Calculus: Early Transcendental Functions

Front Cover
Title Page
Copyright Page
CONTENTS
Preface
	Your Course. Your Way.
1. Preparation for Calculus
	1.1: Graphs and Models
	1.2: Linear Models and Rates of Change
	1.3: Functions and Their Graphs
	1.4: Fitting Models to Data
	1.5: Inverse Functions
	1.6: Exponential and Logarithmic Functions
	Review Exercises
	P.S. Problem Solving
2. Limits and Their Properties
	2.1: A Preview of Calculus
	2.2: Finding Limits Graphically and Numerically
	2.3: Evaluating Limits Analytically
	2.4: Continuity and One-Sided Limits
	2.5: Infinite Limits
	Review Exercises
	P.S. Problem Solving
3. Differentiation
	3.1: The Derivative and the Tangent Line Problem
	3.2: Basic Differentiation Rules and Rates of Change
	3.3: Product and Quotient Rules and Higher-Order Derivatives
	3.4: The Chain Rule
	3.5: Implicit Differentiation
	3.6: Derivatives of Inverse Functions
	3.7: Related Rates
	3.8: Newton\'s Method
	Review Exercises
	P.S. Problem Solving
4. Applications of Differentiation
	4.1: Extrema on an Interval
	4.2: Rolle\'s Theorem and the Mean Value Theorem
	4.3: Increasing and Decreasing Functions and the First Derivative Test
	4.4: Concavity and the Second Derivative Test
	4.5: Limits at Infinity
	4.6: A Summary of Curve Sketching
	4.7: Optimization Problems
	4.8: Differentials
	Review Exercises
	P.S. Problem Solving
5. Integration
	5.1: Antiderivatives and Indefinite Integration
	5.2: Area
	5.3: Riemann Sums and Definite Integrals
	5.4: The Fundamental Theorem of Calculus
	5.5: Integration by Substitution
	5.6: Numerical Integration
	5.7: The Natural Logarithmic Function: Integration
	5.8: Inverse Trigonometric Functions: Integration
	5.9: Hyperbolic Functions
	Review Exercises
	P.S. Problem Solving
6. Differential Equations
	6.1: Slope Fields and Euler\'s Method
	6.2: Differential Equations: Growth and Decay
	6.3: Differential Equations: Separation of Variables
	6.4: The Logistic Equation
	6.5: First-Order Linear Differential Equations
	6.6: Predator-Prey Differential Equations
	Review Exercises
	P.S. Problem Solving
7. Applications of Integration
	7.1: Area of a Region between Two Curves
	7.2: Volume: The Disk Method
	7.3: Volume: The Shell Method
	7.4: Arc Length and Surfaces of Revolution
	7.5: Work
	7.6: Moments, Centers of Mass, and Centroids
	7.7: Fluid Pressure and Fluid Force
	Review Exercises
	P.S. Problem Solving
8. Integration Techniques, L\'Hopital\'s Rule, and Improper Integrals
	8.1: Basic Integration Rules
	8.2: Integration by Parts
	8.3: Trigonometric Integrals
	8.4: Trigonometric Substitution
	8.5: Partial Fractions
	8.6: Integration by Tables and Other Integration Techniques
	8.7: Indeterminate Forms and L\'Hopital\'s Rule
	8.8: Improper Integrals
	Review Exercises
	P.S. Problem Solving
9. Infinite Series
	9.1: Sequences
	9.2: Series and Convergence
	9.3: The Integral Test and p-Series
	9.4: Comparisons of Series
	9.5: Alternating Series
	9.6: The Ratio and Root Tests
	9.7: Taylor Polynomials and Approximations
	9.8: Power Series
	9.9: Representation of Functions by Power Series
	9.10: Taylor and Maclaurin Series
	Review Exercises
	P.S. Problem Solving
10. Conics, Parametric Equations, and Polar Coordinates
	10.1: Conics and Calculus
	10.2: Plane Curves and Parametric Equations
	10.3: Parametric Equations and Calculus
	10.4: Polar Coordinates and Polar Graphs
	10.5: Area and Arc Length in Polar Coordinates
	10.6: Polar Equations of Conics and Kepler\'s Laws
	Review Exercises
	P.S. Problem Solving
11. Vectors and the Geometry of Space
	11.1: Vectors in the Plane
	11.2: Space Coordinates and Vectors in Space
	11.3: The Dot Product of Two Vectors
	11.4: The Cross Product of Two Vectors in Space
	11.5: Lines and Planes in Space
	11.6: Surfaces in Space
	11.7: Cylindrical and Spherical Coordinates
	Review Exercises
	P.S. Problem Solving
12. Vector-Valued Functions
	12.1: Vector-Valued Functions
	12.2: Differentiation and Integration of Vector-Valued Functions
	12.3: Velocity and Acceleration
	12.4: Tangent Vectors and Normal Vectors
	12.5: Arc Length and Curvature
	Review Exercises
	P.S. Problem Solving
13. Functions of Several Variables
	13.1: Introduction to Functions of Several Variables
	13.2: Limits and Continuity
	13.3: Partial Derivatives
	13.4: Differentials
	13.5: Chain Rules for Functions of Several Variables
	13.6: Directional Derivatives and Gradients
	13.7: Tangent Planes and Normal Lines
	13.8: Extrema of Functions of Two Variables
	13.9: Applications of Extrema
	13.10: Lagrange Multipliers
	Review Exercises
	P.S. Problem Solving
14. Multiple Integration
	14.1: Iterated Integrals and Area in the Plane
	14.2: Double Integrals and Volume
	14.3: Change of Variables: Polar Coordinates
	14.4: Center of Mass and Moments of Inertia
	14.5: Surface Area
	14.6: Triple Integrals and Applications
	14.7: Triple Integrals in Other Coordinates
	14.8: Change of Variables: Jacobians
	Review Exercises
	P.S. Problem Solving
15. Vector Analysis
	15.1: Vector Fields
	15.2: Line Integrals
	15.3: Conservative Vector Fields and Independence of Path
	15.4: Green\'s Theorem
	15.5: Parametric Surfaces
	15.6: Surface Integrals
	15.7: Divergence Theorem
	15.8: Stokes\'s Theorem
	Review Exercises
	P.S. Problem Solving
16. Additional Topics in Differential Equations (from WEB)
	16.1 Exact First-Order Equations
	16.1 Exercises
	16.2 Second-Order Homogeneous Linear Equations
	16.2 Exercises
	16.3 Second-Order Nonhomogeneous Linear Equations
	16.3 Exercises
	16.4 Series Solutions of Differential Equations
	16.4 Exercises
	Review Exercises
	P.S. Problem Solving
APPENDICES
	A: Proofs of Selected Theorems
	B: Integration Tables
	C: Precalculus Review
	D: Rotation and the General Second-Degree Equation (from WEB)
	E: Complex Numbers (from WEB)
	F: Business and Economic Applications (from WEB)
	G: Vector Analysis (from WEB)
ANSWERS to Odd-Numbered Exercises
	ch01
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	appC
INDEX
	A
	B
	C
	D
	E
	F
	G
	H, I
	J, K
	L
	M
	N, O, P
	Q
	R
	S
	T
	U, V
	W, X, Y, Z
Index of Applications
Index of Applications (cont\'d)
Derivatives & Integrals
Trigonometry
Algebra
Formulas from Geometry