SUGGESTED TOPICS FOR CALCULUS PRESENTATION


At the beginning of the term in which they intend to give the calculus presentation, students should choose a topic for their presentation.  Topics may be selected from, but are not limited to, the following list of topics that are commonly addressed in Maths 165 or 166.


Anti-differentiation
Continuity
Curve sketching
Def. of the definite Riemann integral
Def. of the derivative
Derivation of the power rule for derivatives
Derivatives of the trigonometric functions
Derivatives of logarithmic and exponential functions
Differential Equations
Implicit differentiation
Intermediate Value Theorem
Limits
Linear and quadratic approximations
Mean Value Theorem
Newton’s Method
Optimization
Related rates
Alternating series
Applications of the definite integral
Arc Length
Convergence/divergence of sequences and series
Convergence tests for positive termed series
Fundamental Theorem of Calculus
Improper integrals
Maclaurin series
Numerical Methods for estimating definite integrals
Power series
Taylor series/Taylor’s Theorem
Volumes, surface areas of surfaces of revolution