Course Syllabus

Contact Information

Prof. Nikola Petrov

Department of Mathematics

Lecture: Tuesday & Thursday, 1:30-2:45 pm in PHSC 222

Office Hours (tentative): Wednesday 11 am -12 pm or by appointment, in PHSC 1103

Zoom link for the office hours (if needed): https://oklahoma.zoom.us/j/91047787149?pwd=0hMzPanSYsPbHW4ABjmad2pE9The8c.1

Meeting ID: 910 4778 7149

Passcode: 65638772

Course Details

Course Catalog Description

Solution of linear and nonlinear equations, approximation of functions, numerical integration and differentiation, introduction to analysis of convergence and errors, pitfalls in automatic computation, one-step methods in the solutions of ordinary differential equations. (F)

Course Prerequisites

MATH 3113 or MATH 3413.

Course Materials

Textbook: R. L. Burden, J. D. Faires. Numerical Analysis. Brooks/Cole, 8th, 9th, or 10th edition.

Course objectives

In this course you will learn:

how floating-point numbers are saved in a computer, where round-off errors come from, and how to deal with them;
how to classify and measure the rate of convergence of numerical algorithms;
how to compute numerically roots of algebraic equations in one variable: bisection, fixed-point iteration, Newton's method and its modifications (secant method, regula falsi), accelerating convergence (Aitken's and Stefensen's methods), [if time permits] zeros of polynomials and Müller's method;
how to interpolate and approximate functions by polynomials: Lagrange polynomials, Newton's divided differences, cubic spline interpolation;
how to compute numerically derivatives of functions: forward- and backward-difference formulae, n-point formulae, Richardson's extrapolation.
how to find the numerical value of definite integrals: trapezoidal, Simpson's and higher-order formulae, composite integration, Romberg integration, Gaussian quadrature (linear spaces, inner product spaces, spaces of polynomials, orthogonalization, Legendre and Hermite polynomials, quadrature formulae);
how to solve numerically initial-value problems for ordinary differential equations: Euler's method, higher-order Taylor methods, Runge-Kutta methods.

Attendance

Attendance and active participation in class activities are crucial to this course and are expected. Class time is to be utilized only for course-related work. Use of cell phones and other communication devices (unless used strictly for approved class content related activities) distracts from class participation and time utilization, therefore, use of these devices in class will not be allowed: texting, emailing, chatting, internet browsing etc. will not be tolerated. If you cannot attend class, please ask a friend from the class for their notes and do your best to catch up.

Communication

Students are expected to check e-mail and Canvas on a frequent and regular basis in order to stay current with course-related communications, recognizing that certain communications may be time-critical. It is recommended that e-mail and Canvas be checked daily.
Likewise, I will be checking my email every day. I will always make every effort to reply within one business day, but do not expect a reply from me outside of regular business hours.

Grading Scheme

Breakdown. The components of your semester grade are given in the table below.


Activity	Weight
Gradescope homework	35 %
Two midterm exams	20 % each
Final exam	25 %

Scale. Your semester grade will be no lower than what is indicated in the table below.

Semester grade	A	B	C	D	F
Percentage	90.00-100.00	80.00-89.99	70.00-79.99	60.00-69.99	50.00-59.99

Course Components

Homework

There will be a homework assignment every 1.5 weeks on average.
The homework will be posted in Canvas.
One homework assignment score will be dropped.

These assignments must be submitted electronically through Gradescope. You can write your solutions by hand, and then create a single PDF file of it using a phone/tablet/scanner. There are many free scanner apps for phones and tablets. On my iPhone I use a very friendly and convenient free scanner app called Genius Scan. Please do not use your photo camera - the files are much larger and usually of worse quality than those created by scanning.
Homework assignments will not be accepted via email.
Late assignments will not be accepted (except in the cases listed under "Make-ups" below).
When submitting your homework, you must satisfy all of the following requirements:

1. You must tag the pages on which each problem appears (i.e., assign each part of each problem to a particular page or pages).
2. Though Gradescope accepts either images or PDFs, the policy in this class is that you must submit a single PDF file.
3. You may need to know how to combine several PDFs into a single file.
  1. You can easily combine pdf files using Adobe Acrobat or (on a Mac) Preview.
  2. You can use an online service such as www.pdfmerge.com.
  3. On Windows, there are various programs that can do this. Just google "combine PDFs in windows" to find more options.
  4. Your homework must be easily readable. Please write your solution with a dark and thick enough pen on a white sheet of paper and scan it in good light.

If your work fails to satisfy any of the above requirements, you may be assigned a grade of 0 for this particular homework.

Exams

There will be two midterm exams, to be held during the usual class period, currently scheduled for:

October 7 (Tuesday),
November 25 (Tuesday).

The final exam will be comprehensive, and will take place online on December 16 (Tuesday), 1:30-3:30 pm, in PHSC 222.
No exam grades will be dropped.
You already have access to your final exam schedule, so do check whether or not you are scheduled to have several finals on the same day.

1. If you have more than two finals on the same day, the instructor(s) giving the third and subsequent finals must offer make-ups.
2. For that to happen, you must notify the affected instructor(s) by the end of the twelfth week of classes (that is, by November 14).

Make-ups

The grading scheme allows you to miss one homework assignment. It will not be possible to make it up after the due date except in the following circumstances:

1. Illness (you have to provide formal documentation from a healthcare provider to excuse the absence).
2. A conflict with a religious observance.
3. A conflict with a Provost-approved University-sponsored responsibility (for example an away game for a varsity team).
4. A conflict with some other legally required activity (e.g., jury duty or emergency military service).

Unless the absence is due to unforeseeable circumstances, you are required to notify me at least two weeks in advance.

The same policies apply to missed midterm exams.

There will be no opportunities to do work for extra credit.

Mathematica and MATLAB software

In order to help us deal with things that are very difficult or impossible to do by hand, like drawing pretty graphs or calculating really complicated derivatives or integrals, we will be using the computer algebra system Mathematica and the programming platform MATLAB.
As an OU student, you can download Mathematica and MATLAB for free from the OU Information Technology web-site.
Install it now, it is a very useful tool which can help you check your calculations, plotting graphs of functions, etc.
If your device does not support installing Mathematica, a limited online alternative that you could use in the classroom can be found at https://www.wolframcloud.com (Links to an external site.)
Wolfram Alpha (Links to an external site.) can also provide some similar functionality.

Help

If you need help, you are welcome to come to my office hours which will be held in PHSC 1103 or, if needed, through Zoom (the link is given above). If you need help and cannot come to the regularly scheduled office hours, you may make an appointment by email. Before coming to the office hours, please do your best to solve all homework problems so that you come with clearly stated questions. You can come to the office hours if you have a question on the material covered in the lectures (not necessarily in a homework), but I will not repeat the lectures during office hours. If you miss a lecture, you are responsible for finding out what you have missed.

University Academic Policies and Student Support

Important Links

Registration and Withdrawal

If you choose to withdraw from this course, you must complete the appropriate University form and turn the form in before the deadline. If you stop attending the course and doing the coursework without doing the required paperwork, your grade will be calculated with missed homework and examination grades entered as zero. This could result in receiving a grade of F in the course. Deadlines are shown in the Academic Calendar, which is available from the Office of the Registrar.