UTA Department of Mathematics

Hristo V. Kojouharov > Teaching > MATH 5300-001

MATH 5300 - 001. Introduction to Scientific Computing
Spring, 2018
TuTh 2:00PM - 3:20PM
Pickard Hall, Room 102

    Tu Th 11:00AM - 11:50AM or by appointment
    ``All fields of science and engineering rely heavily on numerical computing. The traditional two branches of science are theoretical science and experimental science. Computational science is now often mentioned as a third branch, having a status that is essentially equal to, perhaps even eclipsing, that of its two older siblings. The availability of greatly improved computational techniques and immensely faster computers allows the routine solution of complicated problems that would have seemed impossible just a generation ago.''
              -- Michael L. Overton, Courant Institute of Mathematical Sciences

    This course provides a deeper look into the computational aspects of many numerical techniques used for solving otherwise intractable problems in science and engineering. It also serves as an introduction to scientific programming in the numerical MATrix LABoratory language MATLAB. MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.
    Students will be able to use the numerical MATrix LABoratory language (MATLAB) for scientific programming applications. Students will be able to demonstrate knowledge of how numbers are represented in a computer system and discuss presence of computer errors in representing numbers. Students will become familiar with a variety of numerical methods for solving mathematical problems that involve systems of linear equations; nonlinear equations/systems; definite integrals; first- and higher-order derivatives; and polynomial interpolation. Students will be able to apply numerical methods to solve real-world problems that involve models of the five mathematical types listed above; to discuss the advantages and disadvantages of the implemented methods; and to write and present a short report (term paper) in front of an audience of peers/classmates.
    Topics covered during the semester in MATH 5300 include:
    • Number Representations and Errors: Chapter 1
    • Getting Started with MATLAB (class meets in LS B27)
    • Direct and Iterative Methods for Solving Linear Systems: Chapters 2 & 8
    • Numerical Methods for Solving Equations of One Variable: Chapter 3
    • Interpolation and Polynomial Approximation: Chapter 4
    • Numerical Methods for Differentiation and Integration: Chapters 4 & 5
    • Numerical Methods for Differential Equations: Chapter 7

    "As the instructor for this course, I reserve the right to adjust this schedule in any way that serves the educational needs of the students enrolled in this course. -Hristo V. Kojouharov."
    Grades are based on weekly homework assignments, two midterm exams, and a term paper. There is no extra credit.
    • Homework Assignments (10%): Theoretical and computational problems will be assigned regularly throughout the semester. Homework will usually be assigned weekly on Thursdays, and written reports will be due the following Thursday. Teamwork is encouraged.
    • Two Mid-Term Exams (70%): Each mid-term exam will be given during a class period and you will have 80 minutes to take it. Exams will be made up of questions similar to the assigned homework problems. A tentative schedule of the exams is as follows: Exam #1 - Thursday, March 22, 2018; Exam #2 - Thursday, April 26, 2018. Topics and exact dates for each exam will be announced in class at least a week in advance. Make-ups for exams will be given only for the university approved absences, and should be discussed prior to the exam.
    • Term Paper (20%): A short report discussing the numerical solutions, interpretation, and comparison of the results of a project must be submitted at least one week before the last day of classes. The project should be about a real-world problem and you should implement two different numerical algorithms, in a computer language of choice or use any available software, to solve it. I highly encourage the use of MATLAB for this project. A hard-copy of the term papers must be submitted by Thursday, May 3, 2018. In addition to a hardcopy submission, the term papers should be orally presented in class during the last week of classes.

        Grading Scale:   A = 90+; B = 80-89; C = 70-79; D = 60-69; F = 59-

    Students are expected to keep track of their performance throughout the semester and seek guidance from available sources (including the instructor) if their performance drops below satisfactory levels.
    Class participation is an important aspect of this course, so be considerate of other students and arrive on time. Please turn off cell phones, tablets, and other electronic devices.