Credits -- 3 (3-0-0)
Term Offered -- Fall
Prerequisite -- M318
- Possible Text
-- - W. Rudin, Principles of
Mathematical Analysis, 3rd ed, McGraw-Hill, New York, 1976
- Topics
-
-- Finite, countable, and uncountable sets.
-- Real and complex number systems, and Euclidean k-space.
-- Metric spaces: open and closed sets, compact and connected sets,
convergent sequences, Cauchy sequences, completeness, continuous
functions, continuity and compactness, and continuity and
connectedness.
-- Numerical sequences and series: tests for convergence, power
series, absolute convergence, conditional convergence, and
rearrangements.
-- Differentiation theory: the derivative, mean value theorems,
l'Hospital's rule, Taylor's theorem, and differentiation of
vector-valued functions.
-- Integration theory: the Riemann-Stieltjes integral, basic properties,
fundamental theorem of calculus, and rectifiable curves.
-- Sequences and series of functions: uniform convergence, uniform
convergence and continuity, uniform convergence and integration,
uniform convergence and differentiation, Weierstrass approximation
theorem, and Stone-Weierstrass theorem.