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Math 4329 (21457): Numerical Analysis

  • Instructor: Dr. Natasha S. Sharma
  • Meeting Times: TR 12:00 pm- 1:20 pm in Education Building 311
  • Office Hours: Thursday 3:00 pm - 4:00 pm, or by appointment.
  • Teaching Assistant: Imran Abdullah (aimran@miners.utep.edu), Office Location: CCSB 2.0902, Office Hours: 10:00 am onwards, Monday.
  • 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
    16th - 18th January
  • 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 posted!
  • 23rd - 25th January
  • Tu:Slides from the second chapter.
  • Th:Slides from introduction to MATLAB.
  • Matlab Introduction Commands
  • Access MATLAB through the website my.apps.utep.edu Matlab Introduction
  • Th:Slides from the third chapter.
  • Worksheet 03
  • Worksheet 04
  • 30th January - 1st February
  • Tu: Bisection Method
  • Th: Newton's Method
  • 6th - 8th February
  • Tu: Review for Midterm 01
  • Th: Midterm 01!
  • Review for Midterm 01 distributed in class
  • 13th - 15th February
  • Tu: Newton's Method and order of convergence
  • Th: Secant Method
  • Worksheet 05
  • Code for Newton's Method
  • 20th - 22nd February
  • Tu: Fixed Point Iteration
  • Th: Fixed Point Iteration and Ill-behaving root finding problems
  • Matlab Function quad_rootfinder.m
  • Worksheet 06
  • 27th February - 1st March
  • Tu: Polynomial Interpolation
  • Th: Error in Polynomial Interpolation
  • 6th - 8th March
  • Tu:Spline Functions
  • Th: Midterm 02 Review
  • Worksheet 07
  • 13th - 15th March
  • Tu: Th: SPRING BREAK!
  • Worksheet 08
  • Worksheet 09
  • 20th - 22nd March
  • Tu: Midterm 02!
  • Th: Numerical Integration Part 1
  • Th: Numerical Integration Part 2
  • 27th - 29th March
  • Tu: Error Formulas
  • Th: DROP DATE FOR COURSE IS 03/29! Gaussian Integration
  • Worksheet 10
  • Worksheet 11
  • 3rd - 5th April
  • Tu: Numerical Differentiation
  • Th: Linear Systems and Matrix Arithmetic
  • Worksheet 13
  • 10th - 12th April
  • Tu:Gaussian Elimination and
  • Th: LU Decomposition
  • Worksheet 14
  • 17th - 19th April
  • Tu: Exam
  • Th: Error in solving Linear Systems and Iterative Methods and Residual Correction Methods
  • 24th - 26th April
  • Tu: Jacobi and Gauss Seidel Iterative Methods
  • Th: Jacobi and Gauss Seidel Iterative Methods
  • Homework 4 GePivot code can be downloaded here.
  • Homework 4 Residual_Correction code.
  • 1st - 3rd May
  • Tu: Extra Topics: Some applications of Numerical Analysis
  • Th: FINAL EXAM REVIEW!
  • 8th - 10th May
  • Tu: FINAL EXAM AT 13:00-16:45