MATH 634: Advanced Calculus I
Syllabus - Spring 2005
Instructor: Marianne Korten
Office: Cardwell 234, 532-0567
Office Hours: Wednesday 11:30
Textbook:
Advanced Calculus: An Introduction to Analysis - Third Edition,
Watson Fulks, John Wiley and Sons, New York, 1978.
Course description:
In this course we will revise, reinforce, and expand the concepts and
tehorems covered in Calculus 3. The focus will now be
on the proofs
of the results: the goal is to develop skills
in constructing and writing proofs. You will be expected to write clean
and
rigorous arguments with
correct logic and grammar. rhis is a foundational course fot graduate
level courses in mathematics
and elsewhere, in particular for Analysis
and Topology.
Syllabus:
Functions of several variables: partial differentiation and implicit
function theorems, curvilinear coordinates, differential geometry
of
curves and surfaces, vectors and vector fields, line and surface
integrals, double and triple integrals, Green's Theorem, Stokes'
Theorem, and Divergence Theorem.
Grading policy:
Attendance and participation are requiered. Homework will be
assigned weekely. Final grades will be
based on witten work and participation, as follows:
33% for homework, 33% for the midterm, and 33% for the
final.
You are encouraged and expected to work on the homework exercises in
groups, and to subject your work to revision by classmates before
handing it in.
You are strongly encouraged to use the advanced
help sessions staffed by the mathematics department to clear doubts
and questions and fine-tune your proofs.
Here I will post your (roughly weekly) assignments.