University Calculus

Series
Pearson
Author
Joel R. Hass / Maurice D. Weir / George B. Thomas  
Publisher
Pearson
Cover
Softcover
Edition
3
Language
English
Total pages
552
Pub.-date
December 2014
ISBN13
9780321999603
ISBN
0321999606



Description

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

 

University Calculus, Early Transcendentals, Multivariable, Third Edition 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. This revision features more examples, more mid-level exercises, more figures, improved conceptual flow, and the best in technology for learning and teaching.

 

Also Available with MyMathLab

MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. MyMathLab includes thousands of assignable algorithmic exercises, the complete eBook, tutorial videos, tools to personalize learning, and more.

 

Features

About the Book

  • The exercises are known for their breadth and quality, with carefully constructed exercise sets that progress from skills problems to applied and theoretical problems. The text contains more than 8,000 exercises in all. End-of-chapter exercises feature review questions, practice exercises covering the entire chapter, and a series of Additional and Advanced Exercises.
  • Figures are conceived and rendered to support conceptual reasoning and provide insight for students. They are also consistently captioned to aid understanding.
  • The use of theorems and proofs is essential to convey the methods and language of mathematics, and in this text results are both carefully stated and proved throughout. At the same time, ideas are introduced with examples and intuitive explanations that are then generalized so that students are not overwhelmed by abstraction. 
  • Key topics, such as the definition of the derivative, are presented both informally and formally. The distinction between the two is clearly stated as each is developed, including an explanation as to why a formal definition is needed. Great care has been taken to point out when intuition is being developed and when ideas are formally stated.   
  • Proofs of major theorems are given, but instructors in some cases may not cover the proofs and focus on content and applications instead.  The book is designed so that instructors can choose how much formal mathematics their students can absorb. The text therefore provides options for the instructor to set the level of rigor for their class.
  • Within examples, the authors include explanatory notes that guide longer computations.  The goal is to indicate to students the steps needed to get from one line of a computation to the next, so that students can focus on the main concept being explained rather than being hung up on why one step follows from another.
  • The flexible table of contents divides complex topics into manageable sections, allowing instructors to tailor their course to meet the specific needs of their students. For example, the precise definition of the limit is contained in its own section and may be skipped.
  • Complete and precise multivariable coverage enhances the connections of multivariable ideas with their single-variable analogues studied earlier in the book.
  • A complete suite of instructor and student supplements saves class preparation time for instructors and improves students’ learning.

 

Also available with MyMathLab 

MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. The MyLabCourse for this text includes all of the following and more:

  • Over 9,000 assignable algorithmic exercises allow you to craft the right assignments for students. NEW! The Third Edition includes hundreds of new assignable exercises to better help you meet student needs.
  • Complete eBook, available to students for the life of the edition.
  • Java applets for multivariable calculus help students visualize and explore concepts.
  • NEW! More than 100 new tutorial videos (over 8 hours’ worth), created by experienced calculus professors, provide help to students beyond office hours. The creators of the videos wanted to avoid the sort of "cookbook" videos that are so prevalent on the Internet, but at the same time realize that students usually seek out videos when they are stuck on specific problems. So they do cover key examples, but in doing so, they address the conceptual underpinnings that are so important to student success in the course.
  • NEW! Integrated Review tools address gaps in prerequisite skills that often impede success in the course. Students can use this content independently, or instructors can target individual student needs by using the built-in diagnostic quizzes and Personalized Homework. MyMathLab provides just-in-time help for skill gaps so that instructors can focus on teaching calculus.

 

New to this Edition

New and updated content and features

  • Updated and added numerous exercises throughout, with emphasis on the mid-level and more in the life science areas
  • Many figures are reworked and many new ones have been added
  • The discussion of conditional convergence has been moved to follow the Alternating Series Test
  • Enhanced! The discussion defining differentiability for functions of several variables now includes more emphasis on linearization
  • The authors show that the derivative along a path generalizes the single-variable chain rule
  • More geometric insight is added to the presentation of the idea of multiple integrals and the meaning of the Jacobian in substitutions for their evaluations
  • Surface integrals of vector fields are developed as generalizations of line integrals
  • The authors have extended and clarified the discussion of the curl and divergence, and added new figures to help visualize their meanings

 

Also available with MyMathLab

MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. MyMathLab includes thousands of assignable algorithmic exercises, the complete eBook, tutorial videos, tools to personalize learning, and more. New features of the MyMathLab course for this edition include the following:

  • Hundreds of new assignable exercises help you better meet student needs.
  • More than 100 new tutorial videos (over 8 hours’ worth), created by experienced calculus professors, provide help to students beyond office hours. The creators of the videos wanted to avoid the sort of "cookbook" videos that are so prevalent on the Internet, but at the same time realize that students usually seek out videos when they are stuck on specific problems. So they do cover key examples, but in doing so, they address the conceptual underpinnings that are so important to student success in the course.
  • Integrated Review tools address gaps in prerequisite skills that often impede success in the course. Students can use this content independently, or instructors can target individual student needs by using the built-in diagnostic quizzes and Personalized Homework. MyMathLab provides just-in-time help for skill gaps so that instructors can focus on teaching calculus.

 

Table of Contents

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 The Binomial Series and Applications of Taylor Series

 

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 in Polar Coordinates

10.5 Areas and Lengths in Polar Coordinates

10.6 Conics in Polar Coordinates

 

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

 

12. Vector-Valued 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

 

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 Multipliers

 

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 Moments and Centers of Mass

14.7 Triple Integrals in Cylindrical and Spherical Coordinates

14.8 Substitutions in Multiple Integrals

 

15. Integration in Vector Fields

15.1 Line Integrals

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

 

16. First-Order Differential Equations (Online)

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)

17.1 Second-Order Linear Equations

17.2 Nonhomogeneous Linear Equations

17.3 Applications

17.4 Euler Equations

17.5 Power Series Solutions

 

Author

Joel Hass received his PhD from the University of California—Berkeley. He is currently a professor of mathematics at the University of California—Davis. He has coauthored six widely used calculus texts as well as two calculus study guides. He is currently on the editorial board of Geometriae Dedicata and Media-Enhanced Mathematics. He has been a member of the Institute for Advanced Study at Princeton University and of the Mathematical Sciences Research Institute, and he was a Sloan Research Fellow. Hass’s current areas of research include the geometry of proteins, three dimensional manifolds, applied math, and computational complexity. In his free time, Hass enjoys kayaking.

 

Maurice D. Weir holds a DA and MS from Carnegie-Mellon University and received his BS at Whitman College. He is a Professor Emeritus of the Department of Applied Mathematics at the Naval Postgraduate School in Monterey, California. Weir enjoys teaching Mathematical Modeling and Differential Equations. His current areas of research include modeling and simulation as well as mathematics education. Weir has been awarded the Outstanding Civilian Service Medal, the Superior Civilian Service Award, and the Schieffelin Award for Excellence in Teaching. He has coauthored eight books, including the University Calculus series and Thomas’ Calculus.