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Math 4329 (11549): Numerical Analysis

  • Instructor: Dr. Natasha S. Sharma

  • Meeting Times: TR 1:30pm-2:50pm in Liberal Arts 122

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

  • Teaching Assistant: Khodeza Begum (kbegum@miners.utep.edu), Office Location: Bio Engineering Building 302, Office Hours: Monday 3:30pm-4:30pm

  • TextBook: Elementary Numerical Analysis, Third Edition by Atkinson and Han, John Wiley and Sons 2004.
  • Click here for the syllabus.

    Course Description

    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 interpret the quality of such solutions.

    Announcements

    Week
    Lecture Topic for the week
    Assignments for the week
    28th August - 1st September
  • Taylor Polynomials Review and Floating Point Representation, Sources of error
  • Homework 01 (Due on 09/12)
    		•
  • Worksheet 01
  • Worksheet 02
    • 4th - 8th September
  • Matlab Introduction Commands
  • Access MATLAB through the website my.apps.utep.edu Matlab Introduction
  • Loss of Significance, Underflow and Overflow of errors
  • Worksheet 03
  • Worksheet 04
    • 11th - 15th September
  • Tu: Homework 1 due and Bisection Method
  • Th: Review of Midterm 01
    		•
    18th - 22nd September
  • Tu: Midterm 01!
  • Th: Introduction to one-point iterative methods and Newton's Method
    • 25th - 29th September
  • Tu: Newton's Method and order of convergence
  • Th: Secant Method
  • Worksheet 05
    		•
    2nd - 6th October
  • Tu: Fixed Point Iteration
  • Th: Fixed Point Iteration and Ill-behaving root finding problems
  • Matlab Function quad_rootfinder.m
  • Worksheet 06
    		•
    9th - 13th October
  • Tu: Polynomial Interpolation
  • Th: Error in Polynomial Interpolation
  • Homework 02 due on 10/10!
    		•
    16th - 20th October
  • Tu: Spline Functions and Midterm 02 Review
  • Th: MIDTERM 02 ON 10/19!
  • Worksheet 07
    		•
    23rd - 27th October
  • Tu: Trapezoidal and Simpson Rule
  • Th: Error Formulas Gaussian Numerical Integration
    		•
  • Worksheet 08
  • Worksheet 09
    		•
    30th October - 3rd November
  • Tu: Numerical Differentiation
  • Th: Systems of Linear Equations
    		•
  • DROP DATE FOR COURSE IS 11/03!
    		•
    6th - 10th November
  • Tu: Matrix Arithmetic
  • Th: Gaussian Elimination
  • Worksheet 10
  • Worksheet 11
    		•
    13th - 17th November
  • Tu: LU Decomposition
  • Th: LU Decomposition
    		•
  • Worksheet 12
    		•
    20th - 24th November
  • Tu: Error in solving Linear Systems
  • Th: HAPPY THANKSGIVING!
  • Worksheet 13
    		•
    27th - 30th November
  • Tu: Iterative Methods and
  • Th: Additional Topics
    		•
  • Worksheet 14
    		•
    4th - 8th December
  • Tu: Additional Topics
  • Th: FINAL EXAM REVIEW!
    		•
    11th - 15th December
  • Th: FINAL EXAM AT 13:00-16:45
    		•