# MATH 410 (04868), Spring 2010

## Matrix Theory

Catalog Description:
Matrix algebra, determinants, solutions of linear systems, eigenvalues and eigenvectors, matrix functions and applications to differential equations, Jordan canonical form, inner products diagonalization and generalized inverses. Intended primarily for students interested in applied mathematics, engineering, and sciences.
Desired Learning Outcomes:
• Students can competently carry out computations involving solutions of linear systems of equations and eigenvalues.
• Students understand and can use the geometry of linear systems and matrices.
• Students can effectively manipulate matrix equations.
• Prerequisites:
MATH 263D
Instructor:
Martin J. Mohlenkamp, mohlenka@ohio.edu, (740)593-1259, 315B Morton Hall.
Office hours: Monday 9:10-10am, Tuesday 9:10-10am, Thursday 9:10-10am, and Friday 9:10-10am.
Web page:
http://www.ohio.edu/people/mohlenka/20103/410-510.
Class hours/ location:
MTuThF 8:10-9am in 215 Morton Hall.
Text:
Matrix Methods: Applied linear Algebra. Third edition, by Richard Bronson and Gabriel Costa, Academic Press 2009; ISBN: 978-0-12-374427-2.
Homework:
Several problems from each section of the book are assigned. These problems will not be collected or graded, but you will need to do them in order to learn.
Good Problems:
Seven Good Problems are assigned, and will be collected and graded. These are homework problems that will be graded half on content and half on presentation. The idea is to practice writing mathematics regularly but in small pieces.
Tests:
There will be three mid-term tests, in class. Calculators are not permitted.
Final Exam:
The final exam is on Thursday, June 10, at 10:10am in our regular classroom. Calculators are not permitted.
Each Good Problem is worth 1 unit, each test is worth 2 units, and the final is worth 5 units. Your lowest 2 units will be dropped and then your average is computed and a 90% guarantees you at least an A-, 80% a B-, 70% a C-, and 60% a D-.
Missed or Late work:
Only reasons given in advance of a missed test will be considered; otherwise a score of 0 will be given. Late Good Problems are penalized 5% for each 24 hour period or part thereof, excluding weekends and holidays. You can resubmit good problems to improve your score, but the late penalty will apply.
Attendance:
Attendance 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.
You are strongly encouraged to work together on the homework. You can work together on the Good Problems, but you must acknowledge in writing what help you received and from whom. 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:
• Video tutorials on linear algebra.
• Wikipedia Mathematics Portal
• # MATH 510 (04880)

For students enrolled in MATH 510, the above syllabus is modified as follows:

Catalog Description
Primarily intended for science and engineering majors. Topics include matrix algebra and matrix calculus, matrix solutions of systems of linear equations, eigenvector and eigenvalue problems, quadratic forms, and inner product spaces.
Material:
You are responsible for the additional material in sections 2.8, 3.6, 5.7, 7.10, and 8.6. These sections provide proofs that are skipped in main text
Tests and Final Exam:
You will have an additional, proof problem on each test.

## Schedule

The Good Problems and Tests are fixed, but we may not cover sections on exactly the days shown.
Week Date Section Homework (Ungraded) Good Problem/ Test
1
Chapter 1: Matrices
Mon Mar 29 1.1 1,3,5,7,11,13
Tue Mar 30 1.2 1,5,7,9,15,19,23,27,29
1.3 1,3,5,9,11,15,17,20,21,23,25,29,31,33,37
Thu Apr 1 1.41,2,3,5,7,9,15,17,23
1.51,3,5,7
Fri Apr 2 1.61,3,5,7,11,13 Good Problem 1: Mathematical Autobiography, using Layout
1.71,3,5,11,13,17
2
Chapter 2: Simultaneous Linear Equations
Mon Apr 5 2.11,3,5,9,13
2.21,3,5,7
Tue Apr 6 2.31,5,7,11,13,17,19,21,23,30,32,34,36
Thu Apr 8 2.41,3,5,9
Fri Apr 92.5 1,5,9,11,21,23,24,25,32,36 Good Problem 2: 2.1 #15 and 2.3 #38 combined, using Flow
3 Mon Apr 12 2.61,3,5,6,12,17,27(drop deadline)
Tue Apr 13 2.71,3,5,7,9
Thu Apr 15Review
Fri Apr 16study guideTest 1 on Chapters 1 and 2
4
Chapter 3: The Inverse
Mon Apr 19 3.11,3,6,11,13,15,27,29,35,37,51
3.21,7,10,11,19,22
Tue Apr 20 3.31,5,7,14
3.41,3,5,8,13
Thu Apr 22 3.51,5,7,13,18,20
Chapter 5: Determinants
Fri Apr 23 5.11,3,5,10,12,21,23,27 Good Problem 3: 3.3 #12, using Logic
5.21,3,7,19,26
5 Mon Apr 26 5.32,3,5,7,13
Tue Apr 27 5.41,5,13,17
5.51,3,7,13
Thu Apr 29 5.61,3,7,11
Chapter 6: Eigenvalues and Eigenvectors
Fri Apr 30 6.11,2,5,6 Good Problem 4: 5.3 #12, using Intros
6.21,3,5,7,9,11,17,19,21,34,35
6 Mon May 3 6.3 1,3,7,9,13,22,24,27(drop deadline with WP/WF)
6.41,3,7,9,10-21
Tue May 4 6.51,3,5,11,15
Thu May 6Review
Fri May 7study guideTest 2 on Chapters 3, 5, and 6
7
Chapter 7: Matrix Calculus
Mon May 10 7.11,3,4,5,7,9,13,16,17
7.21,3,5
Tue May 11 7.31,2,7,13,19,21,25
7.41,2,3,7,8,9,12
Thu May 13 7.51,3,9,13,15
Fri May 14 7.61,3,7 Good Problem 5: 7.4 #13, using Symbols
7.71,3,7
8
Mon May 17 7.81,3,6,8
7.91,2,6
Chapter 8: Linear Differential Equations
Tue May 18 8.11,3,5,7,9
8.21,5,7
Thu May 20 8.31,5,8
Fri May 21 8.42,3,7,9,11,13 Good Problem 6: 8.2 #8
9 Mon May 24 8.51,2
Tue May 25
Thu May 27Review
Fri May 28study guideTest 3 on Chapters 7 and 8
10
Mon May 31Memorial Day, no class
Chapter 10: Real Inner Products and Least Square
Tue June 1 10.11,3,7,15,18,24,29-33,35,36,37
10.21,3,7,11,13
Thu June 3 10.51,5,11
Fri June 4 Good problem 7: Section 10.2 #15
11 June 10 study guide Final Exam Thursday at 10:10am, in our classroom

Martin J. Mohlenkamp