Worldwide Multivariable Calculus

David B. Massey




Worldwide Multivariable Calculus

Worldwide Multivariable Calculus
David B. Massey – Northeastern University

ISBN-10: 0-9842071-3-9
ISBN-13: 978-0-9842071-3-8
605 Pages
©2015 Worldwide Center of Mathematics, LLC

Digital PDF | $9.95
Print BW | $29.95


Multivariable Calculus is the study of the Calculus of functions of more than one variable, and includes differential and integral aspects. This book is written by David B. Massey, Ph.D., an award-winning teacher and world-renowned research mathematician, who has been teaching college students for 30 years. He emphasizes intuitive ideas in conjunction with rigorous statements of theorems, and provides a large number of illustrative examples. In the accompanying videos, Dr. Massey lectures on the core material from each section.




Chapter 1 Multivariable Spaces and Functions
1.1 Euclidean Space
1.1.1 Exercises
1.2 Rn as a Vector Space
1.2.1 Exercises
1.3 Dot Product, Angles & Projection
1.3.1 Exercises
1.4 Lines, Planes, and Hyperplanes
1.4.1 Exercises
1.5 The Cross Product
1.5.1 Exercises
1.6 Functions of a Single Variable
1.6.1 Exercises
1.7 Multivariable Functions
1.7.1 Exercises
1.8 Graphing Surfaces
1.8.1 Exercises

Chapter 2 Multivariable Derivatives

2.1 Partial Derivatives
2.1.1 Exercises
2.2 The Total Derivative
2.2.1 Exercises
2.3 Linear Approximation, Tangent Planes, and the Differential
2.3.1 Exercises
2.4 Differentiation Rules
2.4.1 Exercises
2.5 The Directional Derivative
2.5.1 Exercises
2.6 Change of Coordinates
2.6.1 Exercises
2.7 Level Sets & Gradient Vectors
2.7.1 Exercises
2.8 Parameterizing Surfaces
2.8.1 Exercises
2.9 Local Extrema
2.9.1 Exercises
2.10 Optimization
2.10.1 Exercises
2.11 Lagrange Multipliers
2.11.1 Exercises
2.12 Implicit Differentiation
2.12.1 Exercises
2.13 Multivariable Taylor Polynomials & Series
2.13.1 Exercises

Chapter 3 Multivariable Integrals

3.1 Iterated Integrals
3.1.1 Exercises
3.2 Integration in R2
3.2.1 Exercises
3.3 Polar Coordinates
3.3.1 Exercises
3.4 Integration in R3 and Rn
3.4.1 Exercises
3.5 Volume
3.5.1 Exercises
3.6 Cylindrical and Spherical Coordinates
3.6.1 Exercises
3.7 Average Value
3.7.1 Exercises
3.8 Density & Mass
3.8.1 Exercises
3.9 Centers of Mass
3.9.1 Exercises
3.10 Moments of Inertia
3.10.1 Exercises
3.11 Surfaces and Area
3.11.1 Exercises

Chapter 4 Integration and Vector Fields
4.1 Vector Fields
4.1.1 Exercises
4.2 Line Integrals
4.2.1 Exercises
4.3 Conservative Vector Fields
4.3.1 Exercises
4.4 Green's Theorem
4.4.1 Exercises
4.5 Flux through a Surface
4.5.1 Exercises
4.6 The Divergence Theorem
4.6.1 Exercises
4.7 Stokes' Theorem
4.7.1 Exercises




- Written by an award-winning mathematics professor with 30 years of teaching experience

- Down-to-Earth exposition

- Completely rigorous definitions, statements of theorems, and illustrative proofs

- External references to more-technical proofs

- Sections are divided into Basics, More Depth, and, where appropriate, +Linear Algebra

- Margin side-remarks and historical references

- Hyperlinked table of contents, index, and cross-references

- Hyperlinks are provided to Wikipedia content on linear algebra

- Embedded video links to full-length lectures

- Video-solutions to select exercises

- PDF format, compatible with all computers, tablets, and mobile devices

- Low cost in electronic or print form




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David Massey
David B. Massey received his Ph.D. in mathematics in 1986 for his results in the area of complex analytic singularities. He taught for two years at Duke as a graduate student, and then for two years, 1986-1988, as a Visiting Assistant Professor at the University of Notre Dame. In 1988, he was awarded a National Science Foundation Postdoctoral Research Fellowship, and went to conduct research on singularities at Northeastern University. In 1991, he assumed a regular faculty position in the Mathematics Department at Northeastern. He has remained at Northeastern University ever since, where he is now a Full Professor.