Thomas' Calculus, Multivariable by Joel R. Hass

Thomas' Calculus, Multivariable

byJoel R. Hass, Christopher D. Heil, Maurice D. Weir

Paperback | January 1, 2017

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For the multivariable component of three-semester or four-quarter courses in Calculus for students majoring in mathematics, engineering, or science


Clarity and precision

Thomas' Calculus, Multivariable helps students reach the level of mathematical proficiency and maturity you require, but with support for students who need it through its balance of clear and intuitive explanations, current applications, and generalized concepts. In the 14th Edition, new co-author Christopher Heil (Georgia Institute of Technology) partners with author Joel Hass to preserve what is best about Thomas' time-tested text while reconsidering every word and every piece of art with today's students in mind. The result is a text that goes beyond memorizing formulas and routine procedures to help students generalize key concepts and develop deeper understanding.


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About The 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 widely used calculus texts as well as calculus study guides. He is currently on the editorial board of several publications, including the Notices of the American M...

Details & Specs

Title:Thomas' Calculus, MultivariableFormat:PaperbackDimensions:624 pages, 10.7 × 8.4 × 1 inPublished:January 1, 2017Publisher:Pearson EducationLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0134606086

ISBN - 13:9780134606088

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Extra Content

Table of Contents

 

10. Infinite Sequences and Series

10.1 Sequences

10.2 Infinite Series

10.3 The Integral Test

10.4 Comparison Tests

10.5 Absolute Convergence; The Ratio and Root Tests

10.6 Alternating Series and Conditional Convergence

10.7 Power Series

10.8 Taylor and Maclaurin Series

10.9 Convergence of Taylor Series

10.10 Applications of Taylor Series

 

11. Parametric Equations and Polar Coordinates

11.1 Parametrizations of Plane Curves

11.2 Calculus with Parametric Curves

11.3 Polar Coordinates

11.4 Graphing Polar Coordinate Equations

11.5 Areas and Lengths in Polar Coordinates

11.6 Conic Sections

11.7 Conics in Polar Coordinates

 

12. Vectors and the Geometry of Space

12.1 Three-Dimensional Coordinate Systems

12.2 Vectors

12.3 The Dot Product

12.4 The Cross Product

12.5 Lines and Planes in Space

12.6 Cylinders and Quadric Surfaces

 

13. Vector-Valued Functions and Motion in Space

13.1 Curves in Space and Their Tangents

13.2 Integrals of Vector Functions; Projectile Motion

13.3 Arc Length in Space

13.4 Curvature and Normal Vectors of a Curve

13.5 Tangential and Normal Components of Acceleration

13.6 Velocity and Acceleration in Polar Coordinates

 

14. Partial Derivatives

14.1 Functions of Several Variables

14.2 Limits and Continuity in Higher Dimensions

14.3 Partial Derivatives

14.4 The Chain Rule

14.5 Directional Derivatives and Gradient Vectors

14.6 Tangent Planes and Differentials

14.7 Extreme Values and Saddle Points

14.8 Lagrange Multipliers

14.9 Taylor's Formula for Two Variables

14.10 Partial Derivatives with Constrained Variables

 

15. Multiple Integrals

15.1 Double and Iterated Integrals over Rectangles

15.2 Double Integrals over General Regions

15.3 Area by Double Integration

15.4 Double Integrals in Polar Form

15.5 Triple Integrals in Rectangular Coordinates

15.6 Applications

15.7 Triple Integrals in Cylindrical and Spherical Coordinates

15.8 Substitutions in Multiple Integrals

 

16. Integrals and Vector Fields

16.1 Line Integrals of Scalar Functions

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

16.3 Path Independence, Conservative Fields, and Potential Functions

16.4 Green's Theorem in the Plane

16.5 Surfaces and Area

16.6 Surface Integrals

16.7 Stokes' Theorem

16.8 The Divergence Theorem and a Unified Theory

 

17. Second-Order Differential Equations (Online at www.goo.gl/MgDXPY)

17.1 Second-Order Linear Equations

17.2 Nonhomogeneous Linear Equations

17.3 Applications

17.4 Euler Equations

17.5 Power-Series Solutions

 

Appendices

1. Real Numbers and the Real Line

2. Mathematical Induction

3. Lines, Circles, and Parabolas

4. Proofs of Limit Theorems

5. Commonly Occurring Limits

6. Theory of the Real Numbers

7. Complex Numbers

8. The Distributive Law for Vector Cross Products

9. The Mixed Derivative Theorem and the Increment Theorem