Research Activites

Math 4329 (11731): Numerical Analysis

  • Instructor: Dr. Natasha S. Sharma
  • Meeting Times: Tu-Th 12:00pm-1:30pm, Liberal Arts Building 122
  • Office Hours: Thursdays 2:30pm-3:30pm, or by appointment.
  • Teaching Assistant: Khodeza Begum (kbegum@miners.utep.edu), Office Location: Bio Engineering Building 302, Office Hours: 12-1:30pm Wednesdays
  • TextBook: Elementary Numerical Analysis, Third Edition by Atkinson and Han, John Wiley and Sons 2004
  • Click here for the syllabus.

    In this course we will learn how to approximate the solutions to the mathematical problems which are traditionally deemed difficult to solve. In particular we study the functions which help us approximating the solutions such as Taylor Polynomials and Spline functions. Emphasis will be also laid on the accuracy of such approximations via the error analysis. We will also focus on solving large system of equations through algorithms including a discussion of how to numerically implement such algorithms. Students will simultaneously be trained in the theory and practice involved in solving large systems of equations and understand and interprete the quality of such solutions.


    Lecture Topic for the week
    Assignments for the week
    17th-20th January
  • Tuesday: Review of Taylor Polynomials
  • Thursday: Taylor Polynomials continued
  • Worksheet 01 was distributed in class. You can download it here.
  • 23rd-27th January
  • Tuesday: Floating point representation, Sources of errors
  • Thursday: More on Floating Point Representation, types of errors
  • Worksheet 02 was distributed in class on 24th. You can download it here.
  • Homework 01 distributed in class due on 02/02.
  • Matlab Introduction
  • 30th January- 3rd February
  • Tuesday: Loss of Significance errors
  • Thursday: Underflow Overflow of errors and propagation of errors
  • Homework 01 due in class on 02/02 !
  • Midterm 1 is on 02/09.
  • Worksheet 03 was distributed in class on 2nd. You can download it here
  • 6th-10th February
  • Tuesday: Midterm Review
  • Thursday: Midterm
  • Midterm review can be downloaded here
    13th -17th February
  • Tuesday: Iterative Methods: Bisection Method
  • Thursday: Iterative Methods: Newton and Secant Method
  • Worksheet 04 was distributed in class on 14th. You can download it here.
  • Homework 2 posted due date 02/23.
  • 20th -24th February
  • Tuesday: Fixed Point Iteration, Ill-behaving root finding problems
  • Thursday: Polynomial Interpolation
  • Worksheet 05 distributed in class on 21st February. You can download it here.
  • 27th February - 3rd March
  • Tuesday: Polynomial Interpolation: Lagrange's Polynomial
  • Thursday: Polynomial Interpolation: Newton's Divided Difference
  • Worksheet 06 distributed in class on 28th February. You can download it here.
  • Worksheet 07 was introduction to splines.
  • 6th-10th March
  • Tuesday: Review for Midterm
  • Thursday: Midterm 2
  • 13th-17th March
    20th - 24th March
  • Tuesday: Numerical Integration and Gaussian Quadrature
  • Thursday: Degree of Precision
  • Worksheet 08 distributed. You can download it here.
  • 27th - 31st March
  • Solving Linear Systems: An introduction and review of matrices
  • Worksheet 09 on Matrix Aritmetic distributed. You can download it here.
  • 3rd - 7th April
  • Solving Linear Systems: Gaussian Elimination and LU Decomposition
  • Homework 03 due on 6th April !
  • Worksheet 10 was distributed. You can download it here.
  • 10th - 14th April
  • Solving Linear Systems: Ill Conditioned Matrices
  • Worksheet 11 was distributed. You can download it here.
  • 17th - 20th April
  • Solving Linear Systems: Using Matlab for Gaussian Elimination and Residual Correction Method
  • Solving Linear Systems using Jacobi Method and Gauss Seidel.
  • GePivot code can be downloaded here.
  • Residual_Correction code.
  • 24th-28th April
  • Solving Nonlinear Equations using Newton's Method.
  • A plot of the intersection of the hyperbola and circle here.
  • MATLAB code to generate the plot above.
  • Homework 04 is due on 27th April !