MATHEMATICS
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code	Course Name	Semester	Theoretical	Practical	Credit	ECTS
MAT4063	Numerical Solutions of Partial Differential Equations	Fall	3	0	3	6

This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction:	English
Type of course:	Departmental Elective
Course Level:	Bachelor’s Degree (First Cycle)
Mode of Delivery:	Face to face
Course Coordinator :	Assoc. Prof. MAKSAT ASHRAYYEV
Recommended Optional Program Components:	None
Course Objectives:	To see the applications and numerical solution of the partial differential equations.

Learning Outcomes

The students who have succeeded in this course;
: by using a computer program (C, C , Fortran, Matlab). The students who succeeded in this course;
o will be able to understand basic finite difference methods for partial differential equations.
o will be able to solve numerically any given linear or nonlinear partial differential equation.
o will be able to understand the concepts of consistency, stability, and convergence.
o will be able to solve partial differential equations
o will be able to discuss the consistency, convergence and stability for schemes.
o will be able to do error analysis.

Course Content

This course focuses on the fundamentals of modern and classical numerical techniques for linear and nonlinear partial differential equations, with application to a wide variety of problems in science, engineering and other fields. The course covers the basic theory of scheme consistency, convergence and stability and various numerical methods.

Weekly Detailed Course Contents

Week	Subject	Related Preparation
1)	Hyperbolic Partial Differential Equations: Finite difference methods.
2)	Consistency, stability, and convergence
3)	The LaxRichtmyer equivalence theorem
4)	The CourantFriedrichsLewy condition Von Neumann Analysis
5)	Order of accuracy Multistep schemes Dissipation anddispersionMIDTERM I
6)	Parabolic Partial Differential Equations: Finite difference methods
7)	Parabolic systems in higher dimensions
8)	ADI methods
9)	Elliptic Partial Differential Equations: Regularity and maximum principles
10)	Finite difference methods Linear iterative methodsMIDTERM II
11)	Multigrid methods
12)	Additional Topics (as time permits)Rigorous convergence analysis
13)	Error estimates
14)	Matrix method for stability analysis Spectral methods

Sources

Course Notes / Textbooks:	Partial Differential Equations with Boundary Value Problems by Larry C. Andrews. Numerical Solution of Partial Differentail Equations by K.W. Morton and D.F. Mayers Numerical Solution of Partial Differential Equations: Finite Difference Methods by G.D. Smith
References:	Partial Differential Equations. Lawrence C. Evans Applied Partial Differential Equations Paul DuChateau, David Zachmann Applied Partial Differential Equations Richard Haberman Applied Partial Differential Equations John R. Ockendon, Sam Howison, John Ockendon, Andrew Lacey, Alexander Movchan

Evaluation System

Semester Requirements	Number of Activities	Level of Contribution
Quizzes	5	% 15
Midterms	2	% 45
Final	1	% 40
Total		% 100
PERCENTAGE OF SEMESTER WORK		% 60
PERCENTAGE OF FINAL WORK		% 40
Total		% 100

ECTS / Workload Table

Activities	Number of Activities	Duration (Hours)	Workload
Course Hours	14	3	42
Study Hours Out of Class	14	2	28
Quizzes	5	2	10
Midterms	2	15	30
Final	1	40	40
Total Workload			150

Contribution of Learning Outcomes to Programme Outcomes

No Effect	1 Lowest	2 Low	3 Average	4 High	5 Highest

	Program Outcomes	Level of Contribution
1)	To have a grasp of basic mathematics, applied mathematics and theories and applications in Mathematics	5
2)	To be able to understand and assess mathematical proofs and construct appropriate proofs of their own and also define and analyze problems and to find solutions based on scientific methods,	5
3)	To be able to apply mathematics in real life with interdisciplinary approach and to discover their potentials,	4
4)	To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself,	4
5)	To be able to tell theoretical and technical information easily to both experts in detail and non-experts in basic and comprehensible way,	4
6)	To be familiar with computer programs used in the fields of mathematics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level,	4
7)	To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement,
8)	To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense,	4
9)	By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere,	4
10)	To be able to continue lifelong learning by renewing the knowledge, the abilities and the competencies which have been developed during the program, and being conscious about lifelong learning,	4
11)	To be able to adapt and transfer the knowledge gained in the areas of mathematics ; such as algebra, analysis, number theory, mathematical logic, geometry and topology to the level of secondary school,	2
12)	To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.	3