Calculus

Front Cover
ABOUT THE AUTHORS
CONTENTS
PREFACE
1 PRECALCULUS REVIEW
	1.1 Real Numbers, Functions, and Graphs
	1.2 Linear and Quadratic Functions
	1.3 The Basic Classes of Functions
	1.4 Trigonometric Functions
	1.5 Technology: Calculators and Computers
	CHAPTER REVIEW EXERCISES
2 LIMITS
	2.1 Limits, Rates of Change, and Tangent Lines
	2.2 Limits: A Numerical and Graphical Approach
	2.3 Basic Limit Laws
	2.4 Limits and Continuity
	2.5 Evaluating Limits Algebraically
	2.6 Trigonometric Limits
	2.7 Limits at Infinity
	2.8 Intermediate Value Theorem
	2.9 The Formal Definition of a Limit
	CHAPTER REVIEW EXERCISES
3 DIFFERENTIATION
	3.1 Definition of the Derivative
	3.2 The Derivative as a Function
	3.3 Product and Quotient Rules
	3.4 Rates of Change
	3.5 Higher Derivatives
	3.6 Trigonometric Functions
	3.7 The Chain Rule
	3.8 Implicit Differentiation
	3.9 Related Rates
	CHAPTER REVIEW EXERCISES
4 APPLICATIONS OF THE DERIVATIVE
	4.1 Linear Approximation and Applications
	4.2 Extreme Values
	4.3 The Mean Value Theorem and Monotonicity
	4.4 The Shape of a Graph
	4.5 Graph Sketching and Asymptotes
	4.6 Applied Optimization
	4.7 Newton’s Method
	CHAPTER REVIEW EXERCISES
5 THE INTEGRAL
	5.1 Approximating and Computing Area
	5.2 The Definite Integral
	5.3 The Indefinite Integral
	5.4 The Fundamental Theorem of Calculus, Part I
	5.5 The Fundamental Theorem of Calculus, Part II
	5.6 Net Change as the Integral of a Rate of Change
	5.7 Substitution Method
	CHAPTER REVIEW EXERCISES
6 APPLICATIONS OF THE INTEGRAL
	6.1 Area Between Two Curves
	6.2 Setting Up Integrals: Volume, Density, Average Value
	6.3 Volumes of Revolution
	6.4 The Method of Cylindrical Shells
	6.5 Work and Energy
	CHAPTER REVIEW EXERCISES
7 EXPONENTIAL FUNCTIONS
	7.1 Derivative of f (x) = b^x and the Number e
	7.2 Inverse Functions
	7.3 Logarithms and Their Derivatives
	7.4 Exponential Growth and Decay
	7.5 Compound Interest and Present Value
	7.6 Models Involving y' = k(y − b)
	7.7 L’Hôpital’s Rule
	7.8 Inverse Trigonometric Functions
	7.9 Hyperbolic Functions
	CHAPTER REVIEW EXERCISES
8 TECHNIQUES OF INTEGRATION
	8.1 Integration by Parts
	8.2 Trigonometric Integrals
	8.3 Trigonometric Substitution
	8.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions
	8.5 The Method of Partial Fractions
	8.6 Strategies for Integration
	8.7 Improper Integrals
	8.8 Probability and Integration
	8.9 Numerical Integration
	CHAPTER REVIEW EXERCISES
9 FURTHER APPLICATIONS OF THE INTEGRAL AND TAYLOR POLYNOMIALS
	9.1 Arc Length and Surface Area
	9.2 Fluid Pressure and Force
	9.3 Center of Mass
	9.4 Taylor Polynomials
	CHAPTER REVIEW EXERCISES
10 INTRODUCTION TO DIFFERENTIAL EQUATIONS
	10.1 Solving Differential Equations
	10.2 Graphical and Numerical Methods
	10.3 The Logistic Equation
	10.4 First-Order Linear Equations
	CHAPTER REVIEW EXERCISES
11 INFINITE SERIES
	11.1 Sequences
	11.2 Summing an Infinite Series
	11.3 Convergence of Series with Positive Terms
	11.4 Absolute and Conditional Convergence
	11.5 The Ratio and Root Tests and Strategies for Choosing Tests
	11.6 Power Series
	11.7 Taylor Series
	CHAPTER REVIEW EXERCISES
12 PARAMETRIC EQUATIONS, POLAR COORDINATES, AND CONIC SECTIONS
	12.1 Parametric Equations
	12.2 Arc Length and Speed
	12.3 Polar Coordinates
	12.4 Area and Arc Length in Polar Coordinates
	12.5 Conic Sections
	CHAPTER REVIEW EXERCISES
13 VECTOR GEOMETRY
	13.1 Vectors in the Plane
	13.2 Vectors in Three Dimensions
	13.3 Dot Product and the Angle Between Two Vectors
	13.4 The Cross Product
	13.5 Planes in 3-Space
	13.6 A Survey of Quadric Surfaces
	13.7 Cylindrical and Spherical Coordinates
	CHAPTER REVIEW EXERCISES
14 CALCULUS OF VECTOR-VALUED FUNCTIONS
	14.1 Vector-Valued Functions
	14.2 Calculus of Vector-Valued Functions
	14.3 Arc Length and Speed
	14.4 Curvature
	14.5 Motion in 3-Space
	14.6 Planetary Motion According to Kepler and Newton
	CHAPTER REVIEW EXERCISES
15 DIFFERENTIATION IN SEVERAL VARIABLES
	15.1 Functions of Two or More Variables
	15.2 Limits and Continuity in Several Variables
	15.3 Partial Derivatives
	15.4 Differentiability and Tangent Planes
	15.5 The Gradient and Directional Derivatives
	15.6 The Chain Rule
	15.7 Optimization in Several Variables
	15.8 Lagrange Multipliers: Optimizing with a Constraint
	CHAPTER REVIEW EXERCISES
16 MULTIPLE INTEGRATION
	16.1 Integration in Two Variables
	16.2 Double Integrals over More General Regions
	16.3 Triple Integrals
	16.4 Integration in Polar, Cylindrical, and Spherical Coordinates
	16.5 Applications of Multiple Integrals
	16.6 Change of Variables
	CHAPTER REVIEW EXERCISES
17 LINE AND SURFACE INTEGRALS
	17.1 Vector Fields
	17.2 Line Integrals
	17.3 Conservative Vector Fields
	17.4 Parametrized Surfaces and Surface Integrals
	17.5 Surface Integrals of Vector Fields
	CHAPTER REVIEW EXERCISES
18 FUNDAMENTAL THEOREMS OF VECTOR ANALYSIS
	18.1 Green’s Theorem
	18.2 Stokes’ Theorem
	18.3 Divergence Theorem
	CHAPTER REVIEW EXERCISES
APPENDIX A - THE LANGUAGE OF MATHEMATICS
APPENDIX B - PROPERTIES OF REAL NUMBERS
APPENDIX C - INDUCTION AND THE BINOMIAL THEOREM
APPENDIX D - ADDITIONAL PROOFS
ANSWERS TO ODD-NUMBERED EXERCISES
REFERENCES
INDEX
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