MTH 420-520, Oregon State University. Class information
Models and Methods of Applied Mathematics; Spring 2026 MWF 11:00-11:50
See the catalogue description of the class
MTH
420-520 .
See also class URL https://math.oregonstate.edu/~mpesz/teaching/420-520_S26/
Prerequisites: (MTH 256 or 256H) and MTH 341. A
minimum grade of C- is required in MTH 256, MTH 256H and MTH
341. Enrollment limited to students with a term class standing of
Junior or Senior.
- We develop, reinforce, and illustrate introductory ideas of
the following methods: linearity, linearization,
convexity, projections, Lagrange multipliers, least squares,
unconstrained and constrained optimization, calculus of
variations, regularization, inverse problems, basis and
expansions, principal component analysis, Fourier analysis; we
also explore a bit of randomness.
-
The course connects some discrete models
formulated in the context of linear algebra with the corresponding
continuous models that are formulated as differential or integral
equations.
The models include the equilibrium problems
Au=f which may be well-posed or ill-posed, their evolution
counterparts (dissipative u_t +Au=f or conservative u_tt + Au
=f) arising from network flows, graph Laplacian, transport of
mass and energy as well as mechanical systems under
constraints. Other applications and examples include the
eigenanimals, inverse problems, data and model fitting and
reduction, and the use of DFT.
- Students practice theory and develop illustrations in
MATLAB. There will be weekly lab meetings.
-
The class complements rather than overlaps with MTH 342, MTH
351, MTH 4/551, MTH 4/581, MTH 4/552, MTH 4/553, and does not
require any of these.
While experience with some of these or other similar coursework can help
students to get more from the class, it can be substituted by their
enthusiasm for applied mathematics.
Please feel free to contact the instructor with questions.