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Math 4329 (16026): Numerical Analysis

  • Instructor: Dr. Natasha S. Sharma

  • Meeting Times: Tu-Th 3:00pm-4:20pm, College of Business Admin Building 321

  • Office Hours: Thursdays 11:00am-12:00pm, or by appointment.

  • Teaching Assistant: Julio Solis (jsolis8@miners.utep.edu)

  • TextBook: Elementary Numerical Analysis, Third Edition by Atkinson and Han, John Wiley and Sons 2004

  • Click here for the syllabus.

    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 interprete the quality of such solutions.

    Announcements

    Week
    Lecture Topic for the week
    Assignments for the week
    22nd-26th August Review of Taylor Polynomials Homework I posted on 08/25
  • Sec 1.1 # 2(a), 2(c); 3(a), 3(b)
  • Sec 1.2: # 1, 2, 6
  • Access Matlab through the website my.apps.utep.edu
    • 29th-2nd September
  • Tuesday: Floating Point Representation, Matlab Tutorial
  • Thursday: More on Floating Point Representation, Loss of Significance
  • Homework 1 due on 09/01
  • Better resource for Floating Point Format can be found here.
  • Matlab Introduction
    • 5th-9th September
  • Tuesday: More on Errors and loss of significance.
  • Thursday: Review for Midterm
  • Save the following code with the name sig_loss.m and run it in Matlab by typing sig_loss in you command window.
  • Loss of Significance Matlab code.
    		•
    12th-16th September
  • Tuesday: Midterm Exam
  • Thursday: Iterative Methods: Bisection and Newton's Method
    • 19th -23rd September
  • Tuesday: Iterative Methods: Secant Method and Fixed Point Iteration
  • Thursday: Iterative Methods and Ill-behaving root finding problems
    		• Homework 2 posted due date 09/29
  • Sec 3.1 #10
  • Sec 3.2 #3, #8
  • Sec 3.4 #6, #8
    • 26th -30th September
  • Tuesday: Polynomial Interpolation
  • Thursday: Error in Polynomial Interpolation
    • 3rd-7th October
  • Tuesday: In class exercise on Polynomial Interpolation
  • Thursday: Matlab session
    		• Matlab homework 1 posted due on 10/20. You can download the latest version here .
    10-14th October
  • Tuesday: Spline Functions and Trapezoidal Rule
  • Thursday: Review for Midterm II.
    • 17th - 21st October
  • Tuesday: Midterm II
  • Thursday: Simpson Rule and Error Formulas
    		• Homework 3 posted due date 11/01
  • Section 5.1: #1, 2 (a) & (b), 3 (a) & (b)
  • Section 5.2: # 5 (a) & (b), 6 (a) & (b)
    • 24th - 27th October
  • Tuesday: Midterm II Discussion and Gaussian Numerical Integration
  • Thursday: Numerical Differentiation (taught by Professor Sewell)
    		• Matlab homework 1 is now due on 10/25!
    31st - 4th November
  • Tuesday: System of Linear Equations: Gaussian Elimination
  • Thursday: WorkSheet with Matrix Arithmetic given in class due on November 8th. View the worksheet here.
    		• Matlab homework 2 posted and due on November 8th!
    7th - 11th November
  • Tuesday: LU Decomposition
  • Thursday: In-class worksheet given on Error in Linear Systems. View the worksheet here.
    		• WorkSheet on Gaussian Elimination and LU Factorization given in class due on November 15th ! View the worksheet here.
    14th - 18th November
  • Tuesday: Error in Solving Linear Systems and Residual Correction Method
  • Thursday: Stability in Solving Linear Systems and Iteration Methods
    		• Worksheet on Iterative Methods and Stability is distributed due on November 17th ! View the worksheet here.
    21st - 25th November
  • Tuesday: Iteration Methods (continued)
  • Thursday: Thanksgiving (No class)
    		• Mock Final Exam distributed in class due on 11/29. Download a copy here.
    28th November - 2nd December
  • Tuesday: Final Exam Review Part-I
  • Thursday: Final Exam Review Part-II
    • December 8th
  • FINAL EXAM AT 4:00PM-6:45PM
    		•