Home Research Publications Group Teaching Other A Tough Research Group

Karen Willcox

Professor, Department of Aeronautics & Astronautics
Co-Director, Center for Computational Engineering
Massachusetts Institute of Technology
77 Massachusetts Avenue
Cambridge, MA 02139

E-mail: kwillcox@mit.edu
Office: Rm 37-447 (map)
Phone: (617) 253-3503




16.06 Principles of Automatic Control
A junior-level required Aero/Astro class taught with Prof. John Deyst. The Fall 2003 version of 16.06 is published on MIT OpenCourseWare.

16.888 Multidisciplinary System Design Optimization
A graduate-level class taught with Prof. Olivier de Weck. The Spring 2004 version of 16.888 is published on MIT OpenCourseWare.

16.90 Computational Methods for Aerospace Engineering
An elective undergraduate class taken by juniors and seniors.

Unified Engineering: Signals and Systems
A sophomore-level required Aero/Astro class taught with Prof. John Deyst.

16.110 Flight Vehicle Aerodynamics
A graduate-level class (usually taught by Prof. Mark Drela).

16.920 Numerical Methods for Partial Differential Equations
A graduate-level class taught with Prof. Tony Patera and Prof. Jacob White.

Educational Research

Explicit linking of mathematics in the undergraduate engineering curriculum
In 2002, I initiated educational research into the gaps that existed with the mathematics abilities of undergraduates in my department. This problem has been documented not only within my department, but also in other MIT engineering departments and at many other institutions across the country. We conducted a study to map the "implicit mathematics curriculum", where we made a systematic mapping of the mathematics skills required for the core undergraduate curriculum of Aeronautics and Astronautics and the associated flow of learning provided by required courses in the Department of Mathematics. In 2004, we received support from the MIT Alumni Fund for a pilot program in 16.06 to create explicit links between engineering courses and upstream mathematics courses. We established a process for explicit linking of mathematics courses and other mathematics resources in engineering courses by creating a lecture-by-lecture mapping that details the specific mathematical skills required in each 16.06 lecture and the associated upstream mathematics course where the concept was previously introduced or taught. We developed a set of supplementary mathematics notes and linkages to provide students with remedial resources for self-study and reference, and modified lecture content to incorporate "flashbacks", or specific references to materials used in upstream mathematics courses. We have worked with MIT OpenCourseWare to create an online version of the supplementary mathematics notes that provides direct links to online mathematics resources.

A paper describing the mapping of the implicit mathematics curriculum throughout the core Aero/Astro engineering classes: Willcox, K. and Bounova, G., Mathematics in Engineering: Identifying, Enhancing and Linking the Implicit Mathematics Curriculum, presented at ASEE Annual Conference, Salt Lake City, UT, June 2004.

A report describing research to create explicit links between engineering courses and upstream mathematics courses, and to incorporate "flashbacks". The approach was implemented in Principles of Automatic Control. Allaire, D. and Willcox, K., Explicit Linking of Mathematics in the Undergraduate Engineering Curriculum.

Supplementary math notes developed to help create explicit links between Principles of Automatic Control and upstream mathematics courses. Allaire, D. and Willcox, K., 16.06 Supplementary Math Notes.

An OpenCourseWare resource to use the mathematics mapping and to help students navigate through mathematics material relevant to Principles of Automatic Control.

Keynote address at 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Portsmouth, VA, September 2006. de Weck, O. and Willcox, K., Trends in Multidisciplinary Engineering Education: 2006 and Beyond.