COURSE UNIT TITLE

: PARTIAL DIFERENTIAL EQUATIONS

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 3056 PARTIAL DIFERENTIAL EQUATIONS COMPULSORY 4 0 0 6

Offered By

Mathematics (English)

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

PROFESSOR DOCTOR BURCU SILINDIR YANTIR

Offered to

Mathematics (English)

Course Objective

Aim of this course is to develop a basic understanding of the partial differential equations and related problems such as initial value, boundary value and initial-boundary value problems in real world.

Learning Outcomes of the Course Unit

1   will be able to classify partial differential equations and solve first order linear partial differential equations
2   will be able to identify quasilinear partial diffrerential equations and find their general solutions by the use of Lagrange theorem
3   will be able to define characteristic curves and solve Cauchy problems of quasilinear partial differential equations
4   will be able to solve first and second linear and nonlinear partial differential equations by using the seperation of variables method
5   will be able to solve linear second order partial differential equations by the use of operator method and establish the solution of D'Alembert problem.
6   will be able to identify initial and boundary value problems of wave,heat and Laplace equations, find their series solutions and prove their uniform and absolute convergence. will be able to define canonical forms of partial differential equations.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Classification of linear,quasilinear, semilinear partial differential equations.
2 Solutions of linear constant coefficient partial differential equations.
3 Solutions of linear non-constant coefficient partial differential equations.
4 Lagrange theorem, its geometric and linear algebraic proof.
5 Deriving general solutions of quasilinear partial differential equations by the use of Lagrange theorem.
6 The characteristic curves, integral surfaces.
7 Solutions of Cauchy problems of quasilinear partial differential equations.
8 Solutions of linear and nonlinear first and second order partial differential equations by the use of seperation of variables method.
9 Solutions of second order partial differential equations by the use of operator method.
10 D'Alembert problem and its solution.
11 Solutions of initial and boundary value problems of wave equation. Uniform and absolute convergence of solutions.
12 Solutions of initial and boundary value problems of heat equation. Uniform and absolute convergence of solutions.
13 Solutions of initial and boundary value problems of Laplace equation. Uniform and absolute convergence of solutions.
14 Canonical forms of partial differential equations.

Recomended or Required Reading

1.Linear partial differential equations for scientists and engineers by Tyn Myint-U, and Lokenath Debnath, Birkhauser Boston Inc.
2.Introduction to partial differential equations, Peter J. Olver, 2014, Springer.
Materials: Lecture notes, problem solving
3.Partial Differential Equations: An Introduction , Walter A. Strauss

Planned Learning Activities and Teaching Methods

Lecture notes and problem solving.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 FIN FINAL EXAM
3 FCG FINAL COURSE GRADE MTE * 0.50 + FIN * 0.50
4 RST RESIT
5 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.50 + RST * 0.50


Further Notes About Assessment Methods

None

Assessment Criteria

The grades of the students that regularly attend the lectures will be determined according to catalogue or curve of the average of the midterm and final notes.

Language of Instruction

English

Course Policies and Rules

The students are responsible for the 70% attendance to the lectures. The students have to obey the lecture timetable. The lecturer behave according to the regulations if the nonethical behaviors take place during lectures and exams. The related regulation of Science Faculty- DEU can be seen in the link http://web.deu.edu.tr/fen.

Contact Details for the Lecturer(s)

E-mail: burcu.silindir@deu.edu.tr
Office: 3018590

Office Hours

The office hour will be determined on a common date available for both the lecturer and the students and will be announced at the beginning of the semester.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 4 56
Preparation for midterm exam 1 33 33
Preparations before/after weekly lectures 14 2 28
Preparation for final exam 1 34 34
Midterm 1 2 2
Final 1 2 2
TOTAL WORKLOAD (hours) 155

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.155344
LO.25534
LO.3555344
LO.455534
LO.5553455
LO.645553455

CONTACT INFORMATION
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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