PAÜ .:. Eğitim Öğretim Bilgi Sistemi

COURSE INFORMATION

Course Code	Course Title	L+P Hour	Semester	ECTS
MAT 231	ENGINEERING MATHEMATICS	3 + 2	3rd Semester	6

COURSE DESCRIPTION

Course Level	Bachelor's Degree
Course Type	Compulsory
Course Objective	Giving preliminary notions of complex functions, Having ability for abstract thinking, Constituting starting point for Analytic function theory of complex variable, Obtaining solution to problems whose exact solution is not possible.
Course Content	Basic concepts of functions of complex variable / Limit, Continuity, Bifurcation points and Riemann surfaces / Derivative, Analytic Functions and Cauchy-Riemann equations / Harmonic functions / Line integral, Cauchy theorem, Cauchy’s integral Formula / Locating roots of equations, Singular and isolated singular points / Cauchy-Goursat theorem / Sequences, Sequences of function / Power series, Taylor series, Laurent series / Residue theorem and calculations of residues, Evaluation of integrals by Residue theorem / Conformal mapping, Existence of conformal mapping / Bilinear transformations, Exponential and logarithmic transformations, Hyperbolic and trigonometric transformations, Schwarz-Christoffel transformations.
Prerequisites	No the prerequisite of lesson.
Corequisite	No the corequisite of lesson.
Mode of Delivery	Face to Face

COURSE LEARNING OUTCOMES

1	He/she can understand the importance and usage purposes of complex variable functions.
2	He/she can solve the line integrals.
3	He/she learns Cauchy theorem and Cauchy integral Formula and solve this integral equations.
4	He/she learns Singular and isolated singular points.
5	He/she knowledges about Taylor series and Laurent series and who can expand these series.
6	He/she learns residue theorem and uses this theorem at integral solutions.
7	He/she conformal mapping and can transform complex structures to more simple structures.

COURSE'S CONTRIBUTION TO PROGRAM

	PO 01	PO 02	PO 03	PO 04	PO 05	PO 06	PO 07	PO 08	PO 09	PO 10	PO 11
LO 001	5	5	4	3	1		2	5
LO 002	5	5	4	2	1		2
LO 003	5	5	4	2	1		3
LO 004	5	4	3	2	1		2
LO 005	5	3	3	2	1		2
LO 006	5	3	2	2	1		2
LO 007	5	3	1	1	1		1
Sub Total	35	28	21	14	7		14	5
Contribution	5	4	3	2	1	0	2	1	0	0	0

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION

Activities	Quantity	Duration (Hour)	Total Work Load (Hour)
Course Duration (14 weeks/theoric+practical)	14	5	70
Hours for off-the-classroom study (Pre-study, practice)	14	4	56
Mid-terms	1	13	13
Final examination	1	17	17
Total Work Load ECTS Credit of the Course			156 6

COURSE DETAILS

Select Year

Course Details

Course Code	Course Title	L+P Hour	Course Code	Language Of Instruction	Course Semester
MAT 231	ENGINEERING MATHEMATICS	3 + 2	3	Turkish	2023-2024 Fall

Course Coordinator	E-Mail	Phone Number	Course Location	Attendance
Prof. Dr. CEYHUN KARPUZ	ckarpuz@pau.edu.tr		MUH A0301	%

Goals		Giving preliminary notions of complex functions, Having ability for abstract thinking, Constituting starting point for Analytic function theory of complex variable, Obtaining solution to problems whose exact solution is not possible.
Content		Basic concepts of functions of complex variable / Limit, Continuity, Bifurcation points and Riemann surfaces / Derivative, Analytic Functions and Cauchy-Riemann equations / Harmonic functions / Line integral, Cauchy theorem, Cauchy’s integral Formula / Locating roots of equations, Singular and isolated singular points / Cauchy-Goursat theorem / Sequences, Sequences of function / Power series, Taylor series, Laurent series / Residue theorem and calculations of residues, Evaluation of integrals by Residue theorem / Conformal mapping, Existence of conformal mapping / Bilinear transformations, Exponential and logarithmic transformations, Hyperbolic and trigonometric transformations, Schwarz-Christoffel transformations.

Topics

Weeks	Topics
1	Basic concepts of functions of complex variable
2	Limit, Continuity, Bifurcation points and Riemann surfaces, Derivative, Analytic Functions and Cauchy-Riemann equations
3	Harmonic functions, Line integral
4	Cauchy theorem, Cauchy’s integral Formula
5	Locating roots of equations,critical points and Singular points
6	Power series, Taylor series, Laurent series
7	Midterm exam
8	Residue theorem and calculations of residues
9	Evaluation of integrals by Residue theorem
10	Evaluation of integrals by Residue theorem
11	Fourier Series
12	Fourier Integral Transform and applications
13	Laplace Integral Transform and applications
14	Partial Differential Equations

Materials

Materials are not specified.

Resources

Resources	Resources Language
1- Theory of Functions of a Complex Variable, Volume1-2, A.I. Markushevich, Translated by Richard A. Silverman, Prentice Hall, Inc.	English
2- Erwin Kreyszig, Advanced Engineering Mathematics, 9th Edition, John Wiley	English
3- Complex Analysis, Ahlfors, L.V., McGraw-Hill, 1979	English
4- Prof. Dr. Mehmet AYDIN vs, “Diferansiyel Denklemler ve Uygulamaları”, Barış Yayınları.	Türkçe
5. Bekir KARAOĞLU, “Fizik ve Mühendislikte Matematik Yöntemler”, Güven Yayınları.	Türkçe

Course Assessment

Assesment Methods	Percentage (%)	Assesment Methods Title
Final Exam	60	Final Exam
Midterm Exam	40	Midterm Exam

L+P: Lecture and Practice
PQ: Program Learning Outcomes
LO: Course Learning Outcomes

Prospective Student