MATH 118 | Course Introduction and Application Information - Department of Mathematics

Course Name

Linear Algebra II

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
MATH 118	Spring	3	0	3	6

Prerequisites

MATH 117 To get a grade of at least FD

Course Language

English

Course Type

Required

Course Level

First Cycle

Mode of Delivery

face to face

Teaching Methods and Techniques of the Course

Problem Solving
Q&A
Lecture / Presentation

National Occupation Classification

-

Course Coordinator

-

Course Lecturer(s)

Doç. Dr. Cemal Murat ÖZKUT

Assistant(s)

Course Objectives	This course aims to teach students to define vector spaces, eigenvalues and eigenvectors, orthogonality and give the applications of them in various fields.
Learning Outcomes	The students who succeeded in this course; define length, cross product and inner product. define linear transformation. define kernel and range of a linear transformation. find eigenvalues and related eigenvectors using several method. employ diagonalization. solve application problems. analyze ortogonallity,ortogonal and orthonormal sets. use Gram-Schmidt process to obtain an orthogonal set.
Course Description	In this course, the concepts of bases, dimensions, linear transformations, orthogonality, inner product spaces, eigenvalues, eigenvectors and diagonalization are discussed.
Related Sustainable Development Goals

Course Category	Core Courses	X
	Major Area Courses
	Supportive Courses
	Media and Management Skills Courses
	Transferable Skill Courses

Week	Subjects	Related Preparation
1	Length and direction in R2 and R3, Cross product in R3	Bernard Kolman, David R. Hill, Elementary Linear Algebra with Applications (Classic Version), 9th edn (Pearson, 2018). Section 5.1, 5.2
2	Inner product spaces, Gram-Schmidt process	Bernard Kolman, David R. Hill, Elementary Linear Algebra with Applications (Classic Version), 9th edn (Pearson, 2018). Section 5.3, 5.4
3	Orthogonal complements	Bernard Kolman, David R. Hill, Elementary Linear Algebra with Applications (Classic Version), 9th edn (Pearson, 2018). Section 5.5
4	Definitions and Examples: Linear transformations and matrices, Kernel and Range of Linear transformation	Bernard Kolman, David R. Hill, Elementary Linear Algebra with Applications (Classic Version), 9th edn (Pearson, 2018). Section 6.1, 6.2
5	Matrix of linear transformation	Bernard Kolman, David R. Hill, Elementary Linear Algebra with Applications (Classic Version), 9th edn (Pearson, 2018). Section 6.3
6	Vector space of Matrices and vector space of linear transformations	Bernard Kolman, David R. Hill, Elementary Linear Algebra with Applications (Classic Version), 9th edn (Pearson, 2018). Section 6.4
7	Vector space of Matrices and vector space of linear transformations	Bernard Kolman, David R. Hill, Elementary Linear Algebra with Applications (Classic Version), 9th edn (Pearson, 2018). Section 6.4
8	Midterm Exam
9	Similarity	Bernard Kolman, David R. Hill, Elementary Linear Algebra with Applications (Classic Version), 9th edn (Pearson, 2018). Section 6.5
10	Eigenvalues and Eigenvectors	Bernard Kolman, David R. Hill, Elementary Linear Algebra with Applications (Classic Version), 9th edn (Pearson, 2018). Section 7.1
11	Eigenvalues and Eigenvectors	Bernard Kolman, David R. Hill, Elementary Linear Algebra with Applications (Classic Version), 9th edn (Pearson, 2018). Section 7.1
12	Diagonalization and Similar Matrices	Bernard Kolman, David R. Hill, Elementary Linear Algebra with Applications (Classic Version), 9th edn (Pearson, 2018). Section 7.2
13	Diagonalization of symmetric Matrices	Bernard Kolman, David R. Hill, Elementary Linear Algebra with Applications (Classic Version), 9th edn (Pearson, 2018). Section 7.3
14	Stable Age Distribution in a Population; Markov Processes, Differential Equations	Bernard Kolman, David R. Hill, Elementary Linear Algebra with Applications (Classic Version), 9th edn (Pearson, 2018). Section 8.1, 8.4
15	Semester review
16	Final Exam

Course Notes/Textbooks

Bernard Kolman, David R. Hill, Elementary Linear Algebra with Applications (Classic Version), 9th edn (Pearson, 2018). ISBN-13: 978-0134718538

Suggested Readings/Materials

David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed. (Pearson,2015). ISBN-13:978-0321982384

Howard Anton, Chris Rorres, ''Elementary Linear Algebra'', Publisher:Wiley, 9th Edition,2005. ISBN-13: 978-0471669593

Seymour Lipschutz, ''Linear Algebra'', Shaum’s Outline Series, 2nd Edition.2011, ISBN-13:9780070380073

Semester Activities	Number	Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques	4	12
Portfolio
Homework / Assignments	1	5
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm	1	33
Final Exam	1	50
Total

Weighting of Semester Activities on the Final Grade	6	50
Weighting of End-of-Semester Activities on the Final Grade	1	50
Total

Semester Activities	Number	Duration (Hours)	Workload
Theoretical Course Hours (Including exam week: 16 x total hours)	16	3	48
Laboratory / Application Hours (Including exam week: '.16.' x total hours)	16		0
Study Hours Out of Class	14	3	42
Field Work			0
Quizzes / Studio Critiques	4	5	20
Portfolio			0
Homework / Assignments	1	1	1
Presentation / Jury			0
Project			0
Seminar / Workshop			0
Oral Exam			0
Midterms	1	30	30
Final Exam	1	39	39
		Total	180

#	Program Competencies/Outcomes	* Contribution Level
#	Program Competencies/Outcomes	1	2	3	4	5
1	To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics.	-	-	-	-	X
2	To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics.	-	-	-	-	-
3	To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials.	-	-	-	-	-
4	To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning.	-	-	-	X	-
5	To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals.	-	-	-	X	-
6	To be able to take responsibility both as a team member or individual in order to solve unexpected complex problems faced within the implementations in the field, planning and managing activities towards the development of subordinates in the framework of a project.	-	-	-	-	-
7	To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge.	-	-	-	-	-
8	To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field.	-	-	-	-	-
9	To be able to possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also environmental protection, worker's health and security.	-	-	-	-	-
10	To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking.	-	X	-	-	-
11	To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language.	-	-	-	-	-
12	To be able to speak a second foreign language at a medium level of fluency efficiently.	-	-	-	-	-
13	To be able to relate the knowledge accumulated throughout the human history to their field of expertise.	-	-	-	-	-