MTH 420 - Sec 001
Models and Methods of Applied Mathematics

MW 2:00-2:50PM
STAG 210

F 2:00-2:50PM
MLC 109

Winter 2018

Professor:	Dr. Nathan Louis Gibson
Office:	Kidd 056
Office Hours:	MWF 3-4PM
Course Website:	http://math.oregonstate.edu/~gibsonn/Teaching/MTH420-001W18
Required Text:	Gilbert Strang, INTRODUCTION TO APPLIED MATHEMATICS
Note:	Text is published by SIAM, and current SIAM members get 30% off list price. So be sure to sign up for your free membership through our student chapter! To formally become a member of the chapter, do the following Find an organization page: http://sli.oregonstate.edu/orgs/findanorg Search: 'Society of Industrial and Applied Mathematics' Click + Join Now. (Need OSU log-in)

Contents

Calendar
Course Description
Grades
Homework
Computational Lab
Exams

Course Description

Discrete and continuous mathematical models and methods for analysis, possibly including linear analysis, equilibrium and minimum principles, calculus of variations, principal component analysis and orthogonal expansions, asymptotic and Fourier analysis, least squares, constrained and unconstrained optimization, inverse problems, and Monte Carlo techniques. Particular models and methods covered may vary annually.

Particular topics this year will additionally include polynomial chaos expansions, Lagrange multipliers, Kalman filter, simplex method, duality, Kuhn-Tucker conditions, and nonlinear programming.

You are expected to actively participate in class and keep up with producing quality written work, including advance preparation for class. The major categories are Homework, Lab, and Exam.

MTH 420 Measurable Student Learning Outcomes:

A successful student who has completed MTH 420 will be able to:

formulate a minimum energy or equilibrium problem as a linear least squares problem, solve, and interpret the solution within the context of the application;
solve contrained optimization problems with Lagrange variables;
recognize the importance of duality in optimization problems including linear programming, optimal control and calculus of variations;
apply the simplex method to linear programming problems;
recognize the importance of orthogonality in polynomial, Fourier, and eigenfunction expansions;
apply polynomial chaos to a random ordinary differential equation;
use Python libraries to solve computational examples of the above problems.

Accommodations:
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.

Students are expected to be familiar with Oregon State University's Statement of Expectations for Student Conduct.

Course Drop/Add Information: See Office of the Registrar and Academic Calendars

As preparation for this class, you should review the materials covered in MTH 256 and MTH 341.

Grades

Grade Distribution

Homework	60%
Computer Assignments	10%
Midterm Exam	10%
Final Exam	20%
Total	100%

Homework

Homework: This course has daily homework, including readings. Each day’s lesson has three equally important homework assignments associated to it:

A. Advanced preparation, where you read pages from the book and formulate questions related to this. These are submitted on-line.
B. Warm-up exercises, where you explore your basic understanding. Your initial work is submitted on-line before class; you also bring a copy to class, as this forms the basis for group work.
C. Graded exercises. These are submitted on-line before the class hour on the day due.

The first two of these are graded as Complete (Check +), Partially Complete (Check), Largely Incomplete (Check −) (Warm-up exercises are considered incomplete if you do not participate in class the day they are due.) The graded exercises will be more thoroughly graded.

You will be submitting the three parts of the homework on a rolling basis. Usually, part A will be due by the class meeting before the lesson (this allows me to discern where any difficulties lie); part B will be due on the day of the lesson (and the class meeting’s activities will be based on it); and part C will be due the next class meeting. All assignments will be posted on Canvas. You are encouraged to discuss homework problems with your classmates outside of class; however, you MUST write up and submit your own work.

Homework may sometimes, at my suggestion, be re-worked after I critique it, to bring it to perfection, due at the next class period after being returned by me. My goal is to help you perfect your work to your and my satisfaction.