Calculus I at SHU covers the material normally associated with a university-level Calc I course. We begin with an overview of functions that most students will have learned in their pre-calculus course (function representations, domains and ranges, the basics of graphs, categories of functions like polynomials, trigonometric functions, exponentials and logarithms). We then discuss the concept of a limit of a function, both intuitive and formal epsilon-delta definitions, and develop the idea through our catalog of functions from the first unit. We then move to continuity with formal definitions and theorems. Next we cover derivatives of continuous functions, beginning with the definition in terms of limits, and follow with the rules, theorems, and shortcuts with all of our functions. Applications such as velocity/acceleration, exponential growth, and related rates are treated at the end of this unit. We wrap up Calc I with the development of the concept of area, the definition of anti-derivative, the Fundamental Theorem, the Mean Value Theorem, and integration by substitution. At present we use Stewart Early Transcendentals 7e, and cover the first 5 chapters completely.

- Text
- Syllabus
- Schedule
- Video Tutorials (Khan and other sources)
- Lesson Outlines (Powerpoint)