Tuesday, November 10, 1998, 3:40 p.m. ECA 225

Abstract: Spreadsheets such as EXCEL provide an almost ideal tool for numerical and graphical explorations on an introductory level -- all the way to numerical solutions of elliptic PDEs. Almost all students have a rudimentary working experience with spreadsheets, and hence "start-up costs" are minimal. Students feel comfortable with such nonthreatening software. EXCEL is widely used in introductory level classes such as ECE 100 (required for all engineering majors), and hence is a suitable means for connecting classes in different disciplines. EXCEL puts formulas, tables of numerical values, and very flexible graphics right next to each other. Immediate updates allow for playful experimentation, e.g. by varying parameter values, boundary data, initial conditions etc.
Typical interactive examples for in-class use, from calculus on up, include: Numerical differentiation, playing with base a to graphically solve y'=y, Riemann sums in one and two dimensions (and higher order schemes), Euler and RK methods, Newton's method, numerical solution of systems of ODEs and PDEs in the plane (not only hyperbolic and parabolic, but also elliptic!).
One of the most exciting features is that formulas like divided differences of any kind, or integration schemes are entered by pointing at the cells -- much like the diagrams familiar from research papers. This allows for the development of a deep conceptual understanding before the step to indexed variables, where the message is easily lost among lots of (i-1,j) and (i,j+1). Typically the step to the traditional formalism is made when demands for higher accuracy ask for finer discretization, or when theretical proofs are desired, e.g. for convergence theorems.
EXCEL has many more, very powerful mathematical capabilities. It routinely solves various optimization problems (e.g. data fitting) at the push of a button. As mathematics instructors we ought to be aware of such features. However, many of these do not lend themselves as well to an inquiry based approach. EXCEL includes a powerful object-oriented programming language. We will show animations of complicated discrete dynamical systems, where EXCEL was chosen as the easiest language in which to program the animated visualization -- note, in EXCEL programs may be recorded (and edited) as opposed to being typed charcater by character.
Events in following weeks: T 11/17  Mark Burtch: Vernier sensors.   T 11/24  John Jones: Abstract Algebra, Number Theory.  12/1 Matthias Kawski: Differential Geometry.   12/8  Kathy Prewitt:  Statistics. For further information please contact: Matthias Kawski. The complete calendar for this seminar series is available on-line at http://math.la.asu.edu/~kawski/classes/fall98/mat591/announce.html.