List of Topics for 2024 Challenge
The following is a list of topics that will be considered “fair game” for coverage on the exams in the Clemson Calculus Challenge. This list is painted in broad strokes, and a participant should be able to solve any of the posed problems by techniques (perhaps with a bit of ingenuity) listed below.
- The concept of a limit (formally and informally)
- Limit laws, tangent lines, and general applications of limits
- Continuity
- Differentiability, theoretical and practical applications of the derivative
- Differentiation rules and practice (product and quotient rules, chain rule, implicit differentiation, logarithmic differentiation, linearizations and related rates)
- Applications of differentiation ((local) extrema, Rolle’s Theorem and the Mean Value Theorem, l’Hospital’s Rule, curve sketching, optimization, and Newton’s Method)
- Integration (definite and indefinite integrals, the Fundamental theorem of Calculus)
- Basic techniques and applications of integration (u-substitution, volumes, integration by parts, area between curves, and volumes)
- Basic differential equations and modeling (exponential growth and decay, Newton’s Law of Cooling, separable equations)