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3.016 Mathematics for Materials Scientists and Engineers, Fall 2003

Parabolic approximation to a surface and local eigenframe.
Parabolic approximation to a surface and local eigenframe.  The surface on the left is a second-­order approximation of a surface at the point where the coordinate axes are drawn. The surface has a local normal at that point which is related to the cross product of the two tangents of the coordinate curves that cross at the that point.  The three direction define a coordinate system.  The coordinate system can be translated so that the origin lies at the point where the surface is expanded and rotated so that the normal n coincides with the z-axis as in the right hand curve. (Image by W. Craig Carter.)

Highlights of this Course

This course includes Mathematica® lecture note suppliments as well as problem sets with solutions.

Course Description

The class will cover mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from 3.012 to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, fourier analysis and random walks.

Technical Requirements

Mathematica® software is required to run the .nb files found on this course site.



Prof. W. Craig Carter

Course Meeting Times

Three sessions / week
1 hour / session




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