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