MATH 208 References
The main text used for this course is
J. E. Marsden and A. J. Tromba, Vector Calculus,
6th edition, W. H. Freeman and Company, 2013, ISBN-13: 978-1-4292-1508-4.
This book will be mostly used as a supplement to my lectures. As such, it will not be followed page-by-page.
Here are three other references that can be useful
for the course, roughly in increasing order of difficulty and sophistication:
S. Lang, Calculus of Several Variables, 3rd edition, Springer,
1987, ISBN-13: 978-0387964058.
A concrete and useful introduction. Slightly more elementary than the level of our course, but it has many worked out problems.
T. M. Apostol, Calculus, vol. 2, 2nd edition,
John Wiley & Sons, 1969, ISBN-13: 978-0471000075.
A masterfully written classic, but (alas) has less geometric flavor than we want.
T. Shifrin, Multivariable Mathematics: Linear Algebra, Multivariable Calculus, and Manifolds, John Wiley, 2004,
ISBN-13: 978-0471526384.
Highly polished and efficient exposition, uses the modern language of manifolds.
Because of the rather theoretical flavor of the course, you may feel the need to do more problems to sharpen your
computational skills. For that purpose, I suggest that you have
a standard calculus textbook at hand and choose from tens of computational
type problems at the end of each section. You could pick any of the gazillion generic
calculus books that are available in the library, such as the second half of
J. Stewart, Calculus, 6th
edition, Brooks-Cole, 2007, ISBN-13: 978-0495011606.
You may also obtain a copy of the following inexpensive book which is a good source of problems with detailed solutions:
R. Wrede and M. Spiegel, Schaum's Outline of Advanced Calculus, 3rd edition, McGraw-Hill, 2010, ISBN-13: 978-0071623667.
Finally, MIT OpenCourseWare project has a video lecture series in multivariable calculus which you may find useful (relevant material start with lecture 16, but it'd be a good idea to watch the beginning lectures in your spare time as a review):
Back to Math 208