Advanced Calculus II
The real numbers, sequences, limits, continuity, differentiation in one variable. Proof writing ideas and techniques. Delta-epsilon arguments [treatments] of limits, continuity, properties of derivatives and proofs of the properties, induction hypothesis, proving irrational numbers such as pi and root 2, transcendental numbers like e, Algebraic numbers, least upper bound. Supremum and Infimum approaches to Integral. Lower sums and upper sums of integrals. Proofs of Fundamental Theorem of Calculus I and II.
