University Calculus: Early Transcendentals, 4th edition
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Overview
University Calculus: Early Transcendentals helps you generalize and apply key ideas of calculus through clear and precise explanations, examples, figures, and exercise sets.
Published by Pearson (July 15th 2020)  Copyright © 2020
ISBN13: 9780136880912
Subject: Calculus
Category: Calculus
Table of contents
Table of Contents
 Functions
 1.1 Functions and Their Graphs
 1.2 Combining Functions; Shifting and Scaling Graphs
 1.3 Trigonometric Functions
 1.4 Graphing with Software
 1.5 Exponential Functions
 1.6 Inverse Functions and Logarithms
 Limits and Continuity
 2.1 Rates of Change and Tangent Lines to Curves
 2.2 Limit of a Function and Limit Laws
 2.3 The Precise Definition of a Limit
 2.4 OneSided Limits
 2.5 Continuity
 2.6 Limits Involving Infinity; Asymptotes of Graphs
 Questions to Guide Your Review
 Practice Exercises
 Additional and Advanced Exercises
 Derivatives
 3.1 Tangent Lines and the Derivative at a Point
 3.2 The Derivative as a Function
 3.3 Differentiation Rules
 3.4 The Derivative as a Rate of Change
 3.5 Derivatives of Trigonometric Functions
 3.6 The Chain Rule
 3.7 Implicit Differentiation
 3.8 Derivatives of Inverse Functions and Logarithms
 3.9 Inverse Trigonometric Functions
 3.10 Related Rates
 3.11 Linearization and Differentials
 Questions to Guide Your Review
 Practice Exercises
 Additional and Advanced Exercises
 Applications of Derivatives
 4.1 Extreme Values of Functions on Closed Intervals
 4.2 The Mean Value Theorem
 4.3 Monotonic Functions and the First Derivative Test
 4.4 Concavity and Curve Sketching
 4.5 Indeterminate Forms and L’Hôpital’s Rule
 4.6 Applied Optimization
 4.7 Newton’s Method
 4.8 Antiderivatives
 Questions to Guide Your Review
 Practice Exercises
 Additional and Advanced Exercises
 Integrals
 5.1 Area and Estimating with Finite Sums
 5.2 Sigma Notation and Limits of Finite Sums
 5.3 The Definite Integral
 5.4 The Fundamental Theorem of Calculus
 5.5 Indefinite Integrals and the Substitution Method
 5.6 Definite Integral Substitutions and the Area Between Curves
 Questions to Guide Your Review
 Practice Exercises
 Additional and Advanced Exercises
 Applications of Definite Integrals
 6.1 Volumes Using CrossSections
 6.2 Volumes Using Cylindrical Shells
 6.3 Arc Length
 6.4 Areas of Surfaces of Revolution
 6.5 Work
 6.6 Moments and Centers of Mass
 Questions to Guide Your Review
 Practice Exercises
 Additional and Advanced Exercises
 Integrals and Transcendental Functions
 7.1 The Logarithm Defined as an Integral
 7.2 Exponential Change and Separable Differential Equations
 7.3 Hyperbolic Functions
 Questions to Guide Your Review
 Practice Exercises
 Additional and Advanced Exercises
 Techniques of Integration
 8.1 Integration by Parts
 8.2 Trigonometric Integrals
 8.3 Trigonometric Substitutions
 8.4 Integration of Rational Functions by Partial Fractions
 8.5 Integral Tables and Computer Algebra Systems
 8.6 Numerical Integration
 8.7 Improper Integrals
 Questions to Guide Your Review
 Practice Exercises
 Additional and Advanced Exercises
 Infinite Sequences and Series
 9.1 Sequences
 9.2 Infinite Series
 9.3 The Integral Test
 9.4 Comparison Tests
 9.5 Absolute Convergence; The Ratio and Root Tests
 9.6 Alternating Series and Conditional Convergence
 9.7 Power Series
 9.8 Taylor and Maclaurin Series
 9.9 Convergence of Taylor Series
 9.10 Applications of Taylor Series
 Questions to Guide Your Review
 Practice Exercises
 Additional and Advanced Exercises
 Parametric Equations and Polar Coordinates
 10.1 Parametrizations of Plane Curves
 10.2 Calculus with Parametric Curves
 10.3 Polar Coordinates
 10.4 Graphing Polar Coordinate Equations
 10.5 Areas and Lengths in Polar Coordinates
 Questions to Guide Your Review
 Practice Exercises
 Additional and Advanced Exercises
 Vectors and the Geometry of Space
 11.1 ThreeDimensional Coordinate Systems
 11.2 Vectors
 11.3 The Dot Product
 11.4 The Cross Product
 11.5 Lines and Planes in Space
 11.6 Cylinders and Quadric Surfaces
 Questions to Guide Your Review
 Practice Exercises
 Additional and Advanced Exercises
 VectorValued Functions and Motion in Space
 12.1 Curves in Space and Their Tangents
 12.2 Integrals of Vector Functions; Projectile Motion
 12.3 Arc Length in Space
 12.4 Curvature and Normal Vectors of a Curve
 12.5 Tangential and Normal Components of Acceleration
 12.6 Velocity and Acceleration in Polar Coordinates
 Questions to Guide Your Review
 Practice Exercises
 Additional and Advanced Exercises
 Partial Derivatives
 13.1 Functions of Several Variables
 13.2 Limits and Continuity in Higher Dimensions
 13.3 Partial Derivatives
 13.4 The Chain Rule
 13.5 Directional Derivatives and Gradient Vectors
 13.6 Tangent Planes and Differentials
 13.7 Extreme Values and Saddle Points
 13.8 Lagrange Multiplier
 Questions to Guide Your Review
 Practice Exercises
 Additional and Advanced Exercises
 Multiple Integrals
 14.1 Double and Iterated Integrals over Rectangles
 14.2 Double Integrals over General Regions
 14.3 Area by Double Integration
 14.4 Double Integrals in Polar Form
 14.5 Triple Integrals in Rectangular Coordinates
 14.6 Applications
 14.7 Triple Integrals in Cylindrical and Spherical Coordinates
 14.8 Substitutions in Multiple Integrals
 Questions to Guide Your Review
 Practice Exercises
 Additional and Advanced Exercises
 Integrals and Vector Fields
 15.1 Line Integrals of Scalar Functions
 15.2 Vector Fields and Line Integrals: Work, Circulation, and Flux
 15.3 Path Independence, Conservative Fields, and Potential Functions
 15.4 Green’s Theorem in the Plane
 15.5 Surfaces and Area
 15.6 Surface Integrals
 15.7 Stokes’ Theorem
 15.8 The Divergence Theorem and a Unified Theory
 Questions to Guide Your Review
 Practice Exercises
 Additional and Advanced Exercises
 FirstOrder Differential Equations (online at bit.ly/2pzYlEq)
 16.1 Solutions, Slope Fields, and Euler’s Method
 16.2 FirstOrder Linear Equations
 16.3 Applications
 16.4 Graphical Solutions of Autonomous Equations
 16.5 Systems of Equations and Phase Planes
 SecondOrder Differential Equations (online at bit.ly/2IHCJyE)
 17.1 SecondOrder Linear Equations
 17.2 Nonhomogeneous Linear Equations
 17.3 Applications
 17.4 Euler Equations
 17.5 PowerSeries Solutions
Appendix
 A.1 Real Numbers and the Real Line
 A.2 Mathematical Induction
 A.3 Lines and Circles
 A.4 Conic Sections
 A.5 Proofs of Limit Theorems
 A.6 Commonly Occurring Limits
 A.7 Theory of the Real Numbers
 A.8 Complex Numbers
 A.9 The Distributive Law for Vector Cross Products
 A.10 The Mixed Derivative Theorem and the increment Theorem
Additional Topics (online at bit.ly/2IDDl8w)
 B.1 Relative Rates of Growth
 B.2 Probability
 B.3 Conics in Polar Coordinates
 B.4 Taylor’s Formula for Two Variables
 B.5 Partial Derivatives with Constrained Variables
Odd Answers
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