Ders Planı

Lesson Information

Course Credit	3.0
Course ECTS Credit	5.0
Teaching Language of Instruction	Türkçe
Level of Course	Bachelor's Degree, TYYÇ: Level 6, EQF-LLL: Level 6, QF-EHEA: First Cycle
Type of Course	Compulsory
Mode of Delivery	Face-to-face
Does the course require compulsory or optional work experience?	Z
Course Coordinator
Instructor (s)
Course Assistant	Doç. Dr. SEVDZHAN HAKKAEV

Purpose and Content

The aim of the course	This module aims to provide an accessible review of the linear algebra from the text book to long after the class. Linear algebra is an essential part of the mathematical background required of mathematicians, engineers, physicists and other scientists. It presents a source for undergraduate students. In general it covers an introduction to linear algebra which will be found helpful to all readers.
Course Content	Matrices, matrix algebra, special types of matrices, elementary row and colon operations, echelon form, rank of a matrix, elementary matrices, inverses, equivalent matrices, determinants, properties of determinants, cofactor and adjoint of a matrix, derivation of inverse matrix, systems of linear equations, solutions of systems of linear equations, Cramer's method, Gauss’s elimination method, vector spaces, subspaces, linear independence, bases and dimension, coordinates, change of basis, inner product spaces, standard inner product, orthogonal subspaces, orthogonal complement of a subspace, inner product, inner product spaces, orthogonal basis, orthogonal matrices, Gram-Schmidt orthogonalization methods, linear transformations, matrix representations of linear transformations, eigen values, eigen vectors, diagonalization, Cayley-Hamilton’s Theorem, quadratic forms, Hermitian forms, numerical applications.

The aim of the course

This module aims to provide an accessible review of the linear algebra from the text book to long after the class. Linear algebra is an essential part of the mathematical background required of mathematicians, engineers, physicists and other scientists. It presents a source for undergraduate students. In general it covers an introduction to linear algebra which will be found helpful to all readers.

Course Content

Matrices, matrix algebra, special types of matrices, elementary row and colon operations, echelon form, rank of a matrix, elementary matrices, inverses, equivalent matrices, determinants, properties of determinants, cofactor and adjoint of a matrix, derivation of inverse matrix, systems of linear equations, solutions of systems of linear equations, Cramer's method, Gauss’s elimination method, vector spaces, subspaces, linear independence, bases and dimension, coordinates, change of basis, inner product spaces, standard inner product, orthogonal subspaces, orthogonal complement of a subspace, inner product, inner product spaces, orthogonal basis, orthogonal matrices, Gram-Schmidt orthogonalization methods, linear transformations, matrix representations of linear transformations, eigen values, eigen vectors, diagonalization, Cayley-Hamilton’s Theorem, quadratic forms, Hermitian forms, numerical applications.

Learning Outcomes

Adequate knowledge in mathematics, physical sciences and subjects to mechatronics engineering; the ability to implement theoretical and practical knowledge in the respective areas in complex engineering problems.
Ability to identify, define, formulate and solve complex engineering problems; ability to select and implement the appropriate analysis and modeling methods in this respect.
Ability to design a complex system, process, device or product to meet specific requirements under realistic restrictions and conditions; ability to implement the modern design methods for this purpose.
Ability to design and conduct experiments for analysing engineering problem sor research subjects spesific to the mechatronics engineering, to collect data, to analyse and interpret the results.
Ability to work in the areas of controll, electronics, mechanics and computer systems; Adequate knowledge ability in analysing and designing of complex electro mechanic devices, hardware and software containing systems in which interact with dynamic systems.
Knowledge of applications in business life such as project management, risk management and change management; awareness about entrepreneurship, innovativeness and sustainable development.
Ability to use, choose and develop modern techniques and means required for analysing and solving complex problems encountered in the mechatronics engineering applications; ability to effectively utilize information technologies.
Ability to work effectively in intra-disciplinary and multi-disciplinary teams; ability to work individually.
Awareness of the necessity of lifelong learning; ability to reach information, follow the latest developments in science and technology; ability to ensure self-renewal perpetually.
Ability to communicate efficiently both in oral and written ways in Turkish; knowledge of at least one foreign language; ability to effectively prepare reports and understand written reports, prepare design and production reports, effective presentation; giving and recieving clear and understandable instructions.
Knowledge on the effects of mechatronics engineering applications on health, environment and safety in universal and social context and information about the engineering problems of the era; awareness on the legal implications of engineering solutions.
Knowledge of physics based on the calculus, knowledge of calculus containing multi variable calculus, derivative equations, derivatition and integrative calculations and complex variables; awareness on the subjects of statistics, optimisation and linear algebra; knowledge on the sensor technologies, computational and engineering sciences.
Acting in line with ethical principles, sense of professional and ethical responsibility; knowledge on the standards of engineering applications.

Weekly Course Subjects

1	Matrices, matrix algebra, special types of matrices, elementary row and colon operations.
2	Echelon form, rank of a matrix, elementary matrices, inverses, equivalent matrices.
3	Determinants, properties of determinants, cofactor and adjoint of a matrix.
4	Systems of linear equations, solutions of systems of linear equations.
5	Cramer's method, Gauss’s elimination method.
6	Vector spaces, subspaces, linear independence. Bases and dimension, coordinates, change of basis.
7	Inner product spaces, standard inner product function, orthogonal subspaces.
8	Orthogonal matrices, orthonormal basis.
9	Gram-Schmidt orthogonalization methods , orthogonal subspaces, orthogonal complement of a subspace.Midterm Exam.
10	Linear transformations, rank and kernel of linear transformations.
11	Matrix representations of linear transformations.
12	Eigen values, eigen vectors, diagonalization.
13	Cayley-Hamilton’s Theorem, quadratic forms, Hermitian forms.
14	Numerical applications.

Resources

1.Hacısalihoğlu, H. H., Lineer Cebir I, Bilim Yayınları, Ankara, 2000.
2.S. J. Leon, "Linear Algebra with Applications", Prentice Hall, 2002, Sixth Edition.
3. S. Lipschutz, Theory and Problems of Linear Algebra , Schaum’s Outline of McGraw-Hill Book Co.,1987,Singapore.

CLASS 1

CLASS 2

CLASS 3

CLASS 4

Lesson Information

Purpose and Content

Learning Outcomes

Weekly Course Subjects

Resources

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