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Math 4329 (19349): Numerical Analysis

  • Instructor: Dr. Natasha S. Sharma

  • Meeting Times: TR 3:00-4:20 pm in Education Building 313

  • Office Hours: MW 2:00-3:00 pm, or by appointment.

  • Teaching Assistant: Imran Abdullah (aimran@miners.utep.edu)

  • 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
    27th-31st August
  • Taylor Polynomials Review and Floating Point Representation, Sources of error
  • Slides from the first lecture.
  • Slides from the second lecture.
    		•
  • Worksheet 01
  • Worksheet 02
  • Homework 01 (Due on 09/13)
    • 3rd-8th September
  • Matlab Introduction Commands
  • Access MATLAB through the website my.apps.utep.edu Matlab Introduction
  • Loss of Significance, Underflow and Overflow of errors
  • Slides from the Bisection Method
    		•
  • Worksheet 03
  • MATLAB bisection.m code
  • Worksheet 04
    • 10th - 14th September
  • Tu: Bisection Method (continued) and order of convergence
  • Th: Newton's Method and order of convergence
    		•
  • Homework 01 is due on 09/13!
  • Worksheet 05
  • Code for Newton's Method
    		•
    17th - 21st September
  • Tu: Secant Method with order of convergence
  • Th: Introduction to one-point iterative methods
  • Worksheet 06
      • Homework 02 Questions:
    1. Problem 4, Section 3.1.
    2. Problem 13, Section 3.1.
    3. Problem 3, Section 3.2.
    4. Problem 8, Section 3.2.
    5. Problem 10, Section 3.2.
      6.
    The above questions are taken from the course textbook and are due on 09/25!
    25th - 29th September
  • Tu: Polynomial Interpolation
  • Th: MIDTERM 01 REVIEW!
  • Worksheet 05
  • Homework 02 due on 09/25!
  • Worksheet 06
    		•
    1st - 5th October
  • Tu: Exam 01 in class
  • Th: Discussion on Exam 01 and Polynomial Interpolation
    • 8th - 12th October
  • Tu: Spline Functions
  • Th: Splines continued
  • Worksheet 07
  • Worksheet 08
  • Homework 03 announced due on 10/18!
    		•
    15th - 19th October
  • Tu: Numerical Integration Part 1
  • Th: Numerical Integration Part 2
  • Worksheet 09
    		•
    22nd October - 26th October
  • Tu: Numerical Differentiation
  • Th: MIDTERM 02 REVIEW!
  • Homework 04 due on 10/25!
    		•
    30th October - 2nd November
  • Tu: Exam 02
  • Th: Systems of Linear Equations
    		•
  • DROP DATE FOR COURSE IS 11/02!
  • MATLAB Function to generate a matrix.
  • Lecture Recording
    		•
    5th - 9th November
  • Tu: Matrix Arithmetic
  • Th: Gaussian Elimination and LU Factorization
  • Condition Number
  • Worksheet 10
  • Worksheet 11
      • Homework 05 Questions:
    1. Problems 1(a), 1(b) Section 6.1.
    2. Problems 4, 5 Section 6.1.
    3. Problem 1 all parts Section 6.2.
    4. Problem 6(c), 6(d) Section 6.3.
    5. Problem 10, Section 6.4.
      6.
    The above questions are taken from the course textbook and are due on 11/13!
    12th - 16th November
  • Tu: Prelude to Iterative Methods
  • Newton's Method in 2D
  • Th: Error in solving Linear Systems and Iterative Methods and Residual Correction Methods
    		•
  • Worksheet 12
  • Homework 06 announced! Due date November
    • 19th - 23rd November
  • Tu: Jacobi and Gauss Seidel Method
  • Th: HAPPY THANKSGIVING!
  • Worksheet 13
  • GePivot code can be downloaded here.
  • Residual_Correction code
    • 26th - 30th November
  • Tu: Convergence of Iterative Methods and Residual Correction Method and Extra Topics
  • Th: Talk by PhD Candidate Ms. Marisol Domininguez on Global Analysis of the Hydrologic Sensitivity to Climate Variability
  • MIDTERM 03 REVIEW!
    		•
    3rd - 8th December
  • Tu: OPTIONAL MIDTERM 03!
  • Th: FINAL EXAM REVIEW!
    		•
    11th - 15th December
  • FINAL EXAM AT 16:00-18:45 ON DECEMBER 13TH
    		•