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Math 4329 (14695): Numerical Analysis

  • Instructor: Dr. Natasha S. Sharma
  • Meeting Times: TR 1:30-2:50 pm in Liberal Arts Building 202
  • Office Hours: Wednesdays 3:00-5:00 pm, or by appointment.
  • Teaching Assistant: John B. Snell email: jbsnell@miners.utep.edu Office Hours: MW Bell Hall 306 2:30-4:00 pm
  • TextBook: Elementary Numerical Analysis, Third Edition by Atkinson and Han, John Wiley and Sons 2004.
  • Click here for the syllabus.
  • Click here for the academic calendar.

    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-29th August
  • Taylor Polynomials Review and Floating Point Representation, Sources of error
  • Slides from the first lecture.
  • Slides from the second lecture.
  • Matlab Introduction Commands
  • Access MATLAB through the website my.apps.utep.edu Matlab Introduction
  • Worksheet 01
  • Worksheet 02
  • Homework 01 (Due on 09/12)
  • 3rd-5th September
  • Floating Point Representation, Sources of error.
  • Loss of Significance, Underflow and Overflow of errors
  • Worksheet 03
  • MATLAB script sig_loss.m
  • MATLAB function quad_rootfinder.m
  • 10th - 12th September
  • Tu: Slides from the Bisection Method
  • Th: Slides from the Bisection Method (continued)
  • Homework 01 is due on 09/12!
  • Worksheet 04
  • MATLAB function bisection.m
  • 17th - 19th September
  • Tu: Newton's Method and order of convergence
  • Th: Secant Method with order of convergence
  • 24th - 26th September
  • Tu: Introduction to one-point iterative methods and Ill-behaving root finding problems
  • Th: MIDTERM 01 REVIEW!
  • Worksheet 05
  • Code for Newton's Method
  • Homework 02 due on 09/26!
  • Worksheet 06
  • 1st - 3rd October
  • Tu: Exam 01 in class on 10/01
  • Th: Discussion on Exam 01 and and Polynomial Interpolation
  • Post Lecture Notes
  • 8th - 10th October
  • Tu: Polynomial Interpolation
  • Th: Spline Functions
  • Post Lecture Notes on Tuesday
  • Post Lecture Notes Thursday.
  • Homework 03 announced!
  • Worksheet 07
  • Worksheet 08
  • 15th - 17th October
  • Tu: Numerical Integration Part 1
  • Th: Numerical Integration Part 2
  • Worksheet 09
  • Post Lecture Notes
  • Homework 03 due on 10/17!
  • 22nd October - 24th October
  • Tu: Numerical Integration Continued
  • Th: MIDTERM 02 REVIEW!
  • Post Lecture Notes Tuesday
  • Post Lecture Notes Thursday
  • 29th October - 31st October
  • Tu: Exam 02
  • Th: Numerical Differentiation
  • DROP DATE FOR COURSE IS 11/01!
  • Worksheet 09
  • Post Lecture Notes Thursday
  • 5th - 7th November
  • Tu: Discussion of Exam, Method of undetermined coefficients and Systems of Linear Equations
  • Th: Systems of Linear Equations
  • Post Lecture Notes Tuesday
  • Post Lecture Notes Thursday
  • Worksheet 10
  • Worksheet 11
  • Worksheet 12
  • Homework 04 announced due on 11/12!
      Homework 04 Questions:
    1. Problem 1, 2, 3 Section 5.4.
    2. Problem 9,10 Section 5.4.
    The above questions are taken from the course textbook and are due on 11/12!
  • 12th - 14th November
  • Tu: Prelude to Iterative Methods
  • Tu: Error in solving Linear Systems and Iterative Methods and Residual Correction Methods
  • Th: Jacobi and Gauss Seidel Method
  • Worksheet 13
  • Post Lecture Notes Tuesday
  • Post Lecture Notes Thursday
  • 19th - 22nd November
  • Tu: Jacobi and Gauss Seidel Method
  • MIDTERM 03 REVIEW!
  • GePivot code can be downloaded here.
  • Residual_Correction code
  • Homework 05 announced due on 12/03!
  • Post Lecture Notes Tuesday
  • MATLAB Function to generate a matrix.
  • Review 03 Solutions
  • 26th - 28th November
  • Tu: Optional Exam 03
  • Th: HAPPY THANKSGIVING!
  • 3rd - 8th December
  • Tu: Newton's Method in 2D
  • Th: FINAL EXAM REVIEW!
  • Post Lecture Notes Tuesday part 1
  • Post Lecture Notes Tuesday part 2
  • Final Exam Review Solutions
  • 11th - 12th December
  • FINAL EXAM AT 13:00-15:45 ON DECEMBER 12TH