MTH 420-520, Oregon State University. Class information

Models and Methods of Applied Mathematics; Spring 2026 MWF 11:00-11:50

Instructor: M. Peszynska,

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.