Calculus with calcChat Calcview 12th ed

Cover
Contents
Preface
Student Resources
Instructor Resources
Acknowledgments
Chapter P: Preparation for Calculus
	P.1 Graphs and Models
	P.2 Linear Models and Rates of Change
	P.3 Functions and Their Graphs
	P.4 Review of Trigonometric Functions
	Review Exercises
	P.S. Problem Solving
Chapter 1: Limits and Their Properties
	1.1 A Preview of Calculus
	1.2 Finding Limits Graphically and Numerically
	1.3 Evaluating Limits Analytically
	1.4 Continuity and One-Sided Limits
	1.5 Infinite Limits
	Review Exercises
	P.S. Problem Solving
Chapter 2: Differentiation
	2.1 The Derivative and the Tangent Line Problem
	2.2 Basic Differentiation Rules and Rates of Change
	2.3 Product and Quotient Rules and Higher-Order Derivatives
	2.4 The Chain Rule
	2.5 Implicit Differentiation
	2.6 Related Rates
	Review Exercises
	P.S. Problem Solving
Chapter 3: Applications of Differentiation
	3.1 Extrema on an Interval
	3.2 Rolle\'s Theorem and the Mean Value Theorem
	3.3 Increasing and Decreasing Functions and the First Derivative Test
	3.4 Concavity and the Second Derivative Test
	3.5 Limits at Infinity
	3.6 A Summary of Curve Sketching
	3.7 Optimization Problems
	3.8 Newton\'s Method
	3.9 Differentials
	Review Exercises
	P.S. Problem Solving
Chapter 4: Integration
	4.1 Antiderivatives and Indefinite Integration
	4.2 Area
	4.3 Riemann Sums and Definite Integrals
	4.4 The Fundamental Theorem of Calculus
	4.5 Integration by Substitution
	Review Exercises
	P.S. Problem Solving
Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions
	5.1 The Natural Logarithmic Function: Differentiation
	5.2 The Natural Logarithmic Function: Integration
	5.3 Inverse Functions
	5.4 Exponential Functions: Differentiation and Integration
	5.5 Bases Other Than e and Applications
	5.6 Indeterminate Forms and L\'Hopital\'s Rule
	5.7 Inverse Trigonometric Functions: Differentiation
	5.8 Inverse Trigonometric Functions: Integration
	5.9 Hyperbolic Functions
	Review Exercises
	P.S. Problem Solving
Chapter 6: Differential Equations
	6.1 Slope Fields and Euler\'s Method
	6.2 Growth and Decay
	6.3 Separation of Variables and the Logistic Equation
	6.4 First-Order Linear Differential Equations
	Review Exercises
	P.S. Problem Solving
Chapter 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
Chapter 8: Integration Techniques 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 Numerical Integration
	8.7 Integration by Tables and Other Integration Techniques
	8.8 Improper Integrals
	Review Exercises
	P.S. Problem Solving
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Appendices
	Appendix A: Proofs of Selected Theorems
	Appendix B: Integration Tables
Answers to Odd-Numbered Exercises
Index