MATH 348. Scientific Computation in Numerical Analysis.

M 383C, Unique #53460, QR Flag, Fall 2015

Solving scientific, engineering, and other problems often requires the use of numerical methods and computers. This course presents various basic numerical methods, discusses their mathematical properties, and provides practice in computer programming.

Instructor:

Prof. Todd Arbogast
Office: RLM 11.162, Phone: 512-471-0166
E-Mail: arbogast@ices.utexas.edu
Office hours: MW 12:30-1:50 p.m.

Teaching Assistant:

Mr. Bing Ai
Office: GDC 6.438C
E-mail: bing.ai@utexas.edu
Office hours: Tu 9:45-10:45 a.m.

Prerequisite:

CS 303E or 307 (or any introductory programming course) and M 341 or 340L with a grade of at least C-.

Meeting:

MWF 9:00-10:00 a.m., BUR 220

Textbooks:

[1] R. L. Burden and J. D. Faires, Numerical Analysis, 9th ed., 2011, Thomson Brooks/Cole Cengage Learning (ISBN-13: 978-0-538-73351-9) (Required).

[2] Mike McGrath, C++ Programming in Easy Steps, 4th ed., 2012, In Easy Steps Limited, Warwickshire, United Kingdom (ISBN-13: 978-1-84078-432-9) (Recommended).

Web Pages:

We use the University's CLIPS and Canvas web site. Please check that your scores are recorded correctly in Canvas.

Course Description:

We will study primarily Chapters 1-6 of the Burden & Faires textbook.
  1. Mathematical Preliminaries and Error Analysis (2 lectures)
    1. Review of Calculus (read)
    2. Round-off Errors and Computer Arithmetic
    3. Algorithms and Convergence
    4. Numerical Software (read)
  2. Solutions of Equations in One Variable (6 lectures)
    1. The Bisection Method
    2. Fixed-Point Iteration
    3. Newton's Method and Its Extensions
    4. Error Analysis for Iterative Methods
    5. Survey of Methods and Software (read)
  3. Interpolation and Polynomial Approximation (6 lectures)
    1. Interpolation and the Lagrange Polynomial
    2. Divided Differences
    3. Hermite Interpolation
    4. Cubic Spline Interpolation
    5. Survey of Methods and Software (read)
  4. Numerical Differentiation and Integration (7 lectures)
    1. Numerical Differentiation
    2. Richardson's Extrapolation
    3. Elements of Numerical Integration
    4. Composite Numerical Integration
    5. Gaussian Quadrature
    6. Survey of Methods and Software (read)
  5. Initial-Value Problems for Ordinary Differential Equations (10 lectures)
    1. The Elementary Theory of Initial-Value Problems
    2. Euler's Method
    3. Higher-Order Taylor Methods
    4. Runge-Kutta Methods
    5. Error Control and the Runge-Kutta-Fehlberg Method
    6. Multistep Methods
    7. Higher-Order Equations and Systems of Differential Equations
    8. Stiff Differential Equations
    9. Survey of Methods and Software (read)
  6. Direct Methods for Solving Linear Systems (6 lectures)
    1. Linear Systems of Equations
    2. Pivoting Strategies
    3. Linear Algebra and Matrix Inversion
    4. The Determinant of a Matrix
    5. Matrix Factorization
    6. Special Types of Matrices (if time permits)
    7. Survey of Methods and Software (read)

Computer Accounts:

A computer account on the Mathematics Department network can be obtained in the Undergraduate Computer Lab, RLM 7.122.

Attendance:

Attendance is required at all class meetings.

Homework and Projects:

Homework and computer projects will be assigned periodically. It is acceptable for groups of students to help each other with the homework exercises and projects; however, each student must write up his or her own work.

Exams:

Two exams will be given during the semester on Friday, October 9 and Friday, November 13. A comprehensive final exam will be given Monday, December 14, 2:00-5:00 p.m.

Final Grade:

In determining the final grade on the letter plus/minus scale, the homework/projects will count 25%, the two midterm exams will count 20% each, and the final exam will count 35%.

The University of Texas at Austin Student Honor Code:

"As a student of The University of Texas at Austin, I shall abide by the core values of the University and uphold academic integrity."

The University of Texas at Austin Code of Conduct:

The core values of The University of Texas at Austin are learning, discovery, freedom, leadership, individual opportunity, and responsibility. Each member of the university is expected to uphold these values through integrity, honesty, trust, fairness, and respect toward peers and community.

Students with Disabilities:

The University provides upon request appropriate academic accommodations for qualified students with disabilities. Contact the Office of the Dean of Students at 471-6259, 471-4641 TTY, and notify your instructor early in the semester.

Religious Holidays:

Appropriate academic accommodation for major religious holidays is provided upon request.

Emergency Classroom Evacuation:

Occupants of University of Texas buildings are required to evacuate when a fire alarm is activated. Alarm activation or announcement requires exiting and assembling outside. Familiarize yourself with all exit doors of each classroom and building you may occupy. Remember that the nearest exit door may not be the one you used when entering the building. Do not re-enter a building unless given instructions by the Austin Fire Department, the University Police Department, or the Fire Prevention Services office.

Counselling and Mental Health Services:

Available at the Counseling and Mental Health Center, Student Services Building (SSB), 5th floor, M-F 8:00 a.m. to 5:00 p.m., phone 512-471-3515, web site www.cmhc.utexas.edu.