Elementary Numerical Analysis II

Winter, 2020

Lecture: MWF, 14:00-14:50, 208 Deady

Instructor: Yuan Xu, Office: Deady 101, Telephone: 346-5619, e-mail: yuan@uoregon.edu .

Webpage: http://pages.uoregon.edu/~yuan/Teaching/M352.html

Office Hours: MF 11:00-11:50, W 1:00-1:50 or by appointmen.

Textbook

Cheney/Kincaid: Numerical Mathematics and Computing, 6ed or 7ed.

Course description

This is the second half of a two term sequece. Here is the link to the course webpage of the first part, M351. I will basically follow the text book. I plan to cover most of the Chapters 2, 8 (sections 8.1 and 8.2), 6, 9, 7 in 7ed of the textbook (or the Chapters 2, 8 (sections 8.1 and 8.2), 9, 12, 11 in 6ed of the textbook). Topics include: solving systems of linear equations, spline functions (Compute Aided Design), smoothing of data and least square method, solving ordinary differential equations. It will certainly be a plus if you have some skill of writting computer program. However, the emphasis is on the mathematical aspects of the algorithms rather than on the computer language used to implement them. We will use Mathematica to handle examples.

Learning outcomes

Students should be able to solve systems of linear equations using gaussian elimination with scaled pivoting, compute error and residual vectors, solve tridiagonal and banded systems, identify strictly diagonal matrices, compute matrix LU factorization and Cholesky factorization, compute the condition number, identify ill-conditioned systems of linear equations, solve systems of linear equations using iterative methods such as Jacobi and Gauss-Siedel iterations and identify when these methods converge. They should be able to identify and compute first and second degree splines, estimate accuracy of spline approximation, identify and compute natural cubic splines, and perform interpolation and approximation using B splines. Students should be able to derive solutions of ordinary differential equations using Taylor series and Runge-Kutta methods and estimate their errors. They should be able to approximate given data using the method of least squares both for polynomial and non-polynomial basis functions.

Mathematica

For in-class computer demonstrations we will use Mathematica , a powerful computer program for symbolic and numerical mathematical computations. You may also want to use it for your homework and project. Mathematica is installed in most of the computer labs on campus. This year students are able to download Mathematica software on their personal computers due to an addition of the student option to UO site license. Here is what you need to do: go to the IT Website https://it.uoregon.edu/software/list; select Mathematica from the software list; Login with their uoregon username and password to view available downloads; and select "Student Mathematica Activation File". This will direct students to the Wolfram Student Portal for the University of Oregon (To get immediate access to Mathematica activation file, you need to login to this portal from your uoregon.edu email address). If you want to learn mathematica, you can start from the following notebook.

Introduction to Mathematica

Some notebooks (Mathematica files) related to the course material will be posted here as we go along.

Example of Ill-conditioned matrix

Gaussian Elimination

Natural cubic interpolation spline function

Bezier curve

B-Spline curve

Least Square

Diff Equation

Homework

There will be a homework assignment for each week. You can check the ASSIGNMENTS here. Homework will be collected each Wednesday in class on the material of the previous week. Late homework will not be accepted. Your lowest homework score will be dropped. It is very important to keep up with your homework. Start it early, do not wait until the night before you have to turn it in.

Project

If you so choose, part of your grade will be based on a programming or research project due on the last day of the class. Possible projects include implementing the algorithms discussed in class in your favorite programming language, or researching a numerical analysis topic. A list of suggested projects will be posted after the midterm.

project.pdf

Exams

There will be one midterm exam in class on Wednesday, Feburary 12. If you must miss this exam due to extraordinary circumstances, you must get my permission and schedule a make-up exam in advance. The final exam is sheduled for Thursday, March 19 at 14:45 in 208 Deary.

Grade

Option 1: If you choose NOT to do a project, your grade will be based on your homework, midterm and final, distributed as

Homework:	20%
Midterm Exam:	40%
Final Exam:	40%

Option 2: If you choose to do a project, your grade will be based on your homework, project, midterm and final, distributed as

Homework:	20%
Project:	20%
Midterm Exam:	30%
Final Exam:	30%

Incomplete

Incomplete are only awarded in the Mathematics Department when two criteria have been satisfied: first, a student must have a passing grade at the time the ``I'' is assigned; secondly, some work could not be completed due to extenuating circumstances (illness, auto accident, etc.). Under no circumstances will an ``I'' be awarded as a substitute for a ``W'', ``D'' or ``F/N''. If you find yourself in trouble, drop the course!

Accessible Education

The University of Oregon is working to create inclusive learning environments. Please notify me if there are aspects of the instruction or design of this course that result in disability-related barriers to your participation. You are also encouraged to contact the Accessible Education Center in 360 Oregon Hall at 541-346-1155 or uoaec@uoregon.edu.

Academic Misconduct

The University Student Conduct Code (available at http://dos.uoregon.edu/conduct) defines academic misconduct. Students are prohibited from committing or attempting to commit any act that constitutes academic misconduct. By way of example, students should not give or receive (or attempt to give or receive) unauthorized help on assignments or examinations without express permission from the instructor. Students should properly acknowledge and document all sources of information (e.g. quotations, paraphrases, ideas) and use only the sources and resources authorized by the instructor. If there is any question about whether an act constitutes academic misconduct, it is the students' obligation to clarify the question with the instructor before committing or attempting to commit the act.