MATHEMATICS 320-3
ADVANCED CALCULUS OF ONE VARIABLE



Spring 1999
DAY COURSE

Instructor: Dr. P. BORWEIN (TLX 10553)

Prerequisites:

MATH 242 and MATH 251.

Textbook:

No textbook for MATH 320.

Calendar Description:

Sequences and series of functions; uniform convergence; consequences of uniform convergence; improper integrals; additional applications of convergence.

Outline:

I. Infinite Series
1. Convergence, absolute and conditional.
2. Series with non-negative terms. Comparison Tests.
3. Series with non-negative terms. Ratio and root tests. Remainders.
4. Series with variable signs.

II. Sequence and Series of Functions. Uniform Convergence

1. Uniform convergence.
2. Consequences of uniform convergence (Integration and differentiation).
3. Abel's and Dirichlet's tests.

III. The Taylor Series

1. Power series. Interval of convergence.
2. Properties of power series.
3. The Taylor and Maclaurin series.
4. The arithmetic of power series.

IV. Improper Integrals (2 weeks)

1. Improper integrals. Conditional and absolute convergence.
2. Improper integrals with non-negative integrands.
3. The Cauchy principal value.
4. Uniform convergence and some consequences.

V. Integral Representions of Functions

1. Generalities
2. Gamma and Beta functions
3. Laplace's Method
4. Stirling's Formula

Notice:

Students should join the Math 320 group in http://caucus.sfu.ca.

Grading:

Midterms - 40%
Assignments - 10%
Final Exam - 50%

The course instructor will inform students of the grade allocation
for this course and the requirements for completion of the course
at the beginning of the semester.



Students should be aware that they have certain rights to confidentiality concerning the return of course papers and the posting of marks. Please pay careful attention to the options discussed in class at the beginning of the semester.

SFU / Math & Stats /mast/courses/99-1/MATH/MATH_320.html
Revised November 1998 by math_www@math.sfu.ca.