Calculus Revisited: Single Variable Calculus

Part I: Sets, Functions, and Limits

In its most common usage, a “set” is any collection of objects and a “function” is simply a rule that that assigns members of one set to members of another set. As an everyday non-mathematical example, consider the situation in which a teacher assigns grades to students. In this case, the teacher is the function that assigns to each member in the set of students a letter in the set whose members are A, B, C, D and F. While the study of sets and functions is important in all computational mathematics courses, it is the study of limits that distinguishes the study of calculus from the study of precalculus. What this means is the topic of Part I of this course.

Lecture 1: Analytic Geometry

Lecture 2: Functions

Lecture 3: Inverse Functions

Lecture 4: Derivatives and Limits

Lecture 5: A More Rigorous Approach to Limits

Lecture 6: Mathematical Induction