MATH 515 - Calculus I

4 Credits
This is a first course in the standard calculus sequence covering differential calculus and an introduction to integral calculus. Topics include: limits and continuity, the definition of the derivative, rules and techniques of differentiation, applications of the derivative (e.g., L’Hôpital’s Rule, curve sketching, optimization, etc.), antiderivatives, Riemann sums, the definition of the definite integral, and the Fundamental Theorem of Calculus. Students taking this course must demonstrate a strong background in the concepts covered in algebra and precalculus.

Fees: Additional course fees apply.
Course Learning Outcomes:
1. Evaluate limits using a variety of methods.
2. Determine continuity and differentiability of a function.
3. Evaluate derivatives using limits, rules of differentiation, tables of derivatives, and implicit differentiation.
4. Employ derivatives to solve related rates, optimization, and other application problems.
5. Construct graphs of functions utilizing their first and second derivatives.
6. Interpret the behavior of functions based on their first and second derivatives.
7. Describe the behavior of the graph with respect to extrema, direction, and concavity.
8. Evaluate antiderivatives and indefinite integrals of elementary functions.
9. Employ antiderivatives to solve initial value problems and applications.
10. Employ finite sums to approximate total change and the area under a curve.
11. Determine the existence of the definite integral of a function for a given interval.