# MTH 420/520 - Sec 010 Models and Methods of Applied Mathematics

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### 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.
MTH 520 Measurable Student Learning Outcomes:

A successful student who has completed MTH 520 will additionally be able to:

• solve real-world linear programming problems with the simplex method;
• analyze polynomial chaos applied to a random ordinary differential equation;
• use object-oriented Python code 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.

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

 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.

### Computational Lab

The will be a laboratory component to this course. Fridays will consist of group and individual guided instruction on Python lab assignments. We will meet in the MLC Computer Lab (Kidder Hall 108J) on Fridays. We will be learning about Linux and Git (Professional Development) and Python (Programming), using the open-source resources available at https://github.com/Foundations-of-Applied-Mathematics. There will be Lab assignments due weekly (with only a few programming problems in each). Collaboration is encouraged, but each student must submit their own code.

### Exams

There will be one take-home midterm exam and one take-home, cummulative, final exam.