COURSE UNIT TITLE

: EQUATIONS OF MATHEMATICAL PHYSICS

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 6072 EQUATIONS OF MATHEMATICAL PHYSICS ELECTIVE 3 0 0 8

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

Offered to

Mathematics
Mathematics

Course Objective

Equations of mathematical physics for the acoustic, electromagnetic, seismic wave propagations are given in the course. The problems of wave propagations are stated in the terms of these equations. Different approaches and methods for solving these problems are described.

Learning Outcomes of the Course Unit

1   will be able to understand the basic equations of mathematical physics
2   will be able to understand the modern theory of modeling and their applications
3   will be able to express the fundamental concepts of the acoustic, elastic and electromagnetic plane-wave propagations and reflections
4   will be able to the perturbation and asymptotic methods for solving problems of equations of mathematical physics.
5   will be able to apply the Hadamards expansion and Sobolevs methods for solving equations of mathematical physics.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Acoustic equation and system and main problems for acoustic system. Existence and uniqueness theorems of IVP for the acoustic equation.
2 Plane waves in acoustic media. Reflection and transmission of acoustic waves. Simulation of 3-D images of acoustic waves.
3 Maxwells equations in different equation form. Maxwells equation and plane waves, sinusoidal waves, potentials for time-varying fields. Electromagmagnetic wave field in the 3-D rectangular box.
4 Maxwells equation as a symmetric hyperbolic system of the first order. Existence and uniqueness theorems for Maxwell s system.
5 Equations of anisotropic elasticity as a symmetric hyperbolic system of the first order. Mathematical models of elastic wave propagations in isotropic and anisotropic media.
6 Existence and uniqueness theorems of IVP for the system of anisotropic elasticity.
7 Midterm
8 Modeling waves in anisotropic crystals by dynamic system of elasticity with polynomial data.
9 Perturbation methods. Regular perturbation methods. Helmholtz equation with a small parameter. Heat conduction with slow radiation. Boundary perturbations for Laplace equation.
10 Asymptotic methods. Equations with a large parameter. Eikonal equation. Method of characteristics for solving eikonal equation.
11 Rays, fronts. Rays in a stratified medium. Refraction shadow region. Transport equation. Integration of the transport equation. Spherical and ray cooridinates.
12 Wave equation and asympotic expansion series. Scattering by a half plane. Method of stationary phase.
13 Diffraction. Diffraction coefficient. An asymptotic solution of the Klein-Gordon equation.
14 Geometrical optics expansion method. Two dimensional wave equation. Klein-Gordon equation.

Recomended or Required Reading

1. Zauderer E., Partial Differential Equations of Applied Mathematics, John Wiley&Sons , New York, 1989.
2. Courant R., Methods of Mathematical Physics, Vol.2, Wiley- Interscience, New York, 1962.
Supplementary Book(s):
3. Romanov V.G., Investigation Methods for Inverse Problems, VSP,Utrecht, The Netherlands, 2002.
4. Smirnov V.I., A Course in Higher Mathematics, Vol.IV, Pergamon Press, Oxford,1964.

Planned Learning Activities and Teaching Methods

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


*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

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)

To be announced.

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
Preparation for final exam 1 25 25
Preparing assignments 10 8 80
Final 1 3 3
Midterm 1 3 3
TOTAL WORKLOAD (hours) 204

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11
LO.155555555
LO.255555555
LO.355555555
LO.4555555
LO.5555555

CONTACT INFORMATION
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