MATH 521 SYLLABUS

Text:  Advanced Calculus by P.M. Fitzpatrick, second edition,
       published by the American Math. Society

References: C.Buck, W. Rudin, R.Courant-F.John, F. Morgan (Real Analysis)

Homework: Given daily and due the following lecture. Assignments will be posted
     on http://www.math.wisc.edu/~rabinowi/

Exams: 6 weeks, 12 weeks and final exam
     ( 6- and 12-week exams will be in the evening)

Grading: 6 and 12 weeks exams: 25%; final: 35%; homework: 15%

Office hours: 11-12 MWF,  Room 625 Van Vleck and by appointment
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Outline of course:

1) Elements of set theory
2) The real numbers, R, and R^n
3) Sequences and series; limits and convergence
4) Functions and their limits
5) Some topology
6) Continuity
7) More topology and properties of continuous functions
8) Differentiation
9) Integration; the fundamental theorem of calculus
10) Sequences of functions
11) Applications:
  a) Infinite series
  b) Power series
  c) The elementary functions 
12) Metric spaces
13) Fourier series