MATH 444 A01 (04872), Fall 2010

Introduction to Numerical Analysis

Catalog Description:
Polynomial interpolation and approximation; numerical integration and differentiation; numerical solution to differential equations; numerical methods for matrix inversion, determination of eigenvalues, and solutions of systems of equations.
Desired Learning Outcomes:
Students will be able to:
  • Construct algorithms to solve mathematical problems based on a common set of strategies.
  • Analyze the accuracy of such algorithms.
  • Analyze the computational cost and efficiency of such algorithms.
  • Identify the sources of failure of such algorithms, and avoid them.
  • Prerequisites:
    MATH 263D & 340 & (CS 210 or above).
    Instructor:
    Martin J. Mohlenkamp, mohlenka@ohio.edu, (740)593-1259, 315-B Morton Hall.
    Office hours: Monday 9-10am, Tuesday 9-10am, Thursday 9-10am, and Friday 9-10am, or by appointment.
    Web page:
    http://www.ohio.edu/people/mohlenka/20111/444-544.
    Class hours/ location:
    MTuThF 1:10-2pm in 326 Morton Hall.
    Text:
    None. We will scavenge materials from the internet. In particular we will use Wikipedia's Numerical Analysis pages, Wikiversity's Numerical Analysis topic, and material borrowed from MATH 344.
    Laptop:
    If you have a laptop that you can conveniently bring to class, please do so.
    Homework:
    There will be weekly homework assignments, consisting of: You may work together in a group of two or three and submit a joint solution.
    Tests:
    There will be two mid-term tests, in class. Calculators are permitted for arithmetic.
    Project:
    Your project during the quarter is to critique and improve Wikipedia's Numerical Analysis pages. At the end of the quarter you will submit a written report and give a presentation on what you did.
    Final Exam:
    The final exam is on Monday, November 22 at 12:20 pm in our regular classroom. Calculators are permitted for arithmetic.
    Grade:
    Your grade is based on homework 40%, tests 30%, final exam 20%, and project 10%. An average of 90% guarantees you at least an A-, 80% a B-, 70% a C-, and 60% a D-.
    Missed or Late work:
    Late homework is penalized 5% for each 24 hour period or part thereof, excluding weekends and holidays. You can resubmit homework to improve your score, but the late penalty will apply.
    Attendance:
    Attendance is assumed but is not counted in your grade. However, you should estimate that for each class you miss your average will decrease by one point due to the learning you missed. It is your responsibility to find out any announcements made in class.
    Academic Dishonesty:
    On the homework you may use any help that you can find, but you must acknowledge in writing what help you received and from whom or where. The tests and final exam must be your own work, and without the aid of notes, etc. Dishonesty will result in a zero on that work, and possible failure in the class and a report to the university judiciaries.
    Special Needs:
    If you have specific physical, psychiatric, or learning disabilities and require accommodations, please let me know as soon as possible so that your learning needs may be appropriately met.
    Learning Resources:
  • Your classmates are your best resource. Use them!
  • LaTeX, Python, and Matlab resources.
  • My Wikiversity user page
  • MATH 544 A01 (04883)

    For students enrolled in MATH 544, the above syllabus is modified as follows:

    Catalog Description:
    Iterative methods for solving nonlinear equations, polynomial interpolation and approximations, numerical differentiation and integration, numerical solution of differential equations, error analysis.
    Prerequisites:
    Advanced Calculus/ Basic Analysis and working knowledge of a programming language such as Matlab.
    Homework
    You must turn in an individual solution.
    Tests and Final Exam
    Expect an additional, harder problem, such as a proof.
    Project:
    Your project is to add or extend a lesson on Wikiversity for Numerical Analysis. At the end of the quarter you will submit a written report and give a presentation on what you did.

    Schedule

    Subject to change.
    Week Date Topic/Materials Homework/Test etc.
    1
    Tue Sep 7 Introduction
    Thu Sep 9 Floating Point, Round off error, Loss of Significance; Numerical Stability, Condition Number (344:28)
    Fri Sep 10 Horner scheme, Taylor's theorem Homework 1 using Layout
    2
    Mon Sep 13 Root-finding, Bisection (344:5)
    Tue Sep 14 Fixed Point, Cobweb Plot, Fixed-point Iteration
    Thu Sep 16 Newton's Method (344:3, 4); Secant method (344:6)
    Fri Sep 17 Rate of convergence Homework 2 using Logic
    3
    Mon Sep 20 Interpolation (344:19) , Polynomial interpolation, Lagrange Polynomial
    Tue Sep 21 Newton polynomial, Divided Differences (drop deadline)
    Thu Sep 23 Neville's Algorithm
    Fri Sep 24 Homework 3 using Flow
    4
    Mon Sep 27 Numerical Differentiation (344:27)
    Tue Sep 28 Richardson Extrapolation
    Thu Sep 30
    Fri Oct 1 study guide Test on material through homework 3
    5
    Mon Oct 4 Numerical Integration, Newton-Cotes formulas (344:21, 22)
    Tue Oct 5 Romberg Integration
    Thu Oct 7 Adaptive Quadrature
    Fri Oct 8 Gaussian Quadrature Homework 4 using Intros
    6
    Mon Oct 11 Numerical ordinary differential equations (344:29); Lipschitz continuity (drop deadline with WP/WF)
    Tue Oct 12 Euler method (344:30)
    Thu Oct 14 Runge-Kutta methods (344:31)
    Fri Oct 15 Explicit and implicit methods Homework 5 using Symbols
    7
    Mon Oct 18 Stiff equation
    Tue Oct 19 Linear multistep method
    Thu Oct 21 Numerical stability
    Fri Oct 22 Homework 6 using Graphs
    8
    Mon Oct 25 System of linear equations, Invertible matrix (344: 8, 10); Gaussian elimination (344: 9)
    Tue Oct 26 Pivoting (344: 11); LU decomposition (344: 12)
    Thu Oct 28 Norm; Normed vector space; Matrix norm; Condition Number
    Fri Oct 29 study guide Test on material through homework 6
    9
    Mon Nov 1 Eigenvalue, eigenvector and eigenspace (344: 14; 15) ; Characteristic polynomial; Spectral radius
    Tue Nov 2 Power iteration, Inverse iteration (344: 16)
    Thu Nov 4 Newton's method (344: 13)
    Fri Nov 5 Neumann series
    10
    Mon Nov 8 Project presentations
    Tues Nov 9 Project presentations
    Thu Nov 11 Veteran's Day, no class
    Fri Nov 12 Project presentations
    11
    Mon Nov 15 Review, study guide Project reports due
    12
    Mon Nov 22 Final Exam 12:20-2:20pm, in our classroom.

    Martin J. Mohlenkamp
    Last modified: Wed Oct 27 15:56:33 EDT 2010