YMF0020 Matemaatilise
füüsika vőrrandid
YMF0020 Equations of
mathematical physics
Content. The concept of partial differential
equation. The concept of solution. General solution, particular
solution. Classification and canonization of second order
equations. Hyperbolic, parabolic and elliptic equation. Simpler
integration methods. Classical equations (equation of vibrating string,
transport equation, heat equation, diffusion equation, Poisson equation,
Laplace equation, Schrödinger equation). Formulation of problems of
mathematical physics. Initial and boundary conditions. Cauchy problems,
boundary value problems, initial boundary value problems. Well-posed and
ill-posed problems. D'Alembert solution. Kirchoff's formula. Method of
characteristics. Method of coordinates. Operator method. Fourier method.
Principle of causality. Conservation laws. Exercises.
Classes are of 2 types: lectures (on Mondays
at 10.00) and practical lessons (on Tuesdays at 12.00). However, this schedule
will not always be followed.
Sometimes we will replace a practical lesson by a lecture and vice versa. All
changes in the schedule will be announced
and an information will be sent to students via őis.
NB! The practical lesson on Tuesday, January 30 will be
replaced by a lecture.
The course
will follow the textbook
P. Drábek,
G. Holubová, Elements of Partial
Differential Equations, De Gruyter 2014.
The book is
electronically available, web address:
NB! In case you have problems to access this book, please
contact me:
Misprints contained in the
textbook
Assessment
The
assessment is based on 2 tests on exercises and 2 tests on theory.
First pair
of tests will take place in the middle of the semester (8. or 9. week) and
comprise the first half of the course material. Second pair of tests will take
place at the end of the semester (provisionally 16. week) and comprise the
second half of the course material. All tests may be done (also repeatedly)
during the examination session, as well.
During a
test on exercises, a student has to solve 3 – 5 exercises.
During a
test on theory, a student will be asked to answer one longer question (that
contains proofs or derivation of formulas) and some (2 – 3) shorter questions.
Preparing an answer to the longer question, all materials may be used.
All tests
are assessed in the scale from 0 to 100 points.
The final grade will be
computed on the basis of sum of points of tests by means of the following
formula:
0 – 200 points: 0
201 – 240 points: 1
241 – 280 points: 2
281 – 320 points: 3
321 – 360 points: 4
361 -
400 points: 5
All current material of the course (incl. questions for the tests on
theory) will be made available here.
Slides of
lectures
Derivation of
equations of mathematical physics
Linear partial
differential equations of the first order
Wave equation in one
spatial variable – Cauchy problem
Diffusion equation in
one spatial variable – Cauchy problem
Poisson equation in
two spatial variables
Initial boundary
value problems on half-line
Initial boundary
value problems on finite interval 0 <
x < l
Laplace and Poisson
equations in higher dimensions. Boundary value problems
Diffusion and
wave equations in higher dimensions
Other material
Exercises solved in
practical lessons and homework exercises
Table fo Laplace
transforms Table of Fourier
transforms
Prof. Jaan Janno, e-mail: jaan.janno@ttu.ee room U05-415,
office hours: W 14.00-15.00 + any
other time by agreement
MSc. Nataliia Kinash, e-mail: nataliia.kinash@ttu.ee, room
U05-411, office hours: T 14.00-15.00 + any other time by agreement
Times for retaking tests:
theory
23.05 12.00 U05-402
6.06 12.00 U05-402
15.06 12.00 U05-402
exercises
24.05 10.00 U05-404
15.06 10.00 U05-404