MATH 2070U: Numerical Methods

Instructor: Greg LewisOffice: UA4033Phone: ext. 2608Email: Use Blackboard ‘Messages’

Text:Applied Numerical Methods with Matlab for Engineers and Scientists, 3rd Ed., Steven C. Chapra

Course Description:There are two dominant themes in this course: applied programming for scientific computing and the theory anddevelopment of numerical algorithms. The first step will consist of learning basic programming techniques with thescientific problem-solving environment Matlab. Subsequently, we will proceed to develop an understanding of thepractical mathematical concerns underlying numerical computations that arise in many scientific and engineeringproblems. The student will develop the ability to choose the method most appropriate for a given problem, and toassess the accuracy or correctness of the numerical solution. A deeper understanding of the mathematics at the coreof these problems develops a sense of when to trust or mistrust calculations produced by computer software.

Grading:Your course mark will be calculated as follows :

Final Exam 55%Midterm 30%Quizzes 15%

Midterm Test and Final Exam:There will be one midterm test that will take place in the regularly scheduled class time, and that will be approxi-mately 75 minutes in length. The final exam will be 3 hours in length and will take place in the regularly scheduleduniversity final exam period. The final exam will test all material covered in the course.

In order to pass the course, you must achieve a mark of 40%, or better, in the final exam.

The midterm is tentatively scheduled for Monday March 3, during class time.

Readings and Quizzes:Throughout the term, there will be approximately 6 quizzes that will be administered during your tutorial; the twoquizzes with the lowest mark will not count toward the final tutorial quiz mark. The quiz will be like an in-tutorialassignment, and will possibly be done in groups of two. Generally, one part of the quiz will be a written problemwhile a second part will involve programming in Matlab.

There will be a weekly reading that is expected to be completed before the material is covered in class. In order totest your comprehension of the readings, there will be on-line quizzes, administered through Blackboard. There willbe approximately 8 such quizzes throughout the term; the two quizzes with the lowest mark will not count towardthe final on-line quiz mark.

All quizzes combined will comprise 15% of your final grade for the course. Tentatively, the tutorial quizzes will be10% of the final grade, while the on-line quizzes will be worth 5%. I reserve the right to adjust this distribution ifappropriate.

Office Hours:The scheduling of my offices hours is to be determined. I will schedule 2 hours a week at times that will be mutuallybeneficial for as many students as possible. Please try to come to my office hours; it is better than e-mail (i.e.messages via Blackboard) because questions can be answered much more effectively with a dialogue than with amonologue. If you can’t come during my regularly scheduled office hours, you can make an appointment with me.To make an appointment contact me, preferably by email, or otherwise by phone. I would prefer that you makean appointment, but you can also try to find me in my office at times outside of my office hours. I will have an‘open-door/closed-door’ policy: if my door is open, please come in and ask a question, if my door is closed, I ameither not there, or I am doing something where I cannot be disturbed. In other words, if the door is closed, pleasedo not knock. Please note, I will not be available at all times.

Discussion Groups:I have set up two discussion groups on the course webpage. One of the groups is entitled ‘Course Material’ whereyou can post questions that may be answered by other students in the course. Only questions relating to coursematerial should be posted. I will monitor this page, and I will make postings when appropriate.

I have also set up another page, entitled ‘Class Messages’ that I will not monitor regularly. Postings here do notnecessarily have to be course material specific.

These groups are not ‘chat pages’, and posting of objectionable material, of any form, will not be tolerated. Notethat the postings are NOT anonymous.

E-mail ‘checklist’:You can e-mail me if you have specific questions. E-mail questions must be very specific. General questions, like ‘Idon’t understand Section 1.1’, should be asked to me, or your tutorial instructor, in person. In addition, before yousend an e-mail, I would ask that you go through a short checklist. If you e-mail me about everything without firstlooking for easier and quicker solutions, I will be overwhelmed with masses of e-mail, and I won’t be able to answerany e-mail in a reasonable amount of time.

Checklist:(1) Ask a classmate.(2) Check the course discussion page.(3) Post the question on the course discussion page.(4) Direct all technical issues to the IT help desk.(5) Make sure your question is specific and clearly stated.

If these don’t work, or you do not feel comfortable with these options, send me an e-mail.

I will try (to the best of my ability) to answer all e-mail within 48 hours. I cannot promise to answer messages fasterthan that.

If appropriate, I reserve the right to post your e-mail (with your name removed) in the discussion group.

Missed Course Work:For all missed course work, the official Faculty of Science policies will be followed. The full policies are postedat: http://www.science.uoit.ca/undergraduate/current-students/academic-policies.php . An incomplete summary ofsome important policies follows. If you miss a midterm test for a legitimate reason and can provide appropriatedocumentation, you will not be penalized. The normal policy in the Faculty of Science is to re-weight the remainingterm work to account for the missed mark. Legitimate reasons are illness or death in the family, and appropriatedocumentation is a UOIT Medical certificate, or death certificate, respectively. Within 5 days of missing thetest, you must provide the proper documentation to the Science Academic Advisor (science.advising@uoit.ca; office:UA4013). Failure to submit the appropriate documentation by the deadline may result in a grade of zero for thetest. If you cannot write a midterm for any other reason, it MUST be discussed with me and the Science AcademicAdvisor at least 2 days BEFORE you are scheduled to write it. A decision will be made on a case by case basis.

Missed quizzes will receive a mark of zero, regardless of the reason you’ve missed it. That is, it will be considered asone of your two lowest quizzes that will not count towards your final quiz mark. If you miss more than two quizzes forlegitimate reasons, please bring the appropriate documentation to me, and your final quiz mark will be re-weightedaccordingly.

Academic Misconduct:Any misconduct in association with quizzes, tests and exams will be dealt with according to University policy (thisis serious).

Course topics include:

1. Modelling, computing and error analysis: Introductory Matlab programming (operators, data types, arrays,graphics, scripts, functions, flow control); mathematical models for engineering applications; machine represen-tations of floating-point numbers; round-off and truncation errors

2. Roots: Scalar nonlinear equations; algorithms for nonlinear equations and minimization

3. Linear systems: Numerical linear algebra; Gaussian elimination, LU factorization, elementary operation counts;Cholesky factorization, condition numbers, iterative methods

4. Curve fitting and interpolation: Linear and nonlinear least-squares regression; polynomial interpolation

5. Numerical integration and differentiation: Quadrature formulas; composite quadrature formulas; adaptivequadrature; finite-difference formulas; partial derivatives

6. Numerical methods for ordinary differential equations: Euler’s method and improved methods for IVPs; Runge-Kutta methods; systems of ODEs; shooting and finite-difference methods for BVPs