8- Further Applications of Integration
	8.1: Arc Length
	8.2: Area of a Surface of Revolution
	8.3: Applications to Physics and Engineering
	8.4: Applications to Economics and Biology
	8.5: Probability
	Review
	Problems Plus
Chapter 9- Differential Equations
	9.1: Modeling with Differential Equations
	9.2: Direction Fields and Euler's Method
	9.3: Separable Equations
	9.4: Models for Population Growth
	9.5: Linear Equations
	9.6: Predator-Prey Systems
	Review
	Problems Plus
Chapter 10- Parametric Equations and Polar Coordinates
	10.1: Curves Defined by Parametric Equations
	10.2: Calculus with Parametric Curves
	10.3: Polar Coordinates
	10.4: Areas and Lengths in Polar Coordinates
	10.5: Conic Sections
	10.6: Conic Sections in Polar Coordinates
	Review
	Problems Plus
Chapter 11- Infinite sequences and Series
	11.1: Sequences
	11.2: Series
	11.3: The Integral Test and Estimates of Sums
	11.4: The Comparison Tests
	11.5: Alternating Series
	11.6: Absolute Convergence and the Ratio and Root Tests
	11.7: Strategy for Testing Series
	11.8: Power Series
	11.9: Representations of Functions as Power Series
	11.10: Taylor and Maclaurin Series
	11.11: Applications of Taylor Polynomials
	Review
	Problems Plus
Chapter 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: Equations of Lines and Planes
	12.6: Cylinders and Quadric Surfaces
	Review
	Problems Plus
Chapter 13- Vector Functions
	13.1: Vector Functions and Space Curves
	13.2: Derivatives and Integrals of Vector Functions
	13.3: Arc Length and Curvature
	13.4: Motion in Space: Velocity and Acceleration
	Review
	Problems Plus
Chapter 14- Partial Derivatives
	14.1: Functions of Several Variables
	14.2: Limits and Continuity
	14.3: Partial Derivatives
	14.4: Tangent Planes and Linear Approximations
	14.5: The Chain Rule
	14.6: Directional Derivatives and the Gradient Vector
	14.7: Maximum and Minimum Values
	14.8: Lagrange Multipliers
	Review
	Problems Plus
Chapter 15- Multiple Integrals
	15.1: Double Integrals over Rectangles
	15.2: Double Integrals over General Regions
	15.3: Double Integrals in Polar Coordinates
	15.4: Applications of Double Integrals
	15.5: Surface Area
	15.6: Triple Integrals
	15.7: Triple Integrals in Cylindrical Coordinates
	15.8: Triple Integrals in Spherical Coordinates
	15.9: Change of Variables in Multiple Integrals
	Review
	Problems Plus
Chapter 16- Vector Calculus
	16.1: Vector Fields
	16.2: Line Integrals
	16.3: The Fundamental Theorem for Line Integrals
	16.4: Green's Theorem
	16.5: Curl and Divergence
	16.6: Parametric Surfaces and Their Areas
	16.7: Surface Integrals
	16.8: Stokes' Theorem
	16.9: The Divergence Theorem
	Review
	Problems Plus
Chapter 17- Second-Order Differential Equations
	17.1: Second-Order Linear Equations
	17.2: Nonhomogeneous Linear Equations
	17.3: Applications of Second-Order Differential Equations
	17.4: Series Solutions
	Review
Appendixes
	A: Numbers, Inequalities, and Absolute Values
	B: Coordinate Geometry and Lines
	C: Graphs of Second-Degree Equations
	D: Trigonometry
	E: Sigma Notation
	G: The Logarithm Defined as an Integral
	H: Complex Numbers