COURSE UNIT TITLE

: NONLINEAR PARTIAL DIFERANTIAL EQUATIONS

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 4034 NONLINEAR PARTIAL DIFERANTIAL EQUATIONS ELECTIVE 4 0 0 7

Offered By

Mathematics (English)

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

DOCTOR MELTEM ALTUNKAYNAK

Offered to

Mathematics (Evening)
Mathematics (English)

Course Objective

The aim of this lecture is to learn the theory of nonlinear partial differential equations and some special methods for finding the solutions of these equations.

Learning Outcomes of the Course Unit

1   Wil be able to learn nonlinear model equations.
2   Wil be able to describe and use the generalized method of characteristics.
3   Wil be able to find complete and singular solutions of first-order equations.
4   Wil be able to apply the Charpit s method and solve Cauchy problem.
5   Will be able to solve Cauchy problem for nonlinear geometric optics analytic dynamics.
6   Will be able to apply the Monge s method for solving second order equations.
7   Will be able to obtain Euler-Lagrange equations.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Basic concepts and definitions.
2 Nonlinear model equations.
3 First-order equations, generalized method of characteristics.
4 Envelope of a surface, characteristic directions.
5 Strip condition, characteristic strip.
6 Complete and singular solutions: special procedures for finding solutions, transformations.
7 Complete integral of nonlinear equation, Charpit's method.
8 Examples of application to nonlinear (geometric) optics and to analytical dynamics.
9 The Cauchy problem, compatible systems.
10 The Cauchy problem in n independent variables.
11 The Cauchy problem for nonlinear geometric optics.
12 The Cauchy problem for nonlinear analytic dynamics.
13 Solutions of second order equations. Monges method.
14 Variational principles and the Euler-Lagrange equations for nonlinear partial differential equations.

Recomended or Required Reading

Textbook(s): Partial Differential Equations, E. Zauderer, John Willey.
Supplementary Book(s): Nonlinear Patrtial Differential Equations for Scientists and Engineers,L. Debnaht, Birkhauser, Prentice Hall.
References:
1. Partial Differential Equations: Methods and Applications, R. McOwen.
2. Partial Differential Equations, Fritz John, Springer Verlag.
3. Theory and Problems of Differential Equations, Frank Ayes, JR, Schaum s Outlines.

Materials: Presentiations

Planned Learning Activities and Teaching Methods

Lecture notes, presentiations, solving problems

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 VZ Vize
2 FN Final
3 BNS BNS VZ * 0.40 + FN * 0.60
4 BUT Bütünleme Notu
5 BBN Bütünleme Sonu Başarı Notu VZ * 0.40 + BUT * 0.60


Further Notes About Assessment Methods

None

Assessment Criteria

Evaluation of exams.

Language of Instruction

English

Course Policies and Rules

Any unethical behavior that occurs either in presentations or in exams will be dealt with as outlined in school policy. You can find the undergraduate policy at https://fen.deu.edu.tr/en/

Contact Details for the Lecturer(s)

e-mail: meltem.topcuoglu@deu.edu.tr
phone : (232) 3018607

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 4 56
Preparation for midterm exam 1 25 25
Preparation for final exam 1 25 25
Preparing assignments 2 7 14
Preparations before/after weekly lectures 14 3 42
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 166

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.1444
LO.25455
LO.354455
LO.4554545
LO.5534434
LO.6533443
LO.7443432

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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