Chemistry (English) Preview
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code:

MATH112

Course Name:

Linear Algebra with Applications

Semester:

Spring

Course Credits:

ECTS

Language of instruction:

English

Course Condition:

Does the Course Require Work Experience?:

Type of course:

Compulsory Courses

Course Level:

Bachelor

TR-NQF-HE:6. Master`s Degree

QF-EHEA:First Cycle

EQF-LLL:6. Master`s Degree

Mode of Delivery:

Face to face

Course Coordinator:

Prof. Dr. ŞÜKRÜ YALÇINKAYA

Course Lecturer(s):

Assist. Prof. Dr. FUNDA ÖZDEMIR

Course Assistants:

Course Objective and Content

Course Objectives:	To improve abstract thinking skills by equipping students with the fundamental concepts of linear algebra and to gain the ability to use these concepts in solving engineering problems.
Course Content:	Systems of linear equations and their solution sets, linear transformations, matrices and matrix operations, determinants, vector spaces, subspaces, linear independence, dimension, bases, change of basis, eigenvalues and eigenvectors, inner product, orthogonality, singular value decomposition.

Learning Outcomes

The students who have succeeded in this course;
1) Solve a system of linear equations using matrix reduction (elimination).
2) Represent linear transformations as matrices and, conversely, interpret matrices as linear maps; do basic arithmetical operations with matrices and find the inverse of an invertible matrix.
3) Compute determinant of a matrix and comprehends the properties of determinants.
4) Find the dimension and basis of a vector space and its subspaces,analyze some fundamental subspaces.
5) Compute eigenvalues and eigenvectors of a matrix via characteristic equation, identify whether a matrix is diagonalizable or not, learn how to diagonalize the symmetric matrices and to learn singular value decomposition.
6) Knows the concepts of length, distance and orthogonality in inner product spaces, and produce an orthogonal basis for any of its subspaces.

Course Flow Plan

Week	Subject	Related Preparation
1)	Systems of linear equations, row reduction and echelon forms
2)	Vector equations, the matrix equation Ax=b, solution sets of linear systems, linear independence
3)	Introduction to linear transformations;, the matrix of a linear transformation
4)	Matrix operations, the inverse of a matrix, characterization of invertible matrices
5)	Partitioned (block) matrices, LU decomposition
6)	Determinants, properties of determinants, Cramer’s rule, volume
7)	Vector spaces, subspaces, null spaces and column spaces, kernel and range of a linear transformation
8)	Midterm Exam
9)	Linearly independent sets, span, bases, coordinates
10)	Dimension, rank, change of basis
11)	Eigenvalues and eigenvectors, characteristic equation, diagonalization
12)	Inner product spaces, length, distance and orthogonality, orthogonal sets
13)	Orthogonal projections, Gram-Schmidt process and QR decomposition
14)	Diagonalization of symmetric matrices, singular value decomposition

Sources

Course Notes / Textbooks:	Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson.
References:	Elementary Linear Algebra, Howard Anton, Chris Rorres, Wiley, 11th Edition.

Course - Program Learning Outcome Relationship

Course Learning Outcomes	1	2	3	4	5	6
Program Outcomes
1) Knows the basic concepts related to the theory and applications of chemistry, uses theoretical and applied knowledge, can select, develop and design methods.
2) Makes experimental planning and application for analysis, synthesis, separation and purification methods, provide solutions to the problems encountered and interpret the results.
3) Expresses the basic principles of sample preparation techniques and instrumental analysis methods used in qualitative and quantitative analysis of items, discusses their application areas.
4) Has knowledge about the sources, production, industrial applications and technologies of chemical substances.
5) Makes structural analyzes of chemical substances and interprets the results.
6) Work individually and in multidisciplinary groups, take responsibility, plan their tasks and use time effectively.
7) Follows the information in the field and communicates with colleagues by using English at a professional level.
8) Uses information and communication technologies along with computer software at the level required by the field.
9) Follows the national and international chemistry literature, transfers the knowledge gained orally or in writing.
10) Determines self-learning needs, manages/directs his/her learning.
11) Takes responsibility and adheres to the ethical values required by these responsibilities.

Course - Learning Outcome Relationship

No Effect	1 Lowest	2 Average	3 Highest

	Program Outcomes	Level of Contribution
1)	Knows the basic concepts related to the theory and applications of chemistry, uses theoretical and applied knowledge, can select, develop and design methods.
2)	Makes experimental planning and application for analysis, synthesis, separation and purification methods, provide solutions to the problems encountered and interpret the results.
3)	Expresses the basic principles of sample preparation techniques and instrumental analysis methods used in qualitative and quantitative analysis of items, discusses their application areas.
4)	Has knowledge about the sources, production, industrial applications and technologies of chemical substances.
5)	Makes structural analyzes of chemical substances and interprets the results.
6)	Work individually and in multidisciplinary groups, take responsibility, plan their tasks and use time effectively.
7)	Follows the information in the field and communicates with colleagues by using English at a professional level.
8)	Uses information and communication technologies along with computer software at the level required by the field.
9)	Follows the national and international chemistry literature, transfers the knowledge gained orally or in writing.
10)	Determines self-learning needs, manages/directs his/her learning.
11)	Takes responsibility and adheres to the ethical values required by these responsibilities.

Assessment & Grading

Semester Requirements	Number of Activities	Level of Contribution
Midterms	1	% 40
Final	1	% 60
total		% 100
PERCENTAGE OF SEMESTER WORK		% 40
PERCENTAGE OF FINAL WORK		% 60
total		% 100

Workload and ECTS Credit Calculation

Activities	Number of Activities	Preparation for the Activity	Spent for the Activity Itself	Completing the Activity Requirements	Workload
Course Hours	13	0	2		26
Application	13	0	2		26
Study Hours Out of Class	13	0	2		26
Midterms	1	13	2		15
Final	1	23	2		25
Total Workload					118