# MATH 444 A01 (04796), Fall 2008

## 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.
...in practice:
The above description includes the material in 445 and 446 as well. Here we cover polynomial interpolation and approximation; numerical integration and differentiation; and solutions of nonlinear 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 3-4pm, and Friday 9-10am.
Web page:
http://www.ohio.edu/people/mohlenka/20091/444-544.
Class hours/ location:
MTuThF 10:10-11am in 326 Morton Hall.
Text:
Numerical Analysis, 8th edition by Richard L. Burden and J. Douglas Faires; Brooks/Cole, 2004 ISBN: 0534392008. This book has online programs.
We will also use Wikipedia's Numerical Analysis pages and background material borrowed from MATH 344.
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 three 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 Tuesday, November 18, at 8:00am 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:
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.
• # MATH 544 A01 (04806)

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
Project:
Your project will also involve Wikipedia, but be more substantial. You may, for example, add a new topic or develop a problem set on Wikiversity for Numerical Analysis or Numerical Algorithms.

## Schedule

Subject to change.
Week Date Topic/Materials Homework/Test
Text Wikipedia Other
1 September 8 Introduction
Basic Concepts, Error Analysis
September 9 1.1Calculus
September 11 1.2Floating Point, Round off error
September 12Loss of Significance Homework 1, using Layout
2 September 15 1.3Numerical Stability, Condition Number344:28
September 16 1.4Mathematical Software
Equations of one variable
September 18 2.1Root-finding, Bisection344:5
September 19 2.2 Fixed Point, Cobweb Plot, Fixed-point Iteration Homework 2, using Flow
September 23 study guide Test on Chapter 1
September 25 2.3Newton's Method, Secant method 344:3, 4
September 26
4 September 29 2.4Rate of convergence Homework 3, using Logic
September 30 2.5Aitken's delta-squared Process, Steffensen's Method
October 2 2.6Horner algorithm
October 3
Interpolation
5 October 6 3.1Interpolation, Lagrange Polynomial, Neville's Algorithm344:19
October 7 Homework 4
October 9 3.2 Newton polynomial, Divided Differences
October 10
6 October 13 3.3Hermite Interpolation (drop deadline with WP/WF)
October 14
October 16 study guide Test on Chapter 2
October 17 3.4Spline Interpolation
7 October 20 3.5Bezier CurveHomework 5, using Intros
October 21
Differentiation and Integration
October 23 4.1Numerical Differentiation344:27
October 24 4.2Richardson Extrapolation Homework 6, using Graphs
8 October 27
October 28 study guide Test on Chapter 3
October 30 4.3Numerical Integration Newton-Cotes formulas344:21, 22
October 31 4.4
9 November 3 4.5