Calculus, 3rd edition
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Overview
Calculus builds from a foundation of strong exercise sets, then draws you into the narrative through writing that reflects an instructor's voice. Examples are stepped out and thoroughly annotated, and figures are designed carefully to work with the content. The 3rd Edition introduces important advances and refinements while retaining its proven hallmark features. Extensively revised exercise sets are rearranged and relabeled, with some modified and other new ones added. Chapter Review exercises are thoroughly revised to provide more exercises (more than 26% are new), more intermediatelevel problems, and more opportunities to choose a strategy of solution.
Published by Pearson (March 17th 2021)  Copyright © 2021
ISBN13: 9780136880639
Subject: Calculus
Category: Calculus
Overview
1. Functions
 1.1 Review of Functions
 1.2 Representing Functions
 1.3 Trigonometric Functions
 Review Exercises
2. Limits
 2.1 The Idea of Limits
 2.2 Definitions of Limits
 2.3 Techniques for Computing Limits
 2.4 Infinite Limits
 2.5 Limits at Infinity
 2.6 Continuity
 2.7 Precise Definitions of Limits
 Review Exercises
3. Derivatives
 3.1 Introducing the Derivative
 3.2 The Derivative as a Function
 3.3 Rules of Differentiation
 3.4 The Product and Quotient Rules
 3.5 Derivatives of Trigonometric Functions
 3.6 Derivatives as Rates of Change
 3.7 The Chain Rule
 3.8 Implicit Differentiation
 3.9 Related Rates
 Review Exercises
4. Applications of the Derivative
 4.1 Maxima and Minima
 4.2 Mean Value Theorem
 4.3 What Derivatives Tell Us
 4.4 Graphing Functions
 4.5 Optimization Problems
 4.6 Linear Approximation and Differentials
 4.7 L'Hôpital's Rule
 4.8 Newton's Method
 4.9 Antiderivatives
 Review Exercises
5. Integration
 5.1 Approximating Areas under Curves
 5.2 Definite Integrals
 5.3 Fundamental Theorem of Calculus
 5.4 Working with Integrals
 5.5 Substitution Rule
 Review Exercises
6. Applications of Integration
 6.1 Velocity and Net Change
 6.2 Regions Between Curves
 6.3 Volume by Slicing
 6.4 Volume by Shells
 6.5 Length of Curves
 6.6 Surface Area
 6.7 Physical Applications
 Review Exercises
7. Logarithmic and Exponential Functions
 7.1 Inverse Functions
 7.2 The Natural Logarithmic and Exponential Functions
 7.3 Logarithmic and Exponential Functions with Other Bases
 7.4 Exponential Models
 7.5 Inverse Trigonometric Functions
 7.6 L' Hôpital's Rule and Growth Rates of Functions
 7.7 Hyperbolic Functions
 Review Exercises
8. Integration Techniques
 8.1 Basic Approaches
 8.2 Integration by Parts
 8.3 Trigonometric Integrals
 8.4 Trigonometric Substitutions
 8.5 Partial Fractions
 8.6 Integration Strategies
 8.7 Other Methods of Integration
 8.8 Numerical Integration
 8.9 Improper Integrals
 Review Exercises
9. Differential Equations
 9.1 Basic Ideas
 9.2 Direction Fields and Euler's Method
 9.3 Separable Differential Equations
 9.4 Special FirstOrder Linear Differential Equations
 9.5 Modeling with Differential Equations
 Review Exercises
10. Sequences and Infinite Series
 10.1 An Overview
 10.2 Sequences
 10.3 Infinite Series
 10.4 The Divergence and Integral Tests
 10.5 Comparison Tests
 10.6 Alternating Series
 10.7 The Ratio and Root Tests
 10.8 Choosing a Convergence Test
 Review Exercises
11. Power Series
 11.1 Approximating Functions with Polynomials
 11.2 Properties of Power Series
 11.3 Taylor Series
 11.4 Working with Taylor Series
 Review Exercises
12. Parametric and Polar Curves
 12.1 Parametric Equations
 12.2 Polar Coordinates
 12.3 Calculus in Polar Coordinates
 12.4 Conic Sections
 Review Exercises
13. Vectors and the Geometry of Space
 13.1 Vectors in the Plane
 13.2 Vectors in Three Dimensions
 13.3 Dot Products
 13.4 Cross Products
 13.5 Lines and Planes in Space
 13.6 Cylinders and Quadric Surfaces
 Review Exercises
14. VectorValued Functions
 14.1 VectorValued Functions
 14.2 Calculus of VectorValued Functions
 14.3 Motion in Space
 14.4 Length of Curves
 14.5 Curvature and Normal Vectors
 Review Exercises
15. Functions of Several Variables
 15.1 Graphs and Level Curves
 15.2 Limits and Continuity
 15.3 Partial Derivatives
 15.4 The Chain Rule
 15.5 Directional Derivatives and the Gradient
 15.6 Tangent Planes and Linear Approximation
 15.7 Maximum/Minimum Problems
 15.8 Lagrange Multipliers
 Review Exercises
16. Multiple Integration
 16.1 Double Integrals over Rectangular Regions
 16.2 Double Integrals over General Regions
 16.3 Double Integrals in Polar Coordinates
 16.4 Triple Integrals
 16.5 Triple Integrals in Cylindrical and Spherical Coordinates
 16.6 Integrals for Mass Calculations
 16.7 Change of Variables in Multiple Integrals
 Review Exercises
17. Vector Calculus
 17.1 Vector Fields
 17.2 Line Integrals
 17.3 Conservative Vector Fields
 17.4 Green's Theorem
 17.5 Divergence and Curl
 17.6 Surface Integrals
 17.7 Stokes' Theorem
 17.8 Divergence Theorem
 Review Exercises
D2 SecondOrder Differential Equations ONLINE
 D2.1 Basic Ideas
 D2.2 Linear Homogeneous Equations
 D2.3 Linear Nonhomogeneous Equations
 D2.4 Applications
 D2.5 Complex Forcing Functions
 Review Exercises
APPENDICES
 Proofs of Selected Theorems
 Algebra Review ONLINE
 Complex Numbers ONLINE
Answers
Index
Table of Integrals
Your questions answered
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