MATHEMATICS FOR MECHANICAL ENGINEERS

MATH209

Course Code: MATH209
Semester: Third Term (Fall)
Theory+Practice: 3 + 1
ECTS: 4

Course Type

Compulsory Course

Course Level

Bachelor's Degree

Year of Study

Semester

Third Term (Fall)

ECTS

Name of Lecturer(s)

Associate Professor Müjdat Kaya

Learning Outcomes

At the end of this course, the students;

Increase the awareness of his mental potential and abilities; gain an ability to utilize a higher percentage the capacity of the mind via brain exercises.
Solidify the patterns of rational or mathematical (and therefore exact) thinking.
Have a knowledge with the Engineering Mathematics needed in diverse areas of science and technology in general, and specific areas of engineering in particular.
Acquire effective analytical thinking ability and study habits; and also deepen and widen his thought and vision.
Develop problem-solving skills.
Will be able to apply the Engineering Mathematics knowledge for solving science and engineering problems.
Acquire the ability of keeping up with the constantly changing science, technology and engineering methods.

Mode of Delivery

Face to face

Prerequisites

Yes(MATH152)

Recommended Optional Programme Components

None

Course Description

This course contains these concepts: R Space, Dot Product of Vectors, Projections, Equations of Line and Plane, Systems of Linear Equations and Solutions, Gauss-Jordan Elimination, Matrices, Transpose and Inverse of Matrix, Matrix Applications, Determinants and Properties, Eigenvalue of Matrices, Cross Product, Scalar Triple Product, Norm, General Vector Spaces, Subspaces, Linear Dependence and Independence, Span, Basis and Dimension, Inner Product Spaces, Gram-Schmidt Orthogonalization Process, Linear Transformations, Kernel and Range, Rank and Nullity, Matrices of Linear Transformations, Eigenvectors of Linear Transform, Diagonalization, Change of Basis, Similarity, Jordan Canonical Form, Quadratic Surfaces, Complex Vector Spaces, Complex Matrices.

Course Contents

WEEK	TOPICS
1^st Week	Introduction, n-space Rn , Scalar(dot) product, Equations of Line and Plane, System of Linear Equations and Solutions
2^nd Week	Gaussian Elimination Method
3^rd Week	Matrices, Transpoze of Matrix, Inverse of Matrix and Properties
4^th Week	Applications of Matrices, Determinants, Properties of Determinants, Eigenvalues of Matrices
5^th Week	Cross Product, Scalar Triple Product and Properties
6^th Week	The vector spaces R2, R3, Rn and Norm of a Vector, Lines and Planes
7^th Week	General Vector Spaces, Subspaces,Linear Dependence, Linear Independence, Spanning, Basis and Dimension
8^th Week	Midterm Exam
9^th Week	Inner Product Spaces, Orthonormal Bases, Gram-Schmidt Process, Linear Transformations
10^th Week	Kernel and Range Spaces, Rank and Nullity, Inverse Linear Transformations
11^th Week	Diagonalization, Change of Bases
12^th Week	Matrices of Linear Transformation, Eigenvalues and Eigenvectors
13^th Week	Similarity, Jordan Canonical Form, Quadratic Forms
14^th Week	Complex Vector Spaces, Complex Inner Product Spaces, Complex Matrices, Unitary, Normal, and Hermitian Matrices

Programme Qualifications / Learning Outcomes

	LO1	LO2	LO3	LO4	LO5	LO6	LO7
K1	X	X	X	X	X	X	X
K2
K3
K4
K5
K6
K7
K8
K9
K10
K11