University Mathematics
Advanced Calculus
A rigorous second look at calculus: the real numbers, limits, continuity, differentiation and integration, proved rather than computed.
Curriculum / Syllabus
- The Real Numbers and the Completeness Axiom
- Sequences, Subsequences and Cauchy Sequences
- Limits and Continuity (epsilon-delta)
- Differentiation and the Mean Value Theorem
- The Riemann Integral
- Sequences and Series of Functions, Uniform Convergence
- Functions of Several Variables
Exam & Course Strategy
Exams mix epsilon-delta proofs with counterexamples. We build a stock of standard arguments and examples so that each new question starts from something familiar.