# MATH 4600 (11839-100), Fall 2012

## Introduction to Numerical Analysis

Catalog Description:
A survey of the ideas, methods, and algorithms in Numerical Analysis.
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 3400 Elementary Differential Equations and (3200 Applied Linear Algebra or 3210 Linear Algebra) and (3600 Applied Numerical Methods or CS 2300 or 2400 or ET 2100).
Instructor:
Martin J. Mohlenkamp, mohlenka@ohio.edu, (740)593-1259, 315-B Morton Hall.
Office hours: Monday, Wednesday, and Friday 10:45-11:40am, or by appointment.
Web page:
http://www.ohio.edu/people/mohlenka/20131/4600-5600.
Class hours/ location:
Monday , Wednesday, and Friday 9:40-10:35am in 219 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 3600.
Internet Access:
If you have a laptop, tablet, or smartphone that you can conveniently bring to class to access the internet, please do so.
Homework:
There will be weekly homework assignments, consisting of:
• Programming problems (I support Matlab and Python, but other languages are acceptable);
• 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. (Some problems, such as your autobiography, will require individual solutions.)
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 Friday, December 14, 8:00-10:00am 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 class day or part thereof. 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 5600 (11825-100)

For students enrolled in MATH 5600, the above syllabus is modified as follows:

Prerequisites:
Formally none. In practice Calculus, Linear Algebra, Elementary Differential Equations, and working knowledge of a programming language such as Matlab are needed.
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
Mon Aug 27 Introduction
Wed Aug 29 Floating Point, Round off error, Loss of Significance; Numerical Stability, Condition Number (3600:28)
Fri Aug 31 Horner scheme, Taylor's theorem Homework 1 using Layout
2
Mon Sep 3Labor day holiday
Wed Sep 5 Root-finding (discussion, resources), Bisection (discussion, exercises, solutions)(3600:5)
Fri Sep 7 Fixed Point, Cobweb Plot, Fixed-point Iteration (discussion, exercises, quiz) Homework 2 using Logic (drop deadline)
3
Mon Sep 10 Newton's Method (exercises, quiz) (3600:3, 4); Secant method (3600:6)
Wed Sep 12 Rate of convergence
Fri Sep 14 Interpolation (3600:19) , Polynomial interpolation (example, exercises), Lagrange Polynomial (example, exercises) Homework 3 using Flow
4
Mon Sep 17 Newton polynomial (example, exercises), Divided Differences
Wed Sep 19 Neville's Algorithm, (quiz)
Fri Sep 21 study guide Test on material through homework 3
5
Mon Sep 24 Numerical Differentiation (3600:27)
Wed Sep 26 Richardson Extrapolation
Fri Sep 28 Homework 4
6
Mon Oct 1 Numerical Integration
Wed Oct 3 Newton-Cotes formulas (3600:21, 22)
Fri Oct 5 Romberg Integration (discussion, code, example, exercises, quiz) Homework 5 using Intros
7
Wed Oct 10 Gaussian Quadrature (discussion, exercises, quiz)
Fri Oct 12 Numerical ordinary differential equations (3600:29); Lipschitz continuity Homework 6 using Symbols
8
Mon Oct 15 Euler method (3600:30), Explicit and implicit methods, Backward Euler method
Wed Oct 17 Runge-Kutta methods (3600:31)
Fri Oct 19 study guide Test on material through homework 6
9
Mon Oct 22 Linear multistep method, (exercises)
Wed Oct 24 Truncation error, Stiff equation
Fri Oct 26 Numerical stability, (discussion, exercises, quiz)(quiz) Homework 7
10
Mon Oct 29
Wed Oct 31 System of linear equations, Invertible matrix (3600: 8, 10); Gaussian elimination (3600: 9)
Fri Nov 2 Pivot element (3600: 11); LU decomposition (exercises, quiz) (3600: 12) (drop deadline with WP/WF)
11
Mon Nov 5 Norm; Normed vector space; Matrix norm (exercises); Condition Number
Wed Nov 7 Homework 8 using Graphs
Fri Nov 9 Eigenvalue, eigenvector and eigenspace (3600: 14; 15) ; Characteristic polynomial; Spectral radius
12
Mon Nov 12Veterans Day holiday (observed)
Wed Nov 14 Power iteration (exercises), Inverse iteration (exercises) (3600: 16)
Fri Nov 16 Newton's method (3600: 13), Neumann series
13
Mon Nov 19 study guide Test on material through homework 8
Wed Nov 21Thanksgiving holiday
Fri Nov 23Thanksgiving (Columbus day) holiday
14
Mon Nov 26
Wed Nov 28 Project presentations start
Fri Nov 30 Project presentations
15
Mon Dec 3 Project presentations
Wed Dec 5 Project presentations
Friday Dec 7 Review, study guide Homework 9 and Project reports due
16
Fri Dec 14 Final Exam 8:00-10:00am, in our classroom.

Martin J. Mohlenkamp