|Christian G J Roettger
Office 382 Carver
Amongst other things, I am interested in
Calculus III projects for Undergraduates
MAA section meeting, Simpson College, Indianola, IA, Oct 5-6, 2012
Abstract. Multivariate Calculus lends itself particularly well to explorations on the computer. Examples include Newton's method, Steepest Descent, two-dimensional Riemann sums, Euler's method for differential equations. Each of these can be presented in various appealing contexts and is immediately plausible for a student who understands the core concepts of the derivative of a multivariate function and Riemann sums, respectively. On the other hand, exploring the 'approximation' aspect of Calculus with paper and pencil and even with a calculator is less satisfactory than using a computer, especially if powerful mathematical software is available (eg SAGE, R, Matlab, Maple, Mathematica). Ideally, the results can be presented in an appealing graphic, and we'll show examples of student work. Finally, we do not assume any programming skills, but this kind of small project is a great opportunity to learn them.
|Hydrology||Contour Plot||Thirsty Hiker||Constrained Optimization|
Recurrences, power series, and ODE
MAA section meeting, Coe College, Cedar Rapids, IA, Oct 22-23, 2010
Abstract. A three-term recurrence is connected to a power series, which solves a second-order ODE. The recurrence can be helpful in solving the ODE explicitly, and in approximating the power series. As is well-known, its growth rate is related to the radius of convergence of the power series. We will use a simple example straight from the textbook to investigate this in the case of a recurrence with *non-constant* coefficients. While the growth rate turns out to be surprisingly resistant to attack, it has great potential to be explored experimentally as well as theoretically - an opportunity for open-ended student projects. The explanation for the curious behavior of the growth rate turns out to be a Mobius transformation.
Sequences and their annihilators
MAA section meeting, Cedar Falls, IA, Oct 9-10 2009
Abstract. Annihilating polynomials have been widely used in geometry and to study sequences over fields and over the integers Z. We use the same simple ideas to study sequences over Z modulo n. There are surprising difficulties, surprisingly nice results and an open conjecture. We can demonstrate some applications to recurrence sequences like the Fibonacci and Lucas numbers, or discrete dynamical systems. Joint work with John Gillespie.
The continuing story of zeta
ISU Combinatorics/Algebra seminar , Ames, Oct 9, 2006
We aim to give a particularly simple proof of the analytic continuation of the Riemann zeta function to the complex plane, obtaining the values of zeta(s) at negative integers in the process in terms of Bernoulli numbers.
Primitive Prime Divisors of Mersenne numbers via Uniform Distribution
MAA Central Section Meeting, ISU, Ames IA, Apr 7-8 2006
Given a sequence a of integers, a primitive divisor of a(n) is an integer which divides a(n) but no earlier term of the sequence. Last year, we presented a result about a weighted average of primitive prime divisors of the well-known Mersenne numbers M(n) = 2^n-1. This year, we have an entirely different, simple proof of a better result, using cyclotomic polynomials and uniform distribution. We are indebted to Carl Pomerance for helpful insights. We will also mention possible applications to other sequences like the Fibonacci numbers.
Math 265: Calculus III
Math 301: Algebra I
Math 350: Elementary Number Theory
Math 141/142 Trigonometry (and analytic geometry)
Math 151: Calculus for Business and Social Sciences
Math 165: Calculus I
Math 166: Calculus II
Math 166H: Honors Calculus II
Math 181: Calculus For the Life Sciences I
Math 195: Math for Elementary Education
Math 201: Intro to Proofs
Math 265: Calculus III
Math 267: Differential Equations, Laplace Transform
Math 297: Intermediate Topics in Elementary Mathematics
Math 301: Algebra I
Math 307: Matrices and Linear Algebra
Math 314: Graphs and Networks
Math 317: Theory of Linear Algebra
Course notes for Analytic Number Theory
My Favorite Quote:"Should array indices start at 0 or 1? My compromise of 0.5 was rejected without, I thought, proper consideration." - Stan Kelly-Bootle
Pros and cons of metric vs imperial system.
This webpage is http://www.public.iastate.edu/~roettger/homepage.html