World Wide Web (Aslib Know How Guides)

Front Cover
Title Page
Copyright Page
Contents
About the Authors
Foreword
Preface
1 Functions and Graphs
	1.1 Preliminaries
	1.2 Lines in the Plane
	1.3 Functions
	1.4 Graphs of Functions
	1.5 Inverse Functions; Inverse Trigonometric Functions
	1.6 Exponential and Logarithmic Functions
	Chapter 1 Review
2 Limits and Continuity
	2.1 What Is Calculus?
	2.2 The Limit of a Function
	2.3 Properties of Limits
	2.4 Continuity
	Chapter 2 Review
	Guest Essay: "Calculus Was Inevitable," John Troutman
3 Differentiation
	3.1 An Introduction to the Derivative: Tangents
	3.2 Techniques of Differentiation
	3.3 Derivatives of Trigonometric, Exponential, and Logarithmic Functions
	3.4 Rates of Change: Rectilinear Motion
	3.5 The Chain Rule
	3.6 Implicit Differentiation
	3.7 Related Rates and Applications
	3.8 Linear Approximation and Differentials
	Chapter 3 Review
	Group Research Project: Chaos
4 Additional Applications of the Derivative
	4.1 Extreme Values of a Continuous Function
	4.2 The Mean Value Theorem
	4.3 First-Derivative Test
	4.4 Concavity and the Second-Derivative Test
	4.5 Curve Sketching: Limits Involving Infinity and Asymptotes
	4.6 Optimization in the Physical Sciences and Engineering
	4.7 Optimization in Business, Economics, and the Life Sciences
	4.8 l'Hôpital's Rule
	Chapter 4 Review
	Group Research Project: Wine Barrel Capacity
5 Integration
	5.1 Antidifferentiation
	5.2 Area as the Limit of a Sum
	5.3 Riemann Sums and the Definite Integral
	5.4 The Fundamental Theorems of Calculus
	5.5 Integration by Substitution
	5.6 Introduction to Differential Equations
	5.7 The Mean Value Theorem for Integrals; Average Value
	5.8 Numerical Integration: The Trapezoidal Rule and Simpson's Rule
	5.9 An Alternative Approach: The Logarithm as an Integral
	Chapter 5 Review
	Guest Essay: "Kinematics of Jogging," Ralph Boas
6 Additional Applications of the Integral
	6.1 Area Between Two Curves
	6.2 Volume by Disks and Washers
	6.3 Volume by Shells
	6.4 Arc Length and Surface Area
	6.5 Physical Applications: Work, Liquid Force, and Centroids
	Chapter 6 Review
	Group Research Project: "Houdini's Escape"
Cumulative Review Problems for Chapters 1-6
7 Methods of Integration
	7.1 Review of Substitution and Integration by Table
	7.2 Integration by Parts
	7.3 Trigonometric Methods
	7.4 The Method of Partial Fractions
	7.5 Summary of Integration Techniques
	7.6 First-Order Differential Equations
	7.7 Improper Integrals
	7.8 The Hyperbolic and Inverse Hyperbolic Functions
	Chapter 7 Review
	Group Research Project: Buoy Design
8 Infinite Series
	8.1 Sequences and Their Limits
	8.2 Introduction to Infinite Series: Geometric Series
	8.3 The Integral Test: p-Series
	8.4 Comparison Tests
	8.5 The Ratio Test and the Root Test
	8.6 Alternating Series; Absolute and Conditional Convergence
	8.7 Power Series
	8.8 Taylor and Maclaurin Series
	Chapter 8 Review
	Group Research Project: Elastic Tightrope Project
9 Polar Coordinates and Parametric Forms
	9.1 The Polar Coordinate System
	9.2 Graphing in Polar Coordinates
	9.3 Area and Tangent Lines in Polar Coordinates
	9.4 Parametric Representation of Curves
	Chapter 9 Review
	Group Research Project: Security Systems
10 Vectors in the Plane and in Space
	10.1 Vectors in the Plane
	10.2 Quadric Surfaces and Graphing in Three Dimensions
	10.3 The Dot Product
	10.4 The Cross Product
	10.5 Lines and Planes in Space
	10.6 Vector Methods for Measuring Distance in R^3
	Chapter 10 Review
	Group Research Project: Star Trek
11 Vector-Valued Functions
	11.1 Introduction to Vector Functions
	11.2 Differentiation and Integration of Vector Functions
	11.3 Modeling Ballistics and Planetary Motion
	11.4 Unit Tangent and Normal Vectors; Curvature
	11.5 Tangential and Normal Components of Acceleration
	Chapter 11 Review
	Guest Essay: "The Stimulation of Science," Howard Eves
Cumulative Review Problems for Chapters 7-11
12 Partial Differentiation
	12.1 Functions of Several Variables
	12.2 Limits and Continuity
	12.3 Partial Derivatives
	12.4 Tangent Planes, Approximations, and Differentiability
	12.5 Chain Rules
	12.6 Directional Derivatives and the Gradient
	12.7 Extrema of Functions of Two Variables
	12.8 Lagrange Multipliers
	Chapter 12 Review
	Group Research Project: Desertification
13 Multiple Integration
	13.1 Double Integration over Rectangular Regions
	13.2 Double Integration over Nonrectangular Regions
	13.3 Double Integrals in Polar Coordinates
	13.4 Surface Area
	13.5 Triple Integrals
	13.6 Mass, Moments, and Probability Density Functions
	13.7 Cylindrical and Spherical Coordinates
	13.8 Jacobians: Change of Variables
	Chapter 13 Review
	Group Research Project: Space-Capsule Design
14 Vector Analysis
	14.1 Properties of a Vector Field: Divergence and Curl
	14.2 Line Integrals
	14.3 Independence of Path
	14.4 Green's Theorem
	14.5 Surface Integration
	14.6 Stokes' Theorem
	14.7 Divergence Theorem
	Chapter 14 Review
	Guest Essay: "Continuous vs. Discrete Mathematics," William F. Lucas
15 Introduction to Differential Equations
	15.1 First-Order Differential Equations
	15.2 Second-Order Homogeneous Linear Differential Equations
	15.3 Second-Order Nonhomogeneous Linear Differential Equations
	Chapter 15 Review
	Group Research Project: Save the Perch Project
Cumulative Review Problems for Chapters 12-15
Appendices
	A: Introduction to the Theory of Limits
	B: Selected Proofs
	C: Significant Digits
	D: Short Table of Integrals
	E: Answers to Selected Problems
		1 Functions and Graphs
		2 Limits and Continuity
		3 Differentiation
		4 Additional Applications of the Derivative
		5 Integration
		6 Additional Applications of the Integral
		Cumulative Review Problems for Chapters 1-6
		7 Methods of Integration
		8 Infinite Series
		9 Polar Coordinates and Parametric Forms
		10 Vectors in the Plane and in Space
		11 Vector-Valued Functions
		Cumulative Review Problems for Chapters 7-11
		12 Partial Differentiation
		13 Multiple Integration
		14 Vector Analysis
		15 Introduction to Differential Equations
		Cumulative Review Problems for Chapters 12-15
	F: Credits
	Index
Teaching Notes for Instructors
	1 Functions and Graphs
	2 Limits and Continuity
	3 Differentiation
	4 Additional Applications of the Derivative
	5 Integration
	6 Additional Applications of the Integral
	7 Methods of Integration
	8 Infinite Series
	9 Polar Coordinates and Parametric Forms
	10 Vectors in the Plane and in Space
	11 Vector-Valued Functions
	12 Partial Differentiation
	13 Multiple Integration
	14 Vector Analysis
	15 Introduction to Differential Equations
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