Calculus I at SHU covers the material normally associated with a university-level Calc I course. As we proceed through the course, students will engage in Liberal Arts learning by becoming conversant with the ideas, contents, and methods of various disciplines for which the course material is applicable. As much as possible, we will begin each unit by setting up real world problems, then pursuing the mathematics needed to solve them. In this way we will connect our course to world at large, including matters of ethics in the pursuit and application of math and science. We begin with a brief review of functions that most students will have learned in their pre-calculus course, focusing on composition and trigonometric and exponential/logarithmic functions. 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.
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