Kocaeli University / European Credit Transfer System (ECTS)

Name of Lecturer(s)

Assistant Prof. Dr. Celal ÖZKALE

Learning Outcomes of the Course Unit
Program Competencies-Learning Outcomes Relation

Learning Outcomes of the Course Unit

1) Knows advanced mathematical methods.
2) Knows theadvanced mathematical techniques for engineering applications.
3) Solves the industrial engineering problems with advanced mathematical methods.

Program Competencies-Learning Outcomes Relation

		Program Competencies
		1	2	3	4	5
Learning Outcomes
	1	High	High	High	High	High
	2	High	High	High	High	High
	3	High	High	High	High	High

Mode of Delivery

Face to Face

Prerequisites and Co-Requisites

None

Recommended Optional Programme Components

Advanced Statistical Analysis

Course Contents

Mathematical foundations of set theory, clustering, countability of sets, Cartesian product, equivalence relation, function types (Cover, Unit, Fixed, Inverse), Compound functions, linear transformations, limit, continuity, Rolle's theorem, mean value theorem, vector spaces, matrix types, determinant, linear dependence, systems of linear equations, solution methods of linear equation systems, probability axioms, concepts of dependence and independence, conditional probability, Bayes theorem, density and distribution functions, expected value, mean, variance, intermittent markov processes, persistent state probabilities.

Weekly Schedule

1) Mathematical foundations of set theory, clustering, countability of sets
2) Cartesian product, equivalence relation, function types
3) Compound functions, linear transformations, limit, continuity
4) Rolle's theorem, mean value theorem
5) Rules of derivative, geometric interpretation of derivative, concavity, convexity ...
6) Integration, area-volume calculations, inhomogeneous ordinary differential equations
7) Partial differential equations, variable transformations and simplifications
8) Midterm exam
9) Vector spaces, matrix types, determinant, linear dependence
10) Solution methods of linear equation systems, probability axioms
11) Concepts of dependence and independence, conditional probability, Bayes theorem
12) Density and distribution functions
13) Expected value, mean, variance
14) Intermittent markov processes
15) Persistent state probabilities
16) Final Exam

Planned Learning Activities and Teaching Methods

1) Lecture
2) Question-Answer
3) Self Study
4) Problem Solving

Assessment Methods and Criteria

Contribution of Semester Studies to Course Grade

70%

		Number	Percentage
Semester Studies	Midterm Examination	1	20%
	Project	1	70%
	Presentation/Seminar	1	10%

Contribution of Final Examination to Course Grade

30%

Total

100%

Language of Instruction

Other

Work Placement(s)

Not Required

Course Unit Title	Course Unit Code	Type of Course Unit	Level of Course Unit	Year of Study	Semester	ECTS Credits
Advanced Engineering Mathematics	MEN615	Compulsory	Doctorate degree	1	Spring	8