Calculus. Concepts and Contexts

Cover
Contents
Preface
To the Student
About the Author
Diagnostic Tests
A Preview of Calculus
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
	1.6 Parametric Curves
	1 Review
	Principles of Problem Solving
Chapter 2: Limits
	2.1 The Tangent and Velocity Problems
	2.2 The Limit of a Function
	2.3 Calculating Limits Using the Limit Laws
	2.4 Continuity
	2.5 Limits Involving Infinity
	2.6 Derivatives and Rates of Change
	2.7 The Derivative as a Function
	2 Review
	Focus on Problem Solving
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 Inverse Trigonometric Functions and Their Derivatives
	3.7 Derivatives of Logarithmic Functions
	3.8 Rates of Change in the Natural and Social Sciences
	3.9 Linear Approximations and Differentials
	3 Review
	Focus on Problem Solving
Chapter 4: Applications of Differentiation
	4.1 Related Rates
	4.2 Maximum and Minimum Values
	4.3 Derivatives and the Shapes of Curves
	4.4 Graphing with Calculus and Technology
	4.5 Indeterminate Forms and L\'Hospital\'s Rule
	4.6 Optimization Problems
	4.7 Newton\'s Method
	4.8 Antiderivatives
	4 Review
	Focus on Problem Solving
Chapter 5: Integrals
	5.1 Areas and Distances
	5.2 The Definite Integral
	5.3 Evaluating Definite Integrals
	5.4 The Fundamental Theorem of Calculus
	5.5 The Substitution Rule
	5.6 Integration by Parts
	5.7 Additional Techniques of Integration
	5.8 Integration Using Tables and Computer Algebra Systems
	5.9 Approximate Integration
	5.10 Improper Integrals
	5 Review
	Focus on Problem Solving
Chapter 6: Applications of Integration
	6.1 More about Areas
	6.2 Volumes
	6.3 Volumes by Cylindrical Shells
	6.4 Arc Length
	6.5 Average Value of a Function
	6.6 Applications to Physics and Engineering
	6.7 Applications to Economics and Biology
	6.8 Probability
	6 Review
	Focus on Problem Solving
Chapter 7: Differential Equations
	7.1 Modeling with Differential Equations
	7.2 Slope Fields and Euler\'s Method
	7.3 Separable Equations
	7.4 Exponential Growth and Decay
	7.5 The Logistic Equation
	7.6 Predator-Prey Systems
	7 Review
	Focus on Problem Solving
Chapter 8: Infinite Sequences and Series
	8.1 Sequences
	8.2 Series
	8.3 The Integral and Comparison Tests; Estimating Sums
	8.4 Other Convergence Tests
	8.5 Power Series
	8.6 Representations of Functions as Power Series
	8.7 Taylor and Maclaurin Series
	8.8 Applications of Taylor Polynomials
	8 Review
	Focus on Problem Solving
Chapter 9: Vectors and the Geometry of Space
	9.1 Three-Dimensional Coordinate Systems
	9.2 Vectors
	9.3 The Dot Product
	9.4 The Cross Product
	9.5 Equations of Lines and Planes
	9.6 Functions and Surfaces
	9.7 Cylindrical and Spherical Coordinates
	9 Review
	Focus on Problem Solving
Chapter 10: Vector Functions
	10.1 Vector Functions and Space Curves
	10.2 Derivatives and Integrals of Vector Functions
	10.3 Arc Length and Curvature
	10.4 Motion in Space: Velocity and Acceleration
	10.5 Parametric Surfaces
	10 Review
	Focus on Problem Solving
Chapter 11: Partial Derivatives
	11.1 Functions of Several Variables
	11.2 Limits and Continuity
	11.3 Partial Derivatives
	11.4 Tangent Planes and Linear Approximations
	11.5 The Chain Rule
	11.6 Directional Derivatives and the Gradient Vector
	11.7 Maximum and Minimum Values
	11.8 Lagrange Multipliers
	11 Review
	Focus on Problem Solving
Chapter 12: Multiple Integrals
	12.1 Double Integrals over Rectangles
	12.2 Iterated Integrals
	12.3 Double Integrals over General Regions
	12.4 Double Integrals in Polar Coordinates
	12.5 Applications of Double Integrals
	12.6 Surface Area
	12.7 Triple Integrals
	12.8 Triple Integrals in Cylindrical and Spherical Coordinates
	12.9 Change of Variables in Multiple Integrals
	12 Review
	Focus on Problem Solving
Chapter 13: Vector Calculus
	13.1 Vector Fields
	13.2 Line Integrals
	13.3 The Fundamental Theorem for Line Integrals
	13.4 Green\'s Theorem
	13.5 Curl and Divergence
	13.6 Surface Integrals
	13.7 Stokes\' Theorem
	13.8 The Divergence Theorem
	13.9 Summary
	13 Review
	Focus on Problem Solving
Appendixes
	Appendix A: Intervals, Inequalities, and Absolute Values
	Appendix B: Coordinate Geometry
	Appendix C: Trigonometry
	Appendix D: Precise Definitions of Limits
	Appendix E: A Few Proofs
	Appendix F: Sigma Notation
	Appendix G: Integration of Rational Functions by Partial Fractions
	Appendix H: Polar Coordinates
	Appendix I: Complex Numbers
	Appendix J: Answers to Odd-Numbered Exercises
Index