NAMEPRACTICAL/TUTORIAL GROUP
Unit Course book
Linear Algebra
Course code:Mth202LA
Unit Coordinator
Woria M. Sediq
2012/2013
Soran University
Faculty of Science
Department of Mathematics
Stage 2
Welcome to department of mathematics at Soran University. This handbook summarise all the general information you need to guide you during the second stage of your selected course. This booklet also describes in details the content of linear algebra unit, the names of academic staff who will teach the unit, and what you will be expected to do to make sure your success in this unit. We hope you enjoy the unit and that you will find the work inspiring and challenging.
Keep in mind that good attendance at lectures and tutorials is important to give you a good basis for work throughout the course. If any students may experience difficulty with this unit, is important to sort things out as soon as possible. Make an appointment with unit coordinator who may be able to help, your year tutor, or other academic staff that involved with this unit.
Please note: you are provided with a hardcopy of teaching materials. It may be necessary to change the order of lectures, deadlines etc, which you will be informed. Therefore, it is ESSENTIAL that you check the Department of Mathematics notice board regularly in order to keep up to date with any changes.
Course Overview and Goals
This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. The class is primarily based on Chapters 1-7 of Lay's book: “Linear Algebra and Its Applications (4th Edition) (David C. Lay)”.
Learning Outcomes
After successful completion of this course, the student will be able to:
* Solving Ax = b for square systems by elimination (pivots, multipliers, back substitution, invertibility of A, factorization into A = LU)
* Complete solution to Ax = b (column space containing b, rank of A, nullspace of A and special solutions to Ax = 0 from row reduced R)
* Basis and dimension (bases for the four fundamental subspaces)
* Orthogonalization by Gram-Schmidt (factorization into A = QR)
* Properties of determinants (leading to the cofactor formula and the sum over all n! permutations, applications to inv(A) and volume)
* Eigenvalues and eigenvectors (diagonalizing A, computing powers A^k and matrix exponentials to solve difference and differential equations)
* Symmetric matrices and positive definite matrices (real eigenvalues and orthogonal eigenvectors, tests for x'Ax > 0, applications)
* Linear transformations and change of basis (connected to the Singular Value Decomposition - orthonormal bases that diagonalize A)
Communications with Academic Staff
This handbook gives information on how to contact and communicate with staff. We provide room numbers and email addresses of staff to you. The staffs in this department want to help you as much as possible so that you will be successful in your programme. We also want to encourage you to take responsibility for yourselves and for your learning so it will help you in your future careers.
The email rules
* Write your email in acceptable English.
* In your emails you must include: full name, stage, department and the unit title.
* We only respond to queries from students using genuine/Soran University email accounts.
* Appointments can be arranged through the email system, if you wish.
* We respond to genuine problems and queries as soon as possible, normally within 7 days.
* We will not respond to emails which do not have a subject line.
Staff associated with the unit
Staff
Room Number
Email
Woria M. Sediq
Instructors Room in Math Dep.
soran_math.woria@yahoo.com
Soran University
Department of Mathematics
Unit: Linear Algebra
Credit: 3+1
Method of Assessment:
Lectures: 2 sessions / week, 2 hours / session
Examination and grading
ACTIVITIES PERCENTAGESHomework 5%Exams 35%Final exam 60%
Homework
There will be HW assignment every time we finish a subject. Any time we assign HW It will be due next Monday and I will not accept any delay in submitting the homework.
Tutorials & Assessments
Attendance at tutorials & Assessments is necessary in order to gain marks for the given exercise.
Course of Action
1. There are penalties for late submission of coursework.
2. There are penalties for plagiarism and collusion.
Unit Timetable/Content
University Academic Week
Lecture Title & Content 1System of Linear Equations2Row Reduction and Echelon Forms3More Row Reduction and Echelon Forms4Vector Equations5The Matrix Equation Ax=b, Solution Sets of Linear Systems6Linear Independence, Introduction to Linear Transformations, The Matrix of a Linear Transformations7Matrix Operations, The Inverse of a Matrix8Characterizations of Invertible Matrices, Partitioned Matrices9Matrix LU Factorization10Subspaces of R^n11Dimension and Rank12Determinants13Cramer’s Rule and Linear Transformations14Winter Holiday15Vector Spaces and Subspaces16Null Spaces, Column Spaces, And Linear Transformations17Linearly Independent Sets; Bases18Coordinate Systems, The Dimension of a Vector Space19Rank, Change of Basis20Eigenvectors and Eigenvalues21The Characteristic Equation22Diagonalization23Eigenvectors and Linear Transformations24Inner Product, Length, and Orthogonality; Orthogonal Sets25Orthogonal Projections, The Gram-Schmidt Process26Diagonalization of Symmetric Matrices27Quadratic Forms, The Singular Value Decomposition28Final Exam
Recommended Reading
• David C. Lay, Linear Algebra and Its Applications,4th edition, (2011) Pearson Publisher.
• Gilbert Strang, Introduction to Linear Algebra, 4th edition, Wellesley Cambridge Press.