MATH 5363 (Fall 2020)

MATH/PHYS 5363 001: Scientific Computation and Numerical Methods, Fall 2020

 

Lecturer: Dr. Kaman
Lecture: Mon, Wed, Fri 11:50 AM – 12:40 PM, KIMP0310
Office Hours: Mon, Wed, Fri 01:00 PM – 02:00 PM or by appointment, SCEN 218.
Email: tkaman@uark.edu
Textbook:
  • Uri Ascher, Chen Greif: A First Course in Numerical Methods. SIAM, 2011.
  • Alfio Quarteroni, Fausto Saleri, Paola Gervasio: Scientific Computing with MATLAB and Octave
  • Lloyd N. Trefethen, David Bau: Numerical Linear Algebra. SIAM, 1997.
Prerequisites: Graduate standing in mathematics or statistics, or departmental consent.
Learning Objectives:
  • Introduce fundamentals of scientific computing
  • Understand the numerical algorithm properties
  • Choice of appropriate numerical method for problems
  • Implement the algorithms efficiently
  • Analyse the numerical results
Course Outline:
1 Numerical algorithms (AG 1)
2 Roundoff errors (AG 2)
3 Nonlinear equations in one variable (AG 3)
4 Direct methods for linear system (AG 4.1-4.3/5)
5 Linear least squares problems (AG 6)
6 Iterative methods for linear system (AG 7)
7 Eigenvalues and singular values (AG 8)
8 (Piecewise) polynomial interpolation (AG 10.1-5/11.1-4)
9 Best approximation (AG 12)
10 Numerical integration (AG 15.1-5)
11 Ordinary differential equations (AG 16.1-6)
Note: At the beginning of the semester, there will be a crash course in Matlab.
Performance Assessments: The course grade is based on homework/lab. assignments, midterm and final exam.

Assignments 30%
Exam-1 15%
Exam-2 15%
Final Exam 40%

Grades are normally assigned according to the percentage scale A≥90, B≥80, C≥70, D≥60, F<60.
Exams: There will be three exams at class time. The two in-class exams are tentatively scheduled. The schedule may change and the changes will be announced in class and on blackboard. No make-up examinations will be given except to participate in a university-approved activity.

Exam-1 Wednesday, October 7, 2020.
Exam-2 Wednesday, November 25, 2020.
Final Exam (comprehensive) Wednesday, December 16, 2020. 12:45 PM to 2:45 PM
Homework: The homework assignments may include a mix of programming and theoretical questions.Homework problem sets with due dates will be posted on blackboard. Late homework will not be accepted. You are encouraged to talk to other students on problems, but you must submit your own solutions. Please specify SciComp20 in the subject field of your email.
Exam Policy:
  • Students must establish their course schedules to ensure no conflicts exist in their final exam schedules.
  • No make-up examinations will be given except to participate in a university-approved activity. To be excused you must notify the instructor by email prior to date of absence.
Academic Integrity Policy: Cases of suspected academic dishonesty are referred to the All University Academic Integrity Board for adjudication and will also incur a grade sanction at the discretion of the instructor. The following passage is quoted from the referenced website and is the policy in this course:

    • As a core part of its mission, the University of Arkansas provides students with the opportunity to further their educational goals through programs of study and research in an environment that promotes freedom of inquiry and academic responsibility. Accomplishing this mission is only possible when intellectual honesty and individual integrity prevail. Each University of Arkansas student is required to be familiar with and abide by the University’s Academic Integrity Policy which may be found at

    http://honesty.uark.edu/policy/index.php

      There are harsh penalties for violations as prescribed by the Sanction Rubric

    http://honesty.uark.edu/sanction-rubric/

Students with questions about how these policies apply to a particular course or assignment should immediately contact their instructor.
Classroom Etiquette: Students and instructors each have an important role in maintaining a classroom environment optimal for learning, and are expected to treat each other with respect during class, using thoughtful dialogue, and keeping disruptive behaviors to a minimum. Both students and faculty perceive abusive language directed towards others as the most disruptive behavior. Other behaviors that can be disruptive are chatting and whispering during class, the use of smartphones or laptops for texting or in other ways unrelated to the course, preparing to leave before class is over, and consistently arriving late to class. Inappropriate behavior in the classroom may result in a request to leave the class and/or a referral to the Office of Academic Integrity and Student Conduct.
Disability Act: If you have a physical, psychological, medical or learning disability that may impact your ability to carry out assigned course work, I would urge you to contact the staff in the Division of Student Affairs, Center for Educational Access cea.uark.edu, 209 ARKU, who will review your concerns and determine with you what accommodations are necessary and appropriate. All information and documentation of disability are confidential.
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