1 / 10

Mathematica -Based Computer Laboratories for the Enhancement Of a Calculus Sequence

Mathematica -Based Computer Laboratories for the Enhancement Of a Calculus Sequence. Mike O’Leary and Raouf Boules Mathematics Department Towson University. ICTCM, 2000. Background (1). Towson is a comprehensive university located in the Baltimore metropolitan area

nat
Download Presentation

Mathematica -Based Computer Laboratories for the Enhancement Of a Calculus Sequence

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Mathematica-Based Computer Laboratories for the Enhancement Of a Calculus Sequence Mike O’Leary and Raouf Boules Mathematics Department Towson University ICTCM, 2000

  2. Background (1) • Towson is a comprehensive university located in the Baltimore metropolitan area • SAT mid range score of entering freshman class in Fall 2000 is 500-590 (Verbal), and 510-590 (Math) • Main textbook in use: Stewart’s Calculus: Early transcendental functions, Brooks/Cole 1999

  3. Background (2) • Audience: Mainly math, math education, computer science, physics and chemistry (lesser degree) • Semester system • Class meets for 4 hours per week for lectures and one hour in a computer laboratory

  4. Philosophy (1) • Material supplements the mathematics of an otherwise traditional course in calculus, and is NOT a substitutefor it (more on this later) • Only small set of built-in functions used in building small programs (Modules) for graphical demonstration or to bypass tedious repetitive calculations

  5. Philosophy (2) • No prior knowledge of Mathematica assumed • Material is based on interactive text(A computer document from which symbolic, numerical, and graphic tools can be invoked. The results of these computations can be pasted into the document so that each learner has an individual record of his or her explorations)

  6. Philosophy (3) • Students are encouraged to experiment and make discoveries • Students may work in small groups but submit a lab report individually • Students are expected to write answers, many comments, observations,…etc

  7. Mathematica Role: Black Box or Teaching Tool (1) • History of Mathematica and its Use: • Wolfram: Born in 1959 and received his PH.D. in Physics from Caltec in 1979 • Began in 1979 constructing a CAS to solve his own problems in physics • Mathematica released in 1988 by Wolfram Research, Inc

  8. Mathematica Role: Black Box or Teaching Tool (2) • History of Mathematica and its Use (cont’d): • Became popular first in the research fields of science, engineering, and economics where it was typically used as a black box to solve complicated problems • Later it entered the scene of education as people realized its potentials for demonstrations and as its front end became more user friendly

  9. Mathematica Role: Black Box or Teaching Tool (3) • Example 1: Using Newton’s method in solving a nonlinear equation in a single variable • Black box approach: use the command FindRoot (This also uses Newton’s method) • Approach adopted: see next demonstration

  10. Mathematica Role: Black Box or Teaching Tool (4) • Example 2: Numerical integration • Black box approach: Use the command NIntegrate (This uses a sophisticated numerical adaptive quadrature algorithm) • Approach adopted: build a module to show the graphical meaning of the tarpezoidal, and Simpson’s rules; another assesses the error in each as function of number of partitions and asks for conjectures

More Related