Calculus: Early Transcendentals, 3rd edition
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Overview
Calculus features clear, instructional narrative and a wealth of meticulously crafted exercise sets. Examples are stepped out and thoughtfully annotated, and figures are designed to help you learn important concepts.
Published by Pearson (September 1st 2020)  Copyright © 2021
ISBN13: 9780136880677
Subject: Calculus
Category: Calculus
Table of contents
Table of Contents
 Functions
 1.1 Review of Functions
 1.2 Representing Functions
 1.3 Inverse, Exponential, and Logarithmic Functions
 1.4 Trigonometric Functions and Their Inverses
 Review Exercises

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

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 Derivatives of Logarithmic and Exponential Functions
 3.10 Derivatives of Inverse Trigonometric Functions
 3.11 Related Rates
 Review Exercises
 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
 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
 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
 Logarithmic, Exponential, and Hyperbolic Functions
 7.1 Logarithmic and Exponential Functions Revisited
 7.2 Exponential Models
 7.3 Hyperbolic Functions
 Review Exercises
 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
 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
 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
 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
 Parametric and Polar Curves
 12.1 Parametric Equations
 12.2 Polar Coordinates
 12.3 Calculus in Polar Coordinates
 12.4 Conic Sections
 Review Exercises
 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
 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
 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
 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
 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
Appendix A. Proofs of Selected Theorems
Appendix B. Algebra Review ONLINE
Appendix C. Complex Numbers ONLINE
Answers
Index
Table of Integrals
Your questions answered
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