MTH 420- 520: MODELS AND METHODS OF APPLIED MATHEMATICS - Spring 2019
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General information
Schedule
General information
Instructor: Malgorzata Peszynska, Professor of Mathematics (Contact information including office hours on instructor's department website)
Class: Lecture: MWF 11:00-11:50pm, STAG 212.
Course information: Credits: 3.00.
Student preparation: MTH 256 and MTH 341 are required. An ability to write at a level appropriate for 4/5XX class and an ability to (learn to) use MATLAB will be expected. Students struggling with math, writing, or MATLAB skills must communicate with the instructor immediately in week one to discuss a plan of action, and will be expected to catch up promptly.
Class announcement.
Textbook, assignments and resources: class notes with ample references will be posted in CANVAS.
Syllabus: The class covers various discrete and continuous mathematical models along with the mathematical methods required to analyze and solve them. The methods include linear analysis, equilibrium and minimum principles, calculus of variations, principal component analysis (singular value decomposition) and orthogonal expansions, Fourier analysis, least squares, and constrained and unconstrained optimization. As time permits, a gentle introduction to inverse problems, machine learning, and stochastic techniques will be included.
Grade for the class will be based on the Homework grade grade (50%), Exam grade (40%) from two exams worth 20% each, and class participation (10%). No late HW will be accepted but one lowest HW grade will be dropped.
Exams: (F 4/19 or W 4/24) and F 5/17 in class. There will be no make-up exams.
Class participation: Attendance in lectures is not taken but students are responsible for the material in course notes and for the material covered in class. Class participation grade will be assigned based on class activities and student presentations of solutions to the exercises posted in course notes. Daily schedule will be posted on class website as a guide, but the instructor may schedule ad-hoc activities as needed.
Course Learning Outcomes:
A successful student who has completed MTH 420 will be able to
  • Follow the mathematical modeling steps for selected applications which translate a given problem to one that can be solved using algebra and differential equations.
  • Solve discrete and continuous quadratic minimization problems arising from physically motivated equilibrium problems and calculus of variations.
  • Apply the basics of Fourier analysis to selected examples.
  • Use the principles of principal component analysis and least squares for solving, in particular, large underdetermined and overdetermined linear systems arising, e.g., from data science.
A successful student who has completed MTH 520 will be able to:
  • Follow the mathematical modeling steps for selected applications which translate a given problem to one that can be solved using algebra and differential equations.
  • Formulate and solve discrete and continuous quadratic minimization problems arising from physically motivated equilibrium problems and calculus of variations.
  • Apply Fourier analysis in discrete and continuous setting and understand its limitations.
  • Use the principles of principal component analysis and least squares for solving, in particular, large underdetermined and overdetermined linear systems arising, e.g., from data science. Select the most appropriate method for a given application.

Statement Regarding Students with Disabilities: Accommodations for students with disabilities are determined and approved by Disability Access Services (DAS). If you, as a student, believe you are eligible for accommodations but have not obtained approval please contact DAS immediately at 541-737-4098 or at http://ds.oregonstate.edu. DAS notifies students and faculty members of approved academic accommodations and coordinates implementation of those accommodations. While not required, students and faculty members are encouraged to discuss details of the implementation of individual accommodations.
Student Conduct Expectations link: http://studentlife.oregonstate.edu/code