Home
Teaching
Research Activites
CV

Math 4329 (26683): Numerical Analysis

  • Instructor: Dr. Natasha S. Sharma
  • Meeting Times: TR 4:30 pm- 5:50 pm in Liberal Arts Building 101
  • Office Hours: Tuesday-Thursday 3:00 pm - 4:00 pm, or by appointment.
  • Teaching Assistant: John B. Snell email: jbsnell@miners.utep.edu Office Location: Bell Hall 306 Office Hours: MW 12:00-1:20 Bell 306
  • 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
    21st - 23rd January
  • Taylor Polynomials Review and Floating Point Representation, Sources of error
  • Slides from the first lecture.
  • Slides from the second lecture.
  • Formula Sheet for Differentiation and Intergration
  • Worksheet 01
  • Post Lecture Notes Tuesday
  • Post Lecture Notes Thursday
  • 28th - 30th January
  • Tu/Th: Slides from the second chapter.
  • Worksheet 02
  • Post Lecture Notes Tuesday
  • Worksheet 1 is due on Thursday!
  • Post Lecture Notes Thursday
  • 4th - 6th February
  • Loss of Significance, Underflow and Overflow of errors.
  • Tu and Th: Slides from introduction to MATLAB.
  • Matlab Introduction Commands
  • Access MATLAB through the website: Soft MATLAB.
  • Homework 01 posted!
  • Install MATLAB by 02/06 and bring your laptop to class!
  • Post Lecture Notes Tuesday
  • Post Lecture Notes Thursday
  • 11th - 13th February
  • Tu: Bisection Method
  • Th: Review for Midterm 01.
  • Worksheet 03
  • Homework 01 submission postponed to 02/13
  • Link to Wolfram: here.
  • Post Lecture Notes Tuesday
  • Post Lecture Notes Thursday (Solutions to the review!)
  • 18th - 20th February
  • Tu: Exam 01
  • Th: Bisection Method
  • Code for Bisection Method
  • txt file for MATLAB Code
  • Code for my_function.m
  • Use bisect.m code to verify the Worksheet 04 answer. Turn in your code.
  • Post Lecture Notes Thursday
  • 25th - 27th February
  • Th: Newton's Method and order of convergence
  • Th: Secant Method
  • Post Lecture Notes from Tuesday
  • Post Lecture Notes from Thursday
  • Worksheet 05
  • Code for Newton's Method
  • Matlab Function quad_rootfinder.m
    1. Homework 02 Questions:
    2. Problem 11, Section 3.1.
    3. Problem 13, Section 3.1.
    4. Problem 3, Section 3.2.
    5. Problem 2, Section 3.2. For each of the seven parts, please indicate the order of convergence.
    6. Problem 8, Section 3.2.
    The above questions are taken from the course textbook and are due on 03/03!
    3rd - 5th March
  • Tu: Fixed Point Iteration and Ill-behaving root finding problems
  • Post Lecture Notes Tuesday
  • Post Lecture Notes Thursday
  • Worksheet 06 Due on Tuesday!
  • 10th - 12th March
  • Polynomial Interpolation
  • Midterm 02 Review
  • Post Lecture Notes Tuesday
  • Post Lecture Notes Thursday
  • Worksheet 07
  • 16th - 20th March
  • Tu--Th: SPRING BREAK!
  • 24th - 26th March
  • Tu--Th: SPRING BREAK EXTENSION!
  • Midterm 02 Review
  • 31st March - 2nd April
  • Tu: Polynomial Interpolation
  • Th:Spline Functions
  • DROP DATE FOR COURSE HAS BEEN EXTENDED TO 04/10!
  • Post Lecture Notes Tuesday. Find the lecture video here.
  • Post Lecture Notes Thursday. Find the lecture video here.
  • Worksheet 08a announced on Blackboard! Do #6 from the review list.
  • 7th - 9th April
  • Tu: Spline Functions continued
  • Th: Numerical Differentiation
  • Post Lecture Notes Tuesday. For the class video please visit the chat window from our online classroom.
  • Post Lecture Notes Thursday.
  • Worksheet 08b announced on Blackboard! Due on 04/14
  • Worksheet 09a announced on Blackboard! Due on 04/19
  • 14th - 16th April
  • Tu: Numerical Differentiation
  • Tu: Numerical Integration Part 1
  • Post Lecture Notes Tuesday.
  • Post Lecture Notes Thursday.
  • 21st - 23rd April
  • Tu: Numerical Integration: Designing Quadrature Rules
  • Th:Numerical Integration: Designing Quadrature Rules (continued)
  • Post Lecture Notes Tuesday part 1.
  • Post Lecture Notes Tuesday part 2.
  • Post Lecture Notes Thursday.
  • 28th - 30th April
  • Tu: System of Linear Systems and Matrix Arithmetic
  • Solving systems using LU Decomposition
  • Th: Jacobi and Gauss Seidel Iterative Methods
  • Post Lecture Notes Tuesday.
  • Post Lecture Notes Thursday.
  • 5th - 7th May
  • Tu: Jacobi and Gauss Seidel Iterative Methods
  • Th: Extra Topics: Some applications of Numerical Analysis
  • Post Lecture Notes Tuesday.
  • Post Lecture Notes Thursday.