• This web page describes an activity within the Department of Mathematics at Ohio University, but is not an official university web page.
• If you have difficulty accessing these materials due to visual impairment, please email me at mohlenka@ohio.edu; an alternative format may be available.

# 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.ohiouniversityfaculty.com/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:
• Programming problems (I support Matlab and Python, but other languages are acceptable); and
• Good Problems, which are graded half on content and half on presentation.
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.
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.
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:
• 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
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