MATH 405 Real Analysis

A study of continuity, differentiability, Riemann-Stieltjes integral, uniform convergence. 

Credits

3

Prerequisite

MATH 230

Offered

As needed

Student Learning Outcomes

1. Know how to use different methods for proving theorems.
2. Know the real number system, completeness of the real numbers, the topology of the real line, compactness.
3. Know convergence of sequences, limit theorems, monotone sequences, Cauchy sequences, subsequences.
4. Know limits of functions, continuous functions, uniform continuity.
5. Know the formal definition of the derivative, properties of derivatives, mean value theorem, intermediate value theorem, L’Hopital’s rule, Taylor’s theorem, Taylor series.
6. Know the Riemann integral, properties of the definite integral, the fundamental theorem of calculus.
7. Use axioms and theorems to prove a given theorem.