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

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 1-semester or 2-quarter courses in multivariable calculus for math, science, and engineering majors.

This package includes MyLab Math.


Clear, precise, concise

University Calculus: Early Transcendentals, Multivariable 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. 


0135308054 / 9780135308059 University Calculus, Multivariable plus MyLab Math with Pearson eText - Access Card Package

Package consists of:

  • 0135165113 / 9780135165119 University Calculus: Early Transcendentals, Multivariable
  • 0135183715 / 9780135183717 MyLab Math with Pearson eText - Standalone Access Card - for University Calculus: Early Transcendentals



Table of contents

1.      Infinite Sequences and Series

1.1   Sequences

1.2   Infinite Series

1.3   The Integral Test

1.4   Comparison Tests

1.5   Absolute Convergence; The Ratio and Root Tests

1.6   Alternating Series and Conditional Convergence

1.7   Power Series

1.8   Taylor and Maclaurin Series

1.9   Convergence of Taylor Series

1.10  Applications of Taylor Series

Questions to Guide Your Review

Practice Exercises

Additional and Advanced Exercises 

 

2.      Parametric Equations and Polar Coordinates

2.1    Parametrizations of Plane Curves

2.2    Calculus with Parametric Curves

2.3    Polar Coordinates

2.4    Graphing Polar Coordinate Equations 

2.5    Areas and Lengths in Polar Coordinates

Questions to Guide Your Review

Practice Exercises

Additional and Advanced Exercises


3.    Vectors and the Geometry of Space

3.1    Three-Dimensional Coordinate Systems

3.2    Vectors

3.3    The Dot Product

3.4    The Cross Product

3.5    Lines and Planes in Space

3.6    Cylinders and Quadric Surfaces

Questions to Guide Your Review

Practice Exercises

Additional and Advanced Exercises

 

4.    Vector-Valued Functions and Motion in Space

4.1Curves in Space and Their Tangents

4.2    Integrals of Vector Functions; Projectile Motion

4.3    Arc Length in Space

4.4    Curvature and Normal Vectors of a Curve  

4.5    Tangential and Normal Components of Acceleration

4.6    Velocity and Acceleration in Polar Coordinates

Questions to Guide Your Review

Practice Exercises

Additional and Advanced Exercises

 

5.    Partial Derivatives        

5.1    Functions of Several Variables

5.2    Limits and Continuity in Higher Dimensions

5.3    Partial Derivatives 

5.4    The Chain Rule

5.5    Directional Derivatives and Gradient Vectors

5.6    Tangent Planes and Differentials

5.7    Extreme Values and Saddle Points

5.8Lagrange Multiplier

Questions to Guide Your Review

Practice Exercises

Additional and Advanced Exercises

 

6.    Multiple Integrals

6.1    Double and Iterated Integrals over Rectangles

6.2    Double Integrals over General Regions

6.3    Area by Double Integration

6.4    Double Integrals in Polar Form

6.5    Triple Integrals in Rectangular Coordinates

6.6    Applications

6.7    Triple Integrals in Cylindrical and Spherical Coordinates

6.8    Substitutions in Multiple Integrals

Questions to Guide Your Review

Practice Exercises

Additional and Advanced Exercises


7.    Integrals and Vector Fields

7.1    Line Integrals of Scalar Functions

7.2    Vector Fields and Line Integrals: Work, Circulation, and Flux

7.3    Path Independence, Conservative Fields, and Potential Functions

7.4    Green’s Theorem in the Plane

7.5    Surfaces and Area

7.6    Surface Integrals

7.7    Stokes’ Theorem

7.8    The Divergence Theorem and a Unified Theory

Questions to Guide Your Review

Practice Exercises

Additional and Advanced Exercises


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