| Course Description:
Advanced Calculus
II is the second half of a
mathematically robust
introduction to the theory of functions on the real line. This
theory will be applied to rigorously recover theorems of introductory
calculus. Of equal importance, and perhaps more interest,
it will
provide a way to produce strong results about real functions that
surpass those of the calculus. It will also set the stage
for
generalizing analytical techniques to spaces other than R.
Methodological themes will be the
development of analytical intuition
and refinement of proof techniques, by exercising these abiliites
in unfamiliar,
counterintuitive contexts. The course text is Understanding Analysis,
by S. Abbott |
| Syllabus
|
| Outline
and Homework |
| Office Hours:
Wednesday 12:20-2, Thursday 4:20-6, Friday 2:10-3 and by appointment,
in
Roop 119 |
| Useful Links:
A classic introductory
analysis
text is Principles
of Mathematical Analysis, by W. Rudin. This
book is a standard reference for graduate students in mathematics (for
example, when studying for preliminary exams). It is available in the JMU library, (#QA300 .R8) and at
various on-line booksellers. Mathematics and Statistics Colloquium Series |
| Exam Information:
Mid-terms will be held in class on 7 February and 30 March. A
take-home mid-term will be distributed 21 February, due 2 March.
The final exam will be due on Wednesday, May 2. |