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

Course Introduction and Application Information

Course Code:

MATH451

Course Name:

Partial Differential Equations

Semester:

Fall

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:

Araş. Gör. GAMZE AKAR UYSAL

Course Lecturer(s):

Prof. Dr. Tofigh Allahviranloo

Course Assistants:

Course Objective and Content

Course Objectives:	In this course the students learn to solve the following equations that have many applications in the engineering sciences.
Course Content:	Wave equation, heat equation, Laplace equation, classification of second order linear equations, initial value problems, boundary value problems, Fourier series, harmonic functions.

Learning Outcomes

The students who have succeeded in this course;
1) will be able to Modeling the several applied mathematical problems like wave and heat equations.
2) will be able to Familiar with some transformation that are applicable in solving the above-mentioned equations and others.
3) will be able to compute the partial differential equations numerically
4) will be able to The concepts of stability, consistency and convergency of the models and numerical methods.

Course Flow Plan

Week	Subject	Related Preparation
1)	Modeling wave and heat equations
2)	Modeling wave and heat equations
3)	Operators and Transformations
4)	Operators and Transformations
5)	Introducing the Numerical methods
6)	Stability, consistency and convergence
7)	Stability, consistency and convergence
8)	Eigen Values and Eigen Vectors
9)	Finite difference methods for Elliptic and Parabolic equations
10)	Finite difference methods for Elliptic and Parabolic equations
11)	Finite difference methods for Elliptic and Parabolic equations
12)	Stability, Consistency and Convergence of the methods
13)	Stability, Consistency and Convergence of the methods
14)	Applications

Sources

Course Notes / Textbooks:	Book: Numerical solution of partial differential equations, G. D. Smith, Brunel University, Oxford press.
References:	"Lecturer Note: Partial Differential Equations, Department of Mathematics Leipzig University MATLAB"

Course - Program Learning Outcome Relationship

Course Learning Outcomes	1	2	3	4
Program Outcomes
1) Have the knowledge of the scope, history, applications, problems, methods of mathematics and knowledge that will be beneficial to humanity as both scientific and intellectual discipline.
2) Have the ability to establish a relationship between mathematics and other disciplines and develop mathematical models for interdisciplinary problems.
3) Have the ability to define, formulate and analyze real life problems with statistical and mathematical techniques.
4) Have the ability to think analytically and use the time effectively in the process of deduction.
5) Have the ability to search the literature, understand and interpret scientific articles.
6) Have the knowledge of basic software to be able to work in the related fields of computer science and have the ability to use information technologies at an advanced level of the European Computer Driving License.
7) Have the ability to work efficiently in interdisciplinary teams.
8) Have the ability to communicate effectively in oral and written form, write effective reports and comprehend the written reports, make effective presentations.
9) Have the consciousness of professional and ethical responsibility and acting ethically; have the knowledge about academic standards.
10) Have the ability to use a foreign language at least at B1 level in terms of European Language Portfolio criteria.
11) Are aware of the necessity of lifelong learning; have the ability to access information, to follow developments in science and technology and to constantly renew themselves.

Course - Learning Outcome Relationship

No Effect	1 Lowest	2 Average	3 Highest

	Program Outcomes	Level of Contribution
1)	Have the knowledge of the scope, history, applications, problems, methods of mathematics and knowledge that will be beneficial to humanity as both scientific and intellectual discipline.	2
2)	Have the ability to establish a relationship between mathematics and other disciplines and develop mathematical models for interdisciplinary problems.	3
3)	Have the ability to define, formulate and analyze real life problems with statistical and mathematical techniques.	2
4)	Have the ability to think analytically and use the time effectively in the process of deduction.
5)	Have the ability to search the literature, understand and interpret scientific articles.
6)	Have the knowledge of basic software to be able to work in the related fields of computer science and have the ability to use information technologies at an advanced level of the European Computer Driving License.
7)	Have the ability to work efficiently in interdisciplinary teams.
8)	Have the ability to communicate effectively in oral and written form, write effective reports and comprehend the written reports, make effective presentations.
9)	Have the consciousness of professional and ethical responsibility and acting ethically; have the knowledge about academic standards.
10)	Have the ability to use a foreign language at least at B1 level in terms of European Language Portfolio criteria.	3
11)	Are aware of the necessity of lifelong learning; have the ability to access information, to follow developments in science and technology and to constantly renew themselves.	2

Assessment & Grading

Semester Requirements	Number of Activities	Level of Contribution
Homework Assignments	1	% 30
Project	1	% 30
Final	1	% 40
total		% 100
PERCENTAGE OF SEMESTER WORK		% 60
PERCENTAGE OF FINAL WORK		% 40
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	3		39
Application	13	0			0
Study Hours Out of Class	13	0	3		39
Midterms	1	0	15		15
Final	1	0	25		25
Total Workload					118