MATH 7383 - Concepts of Calculus 1

(4) Study of the conceptual underpinnings of differential calculus of one real variable. Topics of study include sequences, limits of sequences, limit laws for sequences, limits of functions, limit laws for functions, relationship between limits of sequences and limits of functions, definitions of continuity, definition of differentiation via limits, definition of differentiation via linear approximation, sequential compactness, differentiation rules via limits, differentiation laws via linear approximation, relationship between notions of continuity and differentiability, high order differentiation, the Extreme Value Theorem, applications of differentiation, antiderivatives. Formal proofs of important theorems are discussed with special emphasis on how to adapt the material to the intended audience. PREREQUISITE(S): Departmental Permit required.