TEXTBOOKS:
Early
Transcendentals Multivariable Calculus, fifth edition,
by James Stewart (The regular version of Stewarts Multivariable
Calculus is identical, except for the page and chapter numbers.)
Student
Solutions Manual
for the above textbook (this is recommended, but not vital)
Calculus on
Manifolds,
by Michael Spivak
REFERENCES:
The following are various reference books for this course, listed
roughly in increasing level of rigour:
Marsden, J.E.
and
Tromba, A.J. Vector Calculus
Apostol, T.M.
Mathematical Analysis
Lang, S.
Calculus of Several Variables
Hubbard, J.H.
and Hubbard, B.B. Vector Calculus, Linear
Algebra, and Differential Forms
Lang, S.
Undergraduate Analysis
Munkres, J.R.
Analysis on Manifolds