APPLIED MATHEMATICS (TURKISH, THESIS)
Master TR-NQF-HE: Level 7 QF-EHEA: Second Cycle EQF-LLL: Level 7

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT5013 Partial Differential Equations Spring 3 0 3 8
The course opens with the approval of the Department at the beginning of each semester

Basic information

Language of instruction: Tr
Type of course: Departmental Elective
Course Level:
Mode of Delivery: Face to face
Course Coordinator : Prof. Dr. CANAN ÇELİK KARAASLANLI
Course Objectives: This course aims to provide an introduction to the basic properties of partial differential equations and to the tecniques that have proved useful in analyzing them.

Learning Outputs

The students who have succeeded in this course;
The students who succeeded in this course;
will be able to define canonical forms.
will be able to solve Wellposed and Illposed problems.
will be able to define Adjoint operators.
will be able to understand D’Alembert Formula and Duhamel principle.
will be able to solve Goursat problem for equation with variable coefficient based on characteristics.
will be able to solve Cauchy problem for equations with variable coefficients by using Riemann method.
will be able to understand Maximum principle for equations with variable coefficients.

Course Content

In this course the subjects such as canonical forms of partial differential equations, solution methods of parabolic, hyperbolic and elliptic equations in different regions will be discussed.

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Classification of PDE’s First-order linear PDE's
2) Initial value problems and the concept of classical solution. Wellposed and Illposed problems.
3) Envelopes
4) Characteristics for Linear and Quasi Linear Second order equations.
5) Wave euation, D!Alambert’s formula and Duhamel's principle.
6) Real analytic functions and Cauchy-Kowalewski Theorem
7) The Lagrange-Green Identity
8) Distribution Solutions
9) Laplace equation, Green's identity and Poisson equation.
10) Maksimum prensibi
11) The Dirichlet problem, Green's functions and Poisson formula.
12) Hadamard's method
13) Energy methodu
14) The heat equation. maximum principle, Uniqueness and regularity.

Sources

Course Notes: 1-Partial Differential Equations, L.C. Evans.AMS.1998. 2-Partial differential equations : An introduction by Walter A.Strauss.
References:

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Attendance % 0
Laboratory % 0
Application % 0
Field Work % 0
Special Course Internship (Work Placement) % 0
Quizzes % 0
Homework Assignments 3 % 10
Presentation % 0
Project % 0
Seminar % 0
Midterms 1 % 40
Preliminary Jury % 0
Final 1 % 50
Paper Submission % 0
Jury % 0
Bütünleme % 0
Total % 100
PERCENTAGE OF SEMESTER WORK % 50
PERCENTAGE OF FINAL WORK % 50
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Laboratory 0 0 0
Application 0 0 0
Special Course Internship (Work Placement) 0 0 0
Field Work 0 0 0
Study Hours Out of Class 3 20 60
Presentations / Seminar 0 0 0
Project 0 0 0
Homework Assignments 3 20 60
Quizzes 0 0 0
Preliminary Jury 0
Midterms 1 18 18
Paper Submission 0
Jury 0
Final 1 20 20
Total Workload 200

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) Ability to assimilate mathematic related concepts and associate these concepts with each other.
2) Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization.
3) Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques.
4) Ability to make individual and team work on issues related to working and social life.
5) Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball.
6) Ability to use mathematical knowledge in technology.
7) To apply mathematical principles to real world problems.
8) Ability to use the approaches and knowledge of other disciplines in Mathematics.
9) Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary.
10) To be able to link abstract thought that one has to concrete events and to transfer the solutions and examine and interpret the results scientifically by forming experiments and collecting data.
11) 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.
12) To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself,