MATH 405 Real Analysis
A study of continuity, differentiability, Riemann-Stieltjes integral, uniform convergence.
Offered
As needed
Student Learning Outcomes
- Know how to use different methods for proving theorems.
- Know the real number system, completeness of the real numbers, the topology of the real line, compactness.
- Know convergence of sequences, limit theorems, monotone sequences, Cauchy sequences, subsequences.
- Know limits of functions, continuous functions, uniform continuity.
- 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.
- Know the Riemann integral, properties of the definite integral, the fundamental theorem of calculus.
- Use axioms and theorems to prove a given theorem.