Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
7MATH413LINEAR AND NONLINEAR WAVES3+036

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Elective
Objectives of the Course Study main properties on linear and nonlinear wave theory and show wide applications to hydrodynamic etc
Course Content Linear Harmonic Oscillator: Simple, Damped, and Forced oscillations, Nonlinear oscillations, Fourier Transform and Convolution, Linear Wave Equations, Plane waves and Dispersion Relation, Linear Dispersive Waves, Wave packets, Nonlinear Waves, Inviscid Burgers equation, Formation of Shocks, Nonlinear diffusive waves and Viscous Burgers Equation, Cole-Hopf transform, Shock and Multi-shock traveling Wave solutions, Self-Similarity solutions, Nonlinear Dispersive Waves, Korteweg-de Vries equation (KdV) and Solitary waves, Non-Linear Schrödinger equation and Solitons.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Prof.Dr. Şirin A. Büyükaşık
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Nonlinear Dynamics by M. Lakshmanan & S. Rajasekar, Springer, 2003.
“Linear and Nonlinear Waves”, G. B. Whitham
“Nonlinear waves, solitons and chaos”, E. Infeld, G. Rowlands

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 2 % 50
Quizzes 0 % 0
Homeworks 4 % 10
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 40
Total
7
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 3 14 42
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 10 10 100
Exams and Exam Preparations 4 10 40
Total Work Load   Number of ECTS Credits 6 182

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 To understand basic principles of the theory
2 To be able to solve typical problems associated with this theory.
3 To learn the mathematical properties of the linear and nonlinear waves
4 To be able to recognize the well-known wave equations
5 To be able to analize and interprete the solutions


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Linear oscillator. Damped oscillator
2 Nonlinear oscillator
3 From oscillators to waves. Linear waves
4 Dispersive and non-dispersive waves
5 Linear hyperbolic wave equation.
6 Fourier transform and solution of IVP. Wave packet
7 Nonlinear dispersive systems
8 Periodic and solitary waves
9 Korteweg-de Vries equation
10 Inviscid Burgers equation. Formation of Shocks.
11 Viscous Burgers equation. Similarity Solutions, Multi-shock traveling waves.
12 Solitons
13 Hirota’s direct bilinear method
14 Nonlinear Schrodinger equation


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
All 2
C1 4
C2 5 3
C3
C4 3
C5 3

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant


https://obs.iyte.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=163242&lang=en