University Calculus: Early Transcendentals, 4th edition
Choose the option that's right for you
Single
$9.99 / mo
4month minimum term for $39.96
 Access this eText title
 Up to 2 devices
 Discounted tutor access
Multi
$14.99 / mo
4month minimum term for $59.96
 Access over 1,500 titles
 Up to 2 devices
 Discounted tutor access
Learn more, spend less

Learn anytime, anywhere
Get the app to access your eText whenever you need it

Make it your own
Your notes. Your highlights. Your eText

Find it fast
Quickly navigate your eText with search

Stay organized
Access all your eTexts in one place

Easily continue access
Keep learning with autorenew
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
1. 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
2. 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
3. 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
4. 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
5. 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
6. 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
7. 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
8. 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
9. 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
10. 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
11. 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
12. 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
13. 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
14. 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
15. 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
16. 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
17. 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 AP6
A.3. Lines and Circles AP10
A.4. Conic Sections AP16
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
Your questions answered
Introducing Pearson+. Reimagined learning, designed for you. Choose from one eText or over 1,500 eTexts and study tools, all in one place, for one low monthly subscription. A new way to buy books that fits your budget. Make the most of your study time with offline access, enhanced search, notes and flashcards — to get organized, get the work done quicker and get results. Plus, with the app, put textbooks in your pocket and learn wherever. It's time to upgrade the textbook and simplify learning, so you can have time to live too.
Pearson eText is an easytouse digital textbook available from Pearson+. Make it your own by adding notes and highlights. Download the Pearson+ mobile app to learn on the go, even offline. Listen on the go with our new audiobook feature, available for most titles.
When you choose a plan, you're signing up for a 4month 'term'. We will charge your payment method each month until your 4month term has ended. You can turn on autorenew in My account at any time to continue your subscription before your 4month term has ended.
When you purchase a Pearson+ subscription, it will last 4 months. Before your initial 4month term ends, you can extend your subscription by turning autorenew on in My account. If you turn autorenew on, we’ll automatically renew your subscription and charge you every month until you turn off autorenew.
To avoid the next payment charge, make sure you turn auto renewal off 1 day before the auto renewal date. You can subscribe again after autorenew has been turned off by purchasing another Pearson+ subscription. We use your credit card to renew your subscription automatically. To make sure your learning is uninterrupted, please check your card details before your first monthly payment.
With a Multi Pearson+ subscription plan, you can download up to 5 titles on the Pearson+ app from My list on each of your authorized devices every month.
When you're using your Multi Pearson+ subscription plan in a browser, you can select and read from as many titles as you like.