Skip to main content Skip to main navigation
  1. Home
  2. Mathematics & Statistics
  3. Calculus
  4. Calculus
  5. University Calculus: Early Transcendentals

University Calculus: Early Transcendentals, 4th edition

  • Joel R. Hass
  • Christopher Heil
  • Przemyslaw Bogacki
  • Maurice D. Weir
  • George B. Thomas

Published by Pearson (January 1st 2019) - Copyright © 2020

4th edition

Choose a format

Overview

NOTE: Before purchasing, check with your instructor to ensure you select the correct ISBN. Several versions of the MyLab™ and Mastering™ platforms exist for each title, and registrations are not transferable. To register for and use MyLab or Mastering, you may also need a Course ID, which your instructor will provide.

 

Used books, rentals, and purchases made outside of Pearson

If purchasing or renting from companies other than Pearson, the access codes for the MyLab platform may not be included, may be incorrect, or may be previously redeemed. Check with the seller before completing your purchase.


For 3-semester or 4-quarter͠courses covering single͠variable and multivariable calculus, taken by students of mathematics, engineering, natural sciences, or economics.

This package includes MyLab Math.


Clear, precise, concise

University Calculus: Early Transcendentals helps students generalize and apply the key ideas of calculus through clear and precise explanations, thoughtfully chosen examples, meticulously crafted figures, and superior exercise sets. This text offers the right mix of basic, conceptual, and challenging exercises, along with meaningful applications. In the 4th Edition, new co-authors Chris Heil (Georgia Institute of Technology) and Przemyslaw Bogacki (Old Dominion University) partner with author Joel Hass to preserve the text’s time-tested features while revisiting every word, figure, and MyLab™ question with today’s students in mind. 


Personalize learning with MyLab Math 

By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student. 


0135257727 / 9780135257722 University Calculus: Early Transcendentals Plus MyLab Math - Title-Specific Access Card Package, 4/e

Package consists of:

  • 0134995546 / 9780134995540 University Calculus: Early Transcendentals
  • 0135183715 / 9780135183717 MyLab Math with Pearson eText - Standalone Access Card - for University Calculus: Early Transcendentals

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   One-Sided 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 Cross-Sections

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

9.10Applications of Taylor Series

Questions to Guide Your Review

Practice Exercises

Additional and Advanced Exercises 

 

10.    Parametric Equations and Polar Coordinates

10.1Parametrizations of Plane Curves

10.2Calculus 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    Three-Dimensional 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.    Vector-Valued Functions and Motion in Space

12.1Curves 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

13.8Lagrange 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.    First-Order Differential Equations (online at  bit.ly/2pzYlEq)

16.1    Solutions, Slope Fields, and Euler’s Method

16.2    First-Order Linear Equations

16.3    Applications

16.4    Graphical Solutions of Autonomous Equations

16.5    Systems of Equations and Phase Planes 


17.    Second-Order Differential Equations (online at bit.ly/2IHCJyE)

17.1    Second-Order Linear Equations

17.2    Non-homogeneous Linear Equations

17.3    Applications

17.4    Euler Equations

17.5    Power-Series Solutions


Appendix

A.1 Real Numbers and the Real Line

A.2 Mathematical Induction AP-6

A.3 Lines and Circles AP-10

A.4 Conic Sections AP-16

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

For teachers

All the material you need to teach your courses.

Discover teaching material