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Math 5329 (12087): Numerical Analysis

  • Instructor: Dr. Natasha S. Sharma

  • Meeting Times: MW 10:30 am-11:50 am, Bell Hall 130A

  • Office Hours: Mondays 1:30 pm - 2:30 pm, or by appointment.

  • Teaching Assistant: Mr. Julio Solis (jsolis8@miners.utep.edu)

  • TextBook: Numerical Analysis: Mathematics of Scientific Computing, Third Edition, by David Kincaid and Ward Cheney.
  • Click here for the syllabus.

    Course Description

    This course introduces students to the algorithms and methods that are needed in Scientific Computing. Students will be introduced to the principles of numerical methods, their implementation and finally their application to practical problems.

    Announcements

    Week
    Lecture Topic for the week
    Assignments for the week

    *In addition to the homeworks, the assignments of the week include the tasks left to students to "verify"*

    28th August - 1st September Floating Point Number System and Normalized Scientific Notation Review the Mathematical Preliminaries as described in Sections 1.1 and 1.2 from the textbook.
    4th - 8th September
    Absolute and Relative Errors
    11th - 15th September
  • Mon: Stable and Unstable Computations
  • Wed: Introduction to iterative methods and Bisection Method
    		•
    18th - 22nd September
  • Mon: Newton's Method and order of convergence
  • Wed: Secant Method and order of convergence
    		•
    25th - 29th September
  • Mon: Introduction to fixed point methods
  • Wed: Matrix Algebra and direct methods
  • Homework 01 due on 09/27!
    • 2nd - 6th October
  • Mon: Gauss Jacobi Method
  • Complexity and the computational work of an algorithm
  • Wed: Midterm 01!
    		•
    9th - 13th October
  • Mon: LU and Cholesky Decomposition
  • Wed: Matrix norms, Gauss Seidel Method
  • SOR Method and its convergence
  • Method of Steepest Descent
  • Midterm 01 corrections due on 10/16
    		•
    16th - 20th October
  • Mon: Method of Conjugate Gradients
  • Wed: Conditioning and Growth of the Spectral Conditioning
  • Homework 02 due on 10/18!
    		•
    23rd - 27th October
  • Mon: Linear Least Squares Method
  • Wed: Polynomial Interpolation: Lagrange, Newton's Divided Differences
    • 30th October - 3rd November
  • Mon: Chebyshev Polynomials, Hermite Interpolation
  • Trigonometric interpolating polynomials, Fourier Transformations
  • Wed: Convergence analysis of interpolating polynomials
  • Homework 03 due on 11/01!
  • DROP DATE FOR COURSE IS 11/03!
    		•
    6th - 10th November
  • Mon: Numerical Integration
  • Wed: Numerical Differentiation
    		•
    13th - 17th November
  • Mon: MIDTERM 02!
  • Wed: Numerical Solutions of ODEs: One Step Methods
    		•
    20th - 24th November
  • Mon: Numerical Solutions of ODEs: Runge Kutta Methods
  • Th: HAPPY THANKSGIVING!
    • 27th - 30th November
  • Mon: Numerical Solutions of ODEs: Multistep Methods
  • Stiff systems
  • Wed: Additional Topics
    		•
  • Homework 04 due on 11/27!
    		•
    4th - 8th December
  • Mon: Additional Topics
  • Wed: FINAL EXAM REVIEW!
    		•
    11th - 15th December
  • Th: FINAL EXAM AT 10:00 AM-12:45 PM ON 12/15!
    		•