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MATH 3600-100 (6930), Fall 2023

Applied Numerical Methods

Syllabus Show/ Hide

Catalog Description:

A survey of numerical methods for engineering, science, and mathematics students. The course simultaneously introduces numerical methods, programming techniques, problem solving skills, and the MATLAB language. Methods are introduced in the context of engineering problems, using a lecture-lab format. Topics include numerical solutions of systems of linear and nonlinear equations, numerical computation of eigenvalues, numerical differentiation and integration, and numerical solution of ordinary and partial differential equations. Essential topics in Linear Algebra and Multi-variable Calculus are integrated into the course by including them with related numerical methods.

Learning Outcomes:

• Students will be able to apply commonly used numerical methods for solving equations and linear systems.
• Students will be able to use MATLAB as a programming and computational tool to effectively implement numerical algorithms.
• Students will be able to apply the principles of Numerical Linear Algebra to efficiently and accurately solve linear systems and find eigenvector and eigenvalues.
• Students will be able to use partial derivative and the multi-variable Newton’s method to approximate solutions of systems of non-linear equations.
• Students will be able to use common algorithms for numerical interpolation, integration and differentiation.
• Students will be able to apply common numerical methods such as Runga-Kutta and Finite Difference methods for appropriate differential equations.
• Students will be able to define and explain the practical consequences of convergence, stability, computational cost, residual, truncation errors, condition numbers and error propagation.
• Students will be able to complete Gaussian elimination with back-substitution by hand to solve linear systems and find eigenvalues and eigenvectors for small matrices.
• Students will be able to compute partial derivatives, gradients, the Jacobian matrices, and multiple integrals analytically.
• Students will be able to explain the basic ideas behind the Finite Elements method.

Prerequisites:

MATH 3400 Elementary Differential Equations.

Web page:

http://www.ohiouniversityfaculty.com/mohlenka/2241/3600/.

Instructor:

Martin J. Mohlenkamp, mohlenka@ohio.edu, Morton Hall 321C, 740-593-1259. The best ways to reach me are email and Teams.

Office hours:

Tentatively Monday and Friday 9:40 AM - 10:35 AM. I may be helping students after class in Morton Hall 314, or back in my office Morton Hall 321C. I am available to meet at other times, just contact me for an appointment.

Computing Environment:

The course uses Matlab. Our classroom Morton Hall 314 has desktop computers for everyone to use. Some other computer labs on campus will also have it installed. To access Matlab using your own computer without buying your own copy, use the university's Virtual Desktop.

Text:

Introduction to Numerical Methods and Matlab Programming for Engineers, Todd Young and Martin Mohlenkamp. Available at http://www.ohiouniversityfaculty.com/youngt/IntNumMeth/. Some sections later in the text may be modified before we get to them, so please download sections as we do them rather than getting the whole book now.

Class hours/ location:

Monday, Wednesday, and Friday 8:35 AM - 9:30 AM in Morton Hall 314.

Group component:

Group formation:

I will randomly assign groups of 3 using Blackboard. The groups will be reset for each new part of the textbook, so you will be in four different groups. (By chance, you might have repeat partners.)

Partner ratings:

At the end of each part of the textbook, you will rate (and be rated by) your former partners on how much they contributed to the group. The ratings you receive are part of your grade.

Group Homework:

Each lecture in the text has a few homework problems. As a group you will submit a single solution for each problem. Submission is online through Blackboard; upload a single file (.docx or .pdf) for each problem. See the section on academic (mis)conduct below for the resources you are and are not allowed to use.

Advice: It will be tempting to just split up the problems. That works poorly because:

1. Many problems depend on previous problems.
2. You will learn less and suffer for it later in the course and in life.

It is best if everyone tries all the problems and then you discuss and compare. Then you can split up the task of writing a clean version of each solution and submitting it.

Individual component:

Individual homework:

One additional problem each week is done individually. Some of these will be mathematical exercises and some will help prepare you for your final project. Submission is online through Blackboard. These problems will be graded both on content and on presentation, using the Good Problems system of handouts. See the section on academic (mis)conduct below for the resources you are and are not allowed to use.

Final project:

As a culminating experience, you will do a project to apply numerical methods using Matlab to a topic outside of this course. It could be something from one of your other courses (that is not already using numerical methods), a hobby or other interest of yours, etc.

Your goal is to demonstrate what you have learned in this course and in particular to demonstrate that you have met the Learning Outcomes listed at the start of this syllabus.

The deliverables for the project are:

• A presentation. (20%; during the week of December 4.)
• A report. (80%; due Wednesday December 13.)

Format of class meetings:

Most of classtime is reserved for you to work in your groups on the group homework. I will be there to help you when you get frustrated or stuck. Occasionally I will give 5-minute lectures on topics that multiple groups are struggling with.

Attendance:

Attendance is not required, but you should do it anyway. Some benefits of attending:

• You can finish most of the homework in class, at the start of the day, rather than having it hang over you.
• It is a convenient time to work with your group and keep them happy with your performance.
• I will be there to help you.

Late Work:

Group and individual homeworks are due at specific times on specific days. Late homework is penalized 5% per day (or part thereof) late. You can resubmit a homework to improve your score, but the late penalty will apply.

Religious Accommodations

In accordance with the university's Interim policy on reasonable religious accommodations [40.003]:

You may be absent for up to three (3) days each academic semester, without penalty, to take time off for reasons of faith or religious or spiritual belief system or to participate in organized activities conducted under the auspices of a religious denomination, church, or other religious or spiritual organization. You are required to notify the me in writing of specific dates requested for alternative accommodations no later than fourteen (14) days after the first day of instruction. These requests will remain confidential. For more information about this policy, students/you may contact the Director and Title IX Coordinator, Equity and Civil Rights Compliance, Lindley Hall 006, 740-593-9140, equity@ohio.edu.

If your absence causes a delay in finishing an assignment, you will receive a 1-day extension on it.

Grade:

Your grade is based on group homework 50%, your partners' ratings of you 10%, your individual homework 20%, and your final project 20%. An average of 90% guarantees you at least an A-, 80% a B-, 70% a C-, and 60% a D-.

Academic (mis)conduct:

You are allowed to use most resources, but there are some limitations.

Unlimited use, without specific acknowledgment:

• The textbook.
• Discussions with me.
• Your partners, for the group homework.
• Matlab documentation.

Broad use, with acknowledgment:

• Websites about numerical methods or Matlab.
• Explanations by members of other groups in this class.
• Explanations by members of your group, for the individual assignments.
• Explanations by students who took this class in the past.
• Explanations by chatbots or other AI.

Acknowledge and describe this help in writing on the problem where it was used. For example, you might write

[Name] explained to me how to do [some part] of this problem.

I found an explanation of [concept] at the website [url].

I asked ChatGPT to [request].

Forbidden:

• The written work or programs from students who took this class in the past.
• Websites such as Chegg that claim to have homework solutions for this class.
• Code produced by chatbots or other AI.
• Direct copying.

A minor, first-time violation of this policy will receive a warning and discussion and clarification of the rules. Serious or second violations will result in a grade penalty on the assignment. Very serious or repeated violations will result in failure in the class and be reported to the Office of Community Standards and Student Responsibility, which may impose additional sanctions. You may appeal any sanctions through the grade appeal process.

Special Needs:

If you have specific physical, psychiatric, or learning disabilities and require accommodations, please let me know as soon as possible so that your learning needs may be appropriately met. You should also register with Student Accessibility Services to obtain written documentation and to learn about the resources they have available.

Responsible Employee Reporting Obligation:

If I learn of any instances of sexual harassment, sexual violence, and/or other forms of prohibited discrimination, I am required to report them. If you wish to share such information in confidence, then use the Office of Equity and Civil Rights Compliance.

Learning Resources:

• Your classmates are your best resource. Use them!
• Linear Algebra free online text.
• Notes on Diffy Qs: Differential Equations for Engineers free online text.
• Octave is an open-source alternative to Matlab, with the same syntax but less functionality. You can do simple Octave computations using a sage cell in octave mode:

Schedule (Subject to change) Show/ Hide

Last modified: Wed Sep 20 12:19:04 UTC 2023