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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 5008 NONLINEAR PROBLEMS OF APPLIED MATHEMATICS ELECTIVE 3 0 0 7

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

Offered to

Mathematics (English) Mathematics (English)

Course Objective

Aim of this course is to study of nonlinear problems of applied mathematics in real world and provide sufficient applications to motivate and illustrate the theory.

Learning Outcomes of the Course Unit

1   will be able to introduce some nonlinear model equations. 2   will be able to understand the first order nonlinear equations. 3   will be able to understand shock waves. 4   will be able to understand water waves. 5   will be able to learn solitary waves.

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. Some nonlinear models equations. 2 Variational principles and Euler-Lagrange equations. 3 First order nonlinear partial differential equations. The method of characteristics 4 Conservation laws. Shock waves, discontinuous solutions. 5 Kinematic waves and real word nonlinear problems. 6 Nonlinear hyperbolic systems. 7 Riemann invariants. 8 Midterm 9 Nonlinear dispersive waves. Whitham's theory. 10 Diffusion-reaction phenomena. Burger's and Fisher equations. The Cole-Hopf transformation. Similarity solutions. 11 Solitons. Inverse scatering transform. 12 KdV equations. 13 Klein-Gordon and Sine-Gordon equations. Inverse Scatering method. 14 Similarity method, method of separation of variables for Sine-Gordon equation.

Recomended or Required Reading

Textbook: Nonlinear Partial Differential Equations for Scientists and Engineers, Lokenath Debnath, Birkhauser, Boston. References: Partial differential Equations: Methods and Apllications, Robert McOwen,Prentice Hall. Materials: Presentations of lectures

Planned Learning Activities and Teaching Methods

Lecture notes, presentations, solving problems

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 ASG ASSIGNMENT 2 MTE MIDTERM EXAM 3 FIN FINAL EXAM 4 FCG FINAL COURSE GRADE ASG * 0.30 + MTE * 0.30 + FIN * 0.40 5 RST RESIT 6 FCGR FINAL COURSE GRADE (RESIT) ASG * 0.30 + MTE * 0.30 + RST * 0.40

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

Email: melda.duman@deu.edu.tr Phone: 0 232 3018583

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 13 3 39 Preparations before/after weekly lectures 13 3 39 Preparation for midterm exam 1 15 15 Preparing assignments 6 8 48 Preparation for final exam 1 25 25 Final 1 3 3 Midterm 1 3 3 TOTAL WORKLOAD (hours) 172

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 LO.1 2 3 3 3 2 LO.2 4 5 3 4 2 4 LO.3 3 3 4 2 4 LO.4 3 3 4 2 4 LO.5 3 3 4 2 3