This paper contains the curriculum requirements, teaching goals, strategies, and techniques, the course outline, and the first lesson plan for an upper division undergraduate course in Numerical Analysis. The class differs from traditional courses in its emphasis on teaching techniques which encourage the students to interact with the course material, other students in the course, and their own learning process. The course will be organized around the construction of tutorials for example ordinary differential equation (ODE) and partial differential equation (PDE) problems.
Numerical analysis is typically a required course for computational science and scientific computing courses. By using teaching techniques provided by educational research, we aim to provide an introductory numerical analysis course which work towards some of the more general ABET engineering requirements. Specifically ABET requires that engineering departments show that their graduates are able to apply knowledge, identify, formulate and solve engineering problems, communicate effectively, engage in life-long learning, and use techniques, skills, and tools in practice.
This numerical analysis course has been developed keeping in mind the pre-existing mental models and experiences typically seen in computer science undergraduates. From a computer science student's perspective the context for a numerical analysis class is usually as a required course for Scientific Computing and Computational Science courses. Scientific Computing is the "development of new software (or hardware) tools for computational applications in science and engineering", and Computational Science "is the use of computers to analyze science and engineering problems" . Since a computer science undergraduate already has software development experience, this course will emphasize the science and engineering applications which use numerical methods.
I first look at the current numerical analysis curriculum requirements and compare how those requirements fail to address the more general skills which ABET requires. Next, we discuss important concepts for structuring a numerical analysis course which can be gleaned from existing course materials. The appendix provides many related web sites. The structure of the course is given followed by a section which describes the various teaching goals, strategies, and techniques which will encourage interaction from the students. Finally, we give a course outline, example lesson plan, and suggest future preparation needed before implementing the course.