CS/MATH 3414: Numerical Methods

Fall 2016

 

Dr. Young Cao

email: ycao@cs.vt.edu

phone: 540-231-1417

Office:  Torgersen Hall 2160L

Office Hours:  TR 10:45am-11:30am and 1:30pm-2pm or by appointment

Website: http://people.cs.vt.edu/~ycao

 

 

 

Class Location/Time: WLH 340, TR 9:30am-10:45am

Course Web page: http://www.cs.vt.edu/~ycao/cs3414/ or Canvas Site

Force Add Link: https://www.cs.vt.edu/F16Force-Add password: 3414y_c#

 

GTA: Andrey Poprov, Office Hours: 9:30-10:30am or by appointment, Location: 106/110 McBryde

Open Door Policy: At any time of a day, if my office door is open, students are welcome to drop by and ask questions.

Note: If you cannot make office hours of either mine or the TAÕs, you are welcome to send emails to us. If your email is sent before 5pm, usually I will respond the same day. If it is after 5pm, I will respond after 10pm or sometimes the next day.

 

Course Description: This course will cover computational methods for numerical solution of non-linear equations, polynomial approximations, iterations, numerical linear algebra, numerical differentiation and integration, methods of least squares, and other topics. Partially duplicates Math 4554.  Cross-listed with Math 3414. (3H, 3C)

 

Prerequisites: A grade of C or better required in CS1044, CS1114 or CS1124, as well as MATH 2214 and MATH 2224.

 

Course Objectives:  Upon completion of this course, students should be able to:

1.     Select and apply appropriate numerical techniques for solving common scientific/engineering problems.

2.     Estimate the accuracy and reliability of common numerical algorithms;

3.     Explain why and when certain routines may fail in special situations.

 

Topics Covered:

            1.     floating point arithmetic

            2.     roots of equations

            3.     numerical linear algebra

            4.     least squares

            5.     interpolation and numerical differentiation

            6.     splines and approximation

            7.     numerical solution of ordinary differential equation (depending on the progress of class)

            8.     eigenvalue problems (depending on the progress of class)

            9.     Basic knowledge of Monte Carlo Methods (depending on the progress of class)

 

Assessment:  Complete descriptions and instructions for completing assessments will be provided when assignment is made.  Dates for assignment of assessment and due dates for assessment completion will be indicated on the course schedule. For midterms, students have an option to skip one midterm upon approval from the instructor, for reasons such as health reason or schedule conflict, etc. In that case, the weight for that midterm will be automatically distributed to the rest exams.

 

Attendance/Quizzes:                                      10%    

Midterm Exam 1                                             10%

Midterm Exam 2                                             15%

Final Exam                                                      20%

Homework/Programs                                      20%

Four Projects                                                  25%  

 

Total:                                                             100%

 

Final Grades: All assignments receive a numeric grade.  Your final grade will be converted to a letter grade as follows (Note: The following are estimated scales. In principle, around 10% of the class will get a letter grade A, and the median of the class should be in the range of B-. Depending on the class performance, the grading scale may change, but your grade will not be lower than the following estimation.):

 

A    90-100%                          A-  85-89.99%

            B+  80-84.99%                       B   75-79.99%                         B-  70-74.99%

            C+  65-69.99%                       C   60-64.99%                         C-  57.50-59.99%

            D+  55-57.49%                        D    52.5-54.99%                     D-  50-52.49%

            F     0 -  49.99% or if ANY honor code violation is involved

 

Textbook:

            W. Cheney and D. Kincaid, Numerical Mathematics and Computing, 6th Ed., Brooks/Cole, 2007

(Note: Stay cheap, you donÕt have to buy the expensive 7th edition, a 6th edition used book is enough and much cheaper. I have no objection if you use previous versions either, as long as you do have a textbook as a good reference for details. Check Canvas and TopHat for more materials I provided online.)

 

Reference books:

Greenbaum, A., & Chartier, T. P. (2012). Numerical methods: design, analysis, and computer implementation of algorithms. Princeton University Press.

            W. Cheney and D. Kincaid, Numerical Mathematics and Computing, 5th Ed., Brooks/Cole, 2003

            W. Cheney and D. Kincaid, Numerical Mathematics and Computing, 4th Ed., Brooks/Cole, 1999, (or 3rd Ed, 1985)

            Daulquist, Numerical Methods, Prentice-Hall, 1974

            Henrici, Elements of Numerical analysis, Wiley, 1964

            C. Moler, Numerical Computing with MATLAB (available online or from SIAM)

Materials:  All additional materials for this course will be provided online, such as Canvas (https://canvas.vt.edu/courses/28459 ) for lecture notes, instructional videos, homework and projects and TopHat (https://app.tophat.com/e/699425 ) for lecture notes, as needed.

 

Technology:  Students in this course will need a working and reliable computer and Internet access that will allow the use of Canvas course site tools, TopHat, MatLab and any online resources provided.

 

Course Structure: Class sessions in this course will consist of a combination of PowerPoint slides and lecture, as well as some material hosted in the Canvas site for viewing prior to and after class. We will also adopt a hybrid teaching style by providing video clips on Canvas for important lecture topics and exercise practices. TopHat (http://tophat.com/) will be used to check attendance and conduct polling and quizzes – all students MUST register for TopHat (note that the expensive textbook is not required). PPT slides and video clips will be available before/after class. They can assist you, but please note that they are too brief to replace the notes you should be taking during class, especially for mathematical derivations. All programs should be written using MatLab, unless otherwise specified.

 

Expectation: In this course, we will introduce many different subjects in the wide area of numerical methods. For each subject we will implement the following procedure:

1.     Instruction in class to explain the problem, the method and the numerical analysis. In this step, it is mainly instruction, but you are encouraged to ask questions. It is recommended that you preview the slides before coming to class. You are expected to attend 90% of the class unless special arrangement is made to adjust your grading. Participation (including attendance check and quiz participation) takes 3% of your total score.
 

2.     In the following class, a review for the same topic is given, and then you are challenged with a quiz question. You are given around five minutes to answer a quiz question (Sometimes when time is not enough, I will also assign an out of class quiz problem, which you will take whatever period of time to solve and submit before or in the next class.). Then the statistics is collected so that the instructor can see how many students grasp the corresponding concept/method. The solution of the quiz is immediately given and explained. In your final grade, we will drop two or three lowest quiz scores (missing a quiz will automatically count as 0) and use the average of the rest to assign the quiz grade (7%).

Both attendance check and quizzes are done through TopHat. Make sure you have the app installed no later than the second week of the semester. 

3.     When each module is about to end, you are given a homework assignment, in which you will run numerical experiments to apply the corresponding numerical method to different problems. Homework is used to help you to explore related knowledge and to gain extensive understanding of the topic, rather than to help you better prepare for the exams. Please be aware that homework in this course could be very challenging. For some problems, you will simply solve the problem (by hand or by your Matlab code), but for some problems, you will find that some unexpected numerical results. You need to think about in what special scenario certain numerical methods may fail. After the assignment is due, all questions are explained in class. For homework assignment, discussion is encouraged but each individual should submit his/her OWN solution. Copying other studentsÕ work is against the honor code and may result in an F grade for this course. At the end the lowest score of the homework is dropped and the average of the rest will be used to assign the homework grade (20%).

4.     Besides quizzes and homework, you will also be given four project assignments so that you can apply numerical methods to solve a more difficult and challenging problem. Students can form a two-person team to work on a project. The idea for the solution of each project will be discussed in class, but the solution and codes will never be shared, even after the due date.

 

Participation:  Participants in this course should expect to spend about 8-10 hours per week involved in the activities and completion of assignments over the semester. This time invested is an average with some weeks requiring more, some less time to complete all assignments and activities. If you have a very tight schedule for this semester and wonÕt be able to spend that much time in this course, please donÕt take this course, otherwise you may have great difficulty as the course gets deeper.

 

Absences:  If circumstances prevent participation or timely completion, students must contact the professor to arrange for adjustments in assignment or schedule in advance of due dates and not after completion date has passed.  Late homework will NOT be accepted unless approved by the instructor in advance (official documents are required to justify any extension).

 


Honor Code:  We will be bound by the Undergraduate Honor Code
.  Please see http://honorsystem.vt.edu/ for specific information regarding expectations and policies related to the Undergraduate Honor Code.

 

Course Support:

 

Technical  - The professor for this course does not provide technical support. Requests for technical support and/or Canvas support can be directed to 4Help by calling (540) 231-HELP (4357).

 

Accommodations for Special Needs:  Any student who has been confirmed by the University as having special needs for learning must notify me in the first two weeks of the course.  For more information please go to http://www.ssd.vt.edu/ .

 

Accessibility Statement: For TopHat, check https://tophat.com/accessibility/. For MatLab, currently they do not have an accessibility statement. For more details, check  http://www.mathworks.com/matlabcentral/answers/270035-can-i-please-get-an-accessibility-statement?requestedDomain=www.mathworks.com.

 

Academic Support Services:  Any student requiring academic support should investigate the UniversityÕs services at http://www.undergraduate.vt.edu/about/aca-supp/index.html.

 

For complete information on student services at Virginia Tech, please see http://www.dsa.vt.edu/students.php