M9150 Partial Differential Equations II

Faculty of Science
Spring 2009
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
doc. RNDr. Ladislav Adamec, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 12:00–13:50 MS2,01022
  • Timetable of Seminar Groups:
M9150/01: Mon 14:00–14:50 MS2,01022, L. Adamec
Prerequisites
M8110 Partial Differential Equations I
Calculus of several variables, basic methods of solving ordinary and partial differential equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
This course is a continuation of the course "Partial differential equations I".
The aim of the course is to aquire techniques necessary for formulating and solving problems using partial differential equations in modern setting.
At the end of this course, students should be able to understand concepts of weak solution of second-order linear partial differential equation elliptic and evolutionary.
Syllabus
  • Modern methods
  • 1) Sobolev spaces of generalized functions
  • 2) Linear seccond-order elliptic equations:
  • - Weak formulation of elliptic problems
  • - Lax-Milgram lemma and existence of solutions
  • - Regularity
  • - Maximum principle
  • 3) Linear parabolic and hyperbolic equations:
  • - Ritz-Galerkin method
  • - Regularity
  • - Semigroup theory
Literature
  • Partial differential equations. Edited by Jürgen Jost. New York: Springer-Verlag, 2002, xi, 325. ISBN 0387954287. info
  • GILBARG, David and Neil S. TRUDINGER. Elliptic partial differential equations of second order. Berlin: Springer-Verlag, 1997, x, 401 s. ISBN 3-540-08007-4-. info
  • BASSANINI, Piero and Alan R. ELCRAT. Theory and applications of partial differential equations. New York: Plenum Press, 1997, ix, 439 s. ISBN 0-306-45640-0. info
  • RENARDY, Michael and Robert ROGERS. An introduction to partial differential equations. New York: Springer-Verlag, 1992, vii, 428. ISBN 0387979522. info
Assessment methods
lectures,class exercises;
oral examination.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is also listed under the following terms Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Spring 2005, Spring 2007.

M9150 Partial Differential Equations II

Faculty of Science
Spring 2007
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
doc. RNDr. Ladislav Adamec, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Ladislav Adamec, CSc.
Timetable
Tue 16:00–17:50 N41
  • Timetable of Seminar Groups:
M9150/01: Tue 18:00–18:50 N41, L. Adamec
Prerequisites
M8110 Partial Differential Equations I
Calculus of several variables, basic methods of solving ordinary and partial differential equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
This course is a continuation of Partial differential equations I. The aim of the first part is to give a broader view on solutions of pde's and their properties, using modern methods. The main tools are functional and Fourier analysis. The aim of the second part is to show on the example of Navier-Stokes equations some techniques for analysis of nonlinear equations and their systems.
Syllabus
  • 1. Modern methods - Sobolev spaces of generalized functions - Weak formulation of elliptic problems - Lax-Milgram lemma and existence of solutions - Variational formulation of elliptical problems - Ritz-Galerkin method - Monotone operators 2. Navier-Stokes equations - Examples of exact solutions - Vorticity, vorticity equation - Leray's formulation - Properties of 2-D flows - Beltrami flow
Literature
  • ARSENIN, Vasilij Jakovlevič. Metody matematičeskoj fiziki i special'nyje funkcii. 2. perer. i dop. izd. Moskva: Nauka, 1984, 382 s. info
Assessment methods (in Czech)
Typ výuky - přednáška a cvičení, zkouška - ústní
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is also listed under the following terms Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Spring 2005, Spring 2009.

M9150 Partial Differential Equations II

Faculty of Science
Spring 2005
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
doc. RNDr. Martin Kolář, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martin Kolář, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Martin Kolář, Ph.D.
Timetable
Wed 16:00–17:50 UM
  • Timetable of Seminar Groups:
M9150/01: Wed 18:00–18:50 UM, L. Adamec
Prerequisites
M8110 Partial Differential Equations I
Calculus of several variables, basic methods of solving ordinary and partial differential equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
This course is a continuation of Partial differential equations I. The aim of the first part is to give a broader view on solutions of pde's and their properties, using modern methods. The main tools are functional and Fourier analysis. The aim of the second part is to show on the example of Navier-Stokes equations some techniques for analysis of nonlinear equations and their systems.
Syllabus
  • 1. Modern methods - Sobolev spaces of generalized functions - Weak formulation of elliptic problems - Lax-Milgram lemma and existence of solutions - Variational formulation of elliptical problems - Ritz-Galerkin method - Monotone operators 2. Navier-Stokes equations - Examples of exact solutions - Vorticity, vorticity equation - Leray's formulation - Properties of 2-D flows - Beltrami flow
Literature
  • ARSENIN, Vasilij Jakovlevič. Metody matematičeskoj fiziki i special'nyje funkcii. 2. perer. i dop. izd. Moskva: Nauka, 1984, 382 s. info
Assessment methods (in Czech)
Typ výuky - přednáška a cvičení, zkouška - ústní
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is also listed under the following terms Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Spring 2007, Spring 2009.

M9150 Partial Differential Equations II

Faculty of Science
Autumn 2003
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Martin Kolář, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martin Kolář, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Martin Kolář, Ph.D.
Timetable of Seminar Groups
M9150/01: No timetable has been entered into IS. M. Kolář
Prerequisites
M8110 Partial Differential Equations I
Calculus of several variables, basic methods of solving ordinary and partial differential equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
This course is a continuation of Partial differential equations I. The aim of the first part is to give a broader view on solutions of pde's and their properties, using modern methods. The main tools are functional and Fourier analysis. The aim of the second part is to show on the example of Navier-Stokes equations some techniques for analysis of nonlinear equations and their systems.
Syllabus
  • 1. Modern methods - Sobolev spaces of generalized functions - Weak formulation of elliptic problems - Lax-Milgram lemma and existence of solutions - Variational formulation of elliptical problems - Ritz-Galerkin method - Monotone operators 2. Navier-Stokes equations - Examples of exact solutions - Vorticity, vorticity equation - Leray's formulation - Properties of 2-D flows - Beltrami flow
Literature
  • ARSENIN, Vasilij Jakovlevič. Metody matematičeskoj fiziki i special'nyje funkcii. 2. perer. i dop. izd. Moskva: Nauka, 1984, 382 s. info
Assessment methods (in Czech)
Typ výuky - přednáška a cvičení, zkouška - ústní
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is also listed under the following terms Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Spring 2005, Spring 2007, Spring 2009.

M9150 Partial Differential Equations II

Faculty of Science
Autumn 2002
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Martin Kolář, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martin Kolář, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Martin Kolář, Ph.D.
Prerequisites
M8110 Partial Differential Equations I
Calculus of several variables, basic methods of solving ordinary and partial differential equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
This course is a continuation of Partial differential equations I. The aim of the first part is to give a broader view on solutions of pde's and their properties, using modern methods. The main tools are functional and Fourier analysis. The aim of the second part is to show on the example of Navier-Stokes equations some techniques for analysis of nonlinear equations and their systems.
Syllabus
  • 1. Modern methods - Sobolev spaces of generalized functions - Weak formulation of elliptic problems - Lax-Milgram lemma and existence of solutions - Variational formulation of elliptical problems - Ritz-Galerkin method - Monotone operators 2. Navier-Stokes equations - Examples of exact solutions - Vorticity, vorticity equation - Leray's formulation - Properties of 2-D flows - Beltrami flow
Literature
  • ARSENIN, Vasilij Jakovlevič. Metody matematičeskoj fiziki i special'nyje funkcii. 2. perer. i dop. izd. Moskva: Nauka, 1984, 382 s. info
Assessment methods (in Czech)
Typ výuky - přednáška a cvičení, zkouška - ústní
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2003, Spring 2005, Spring 2007, Spring 2009.

M9150 Partial Differential Equations II

Faculty of Science
Autumn 2001
Extent and Intensity
2/1/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Martin Kolář, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martin Kolář, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Martin Kolář, Ph.D.
Prerequisites (in Czech)
M8110 Partial Differential Equations I
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
1. Modern methods - Sobolev spaces of generalized functions - Weak formulation of elliptic problems - Lax-Milgram lemma and existence of solutions - Variational formulation of elliptical problems - Ritz-Galerkin method - Monotone operators 2. Navier-Stokes equations - Examples of exact solutions - Vorticity, vorticity equation - Leray's formulation - Properties of 2-D flows - Beltrami flow
Literature
  • ARSENIN, Vasilij Jakovlevič. Metody matematičeskoj fiziki i special'nyje funkcii. 2. perer. i dop. izd. Moskva: Nauka, 1984, 382 s. info
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 1999, Autumn 2000, Autumn 2002, Autumn 2003, Spring 2005, Spring 2007, Spring 2009.

M9150 Partial Differential Equations II

Faculty of Science
Autumn 2000
Extent and Intensity
2/1/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Martin Kolář, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martin Kolář, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Martin Kolář, Ph.D.
Prerequisites (in Czech)
M8110 Partial Diff. Equations
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
1. Modern methods - Sobolev spaces of generalized functions - Weak formulation of elliptic problems - Lax-Milgram lemma and existence of solutions - Variational formulation of elliptical problems - Ritz-Galerkin method - Monotone operators 2. Navier-Stokes equations - Examples of exact solutions - Vorticity, vorticity equation - Leray's formulation - Properties of 2-D flows - Beltrami flow
Literature
  • ARSENIN, Vasilij Jakovlevič. Metody matematičeskoj fiziki i special'nyje funkcii. 2. perer. i dop. izd. Moskva: Nauka, 1984, 382 s. info
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 1999, Autumn 2001, Autumn 2002, Autumn 2003, Spring 2005, Spring 2007, Spring 2009.

M9150 Partial Differential Equations II

Faculty of Science
Autumn 1999
Extent and Intensity
2/1/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Martin Kolář, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martin Kolář, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Martin Kolář, Ph.D.
Prerequisites (in Czech)
M8110 Partial Differential Equations I
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Syllabus
  • 1. Modern methods - Sobolev spaces of generalized functions - Weak formulation of elliptic problems - Lax-Milgram lemma and existence of solutions - Variational formulation of elliptical problems - Ritz-Galerkin method - Monotone operators 2. Navier-Stokes equations - Examples of exact solutions - Vorticity, vorticity equation - Leray's formulation - Properties of 2-D flows - Beltrami flow
Literature
  • ARSENIN, Vasilij Jakovlevič. Metody matematičeskoj fiziki i special'nyje funkcii. 2. perer. i dop. izd. Moskva: Nauka, 1984, 382 s. info
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Spring 2005, Spring 2007, Spring 2009.

M9150 Partial Differential Equations - Modern Methods

Faculty of Science
Spring 2016

The course is not taught in Spring 2016

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M8110 Partial Diff. Equations
Calculus of several variables, basic methods of solving ordinary and partial differential equations.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The course is a continuation of the course "Partial differential equations - classical methods".
Students will acquire techniques necessary for formulating and solving problems using partial differential equations in modern setting.
At the end of this course, students will be able to understand concepts of weak solution of second-order linear elliptic and evolutionary partial differential equation.
Syllabus
  • Modern methods
  • 1) Sobolev spaces of generalized functions
  • 2) Linear seccond-order elliptic equations:
  • - Weak formulation of elliptic problems
  • - Lax-Milgram lemma and existence of solutions
  • - Regularity
  • - Maximum principle
  • 3) Linear parabolic and hyperbolic equations:
  • - Ritz-Galerkin method
  • - Regularity
  • - Semigroup theory
Literature
  • Partial differential equations. Edited by Jürgen Jost. New York: Springer-Verlag, 2002, xi, 325. ISBN 0387954287. info
  • GILBARG, David and Neil S. TRUDINGER. Elliptic partial differential equations of second order. Berlin: Springer-Verlag, 1997, x, 401 s. ISBN 3-540-08007-4-. info
  • BASSANINI, Piero and Alan R. ELCRAT. Theory and applications of partial differential equations. New York: Plenum Press, 1997, ix, 439 s. ISBN 0-306-45640-0. info
  • RENARDY, Michael and Robert ROGERS. An introduction to partial differential equations. New York: Springer-Verlag, 1992, vii, 428. ISBN 0387979522. info
Teaching methods
Lectures,class exercises;
Assessment methods
Oral examination.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Spring 2005, Spring 2007, Spring 2009.

M9150 Partial Differential Equations - Modern Methods

Faculty of Science
Spring 2015

The course is not taught in Spring 2015

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M8110 Partial Diff. Equations
Calculus of several variables, basic methods of solving ordinary and partial differential equations.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The course is a continuation of the course "Partial differential equations - classical methods".
Students will acquire techniques necessary for formulating and solving problems using partial differential equations in modern setting.
At the end of this course, students will be able to understand concepts of weak solution of second-order linear elliptic and evolutionary partial differential equation.
Syllabus
  • Modern methods
  • 1) Sobolev spaces of generalized functions
  • 2) Linear seccond-order elliptic equations:
  • - Weak formulation of elliptic problems
  • - Lax-Milgram lemma and existence of solutions
  • - Regularity
  • - Maximum principle
  • 3) Linear parabolic and hyperbolic equations:
  • - Ritz-Galerkin method
  • - Regularity
  • - Semigroup theory
Literature
  • Partial differential equations. Edited by Jürgen Jost. New York: Springer-Verlag, 2002, xi, 325. ISBN 0387954287. info
  • GILBARG, David and Neil S. TRUDINGER. Elliptic partial differential equations of second order. Berlin: Springer-Verlag, 1997, x, 401 s. ISBN 3-540-08007-4-. info
  • BASSANINI, Piero and Alan R. ELCRAT. Theory and applications of partial differential equations. New York: Plenum Press, 1997, ix, 439 s. ISBN 0-306-45640-0. info
  • RENARDY, Michael and Robert ROGERS. An introduction to partial differential equations. New York: Springer-Verlag, 1992, vii, 428. ISBN 0387979522. info
Teaching methods
Lectures,class exercises;
Assessment methods
Oral examination.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Spring 2005, Spring 2007, Spring 2009.

M9150 Partial Differential Equations - Modern Methods

Faculty of Science
Spring 2014

The course is not taught in Spring 2014

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M8110 Partial Diff. Equations
Calculus of several variables, basic methods of solving ordinary and partial differential equations.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The course is a continuation of the course "Partial differential equations - classical methods".
Students will acquire techniques necessary for formulating and solving problems using partial differential equations in modern setting.
At the end of this course, students will be able to understand concepts of weak solution of second-order linear elliptic and evolutionary partial differential equation.
Syllabus
  • Modern methods
  • 1) Sobolev spaces of generalized functions
  • 2) Linear seccond-order elliptic equations:
  • - Weak formulation of elliptic problems
  • - Lax-Milgram lemma and existence of solutions
  • - Regularity
  • - Maximum principle
  • 3) Linear parabolic and hyperbolic equations:
  • - Ritz-Galerkin method
  • - Regularity
  • - Semigroup theory
Literature
  • Partial differential equations. Edited by Jürgen Jost. New York: Springer-Verlag, 2002, xi, 325. ISBN 0387954287. info
  • GILBARG, David and Neil S. TRUDINGER. Elliptic partial differential equations of second order. Berlin: Springer-Verlag, 1997, x, 401 s. ISBN 3-540-08007-4-. info
  • BASSANINI, Piero and Alan R. ELCRAT. Theory and applications of partial differential equations. New York: Plenum Press, 1997, ix, 439 s. ISBN 0-306-45640-0. info
  • RENARDY, Michael and Robert ROGERS. An introduction to partial differential equations. New York: Springer-Verlag, 1992, vii, 428. ISBN 0387979522. info
Teaching methods
Lectures,class exercises;
Assessment methods
Oral examination.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Spring 2005, Spring 2007, Spring 2009.

M9150 Partial Differential Equations - Modern Methods

Faculty of Science
Spring 2013

The course is not taught in Spring 2013

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M8110 Partial Diff. Equations
Calculus of several variables, basic methods of solving ordinary and partial differential equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
The course is a continuation of the course "Partial differential equations - classical methods".
Students will acquire techniques necessary for formulating and solving problems using partial differential equations in modern setting.
At the end of this course, students will be able to understand concepts of weak solution of second-order linear elliptic and evolutionary partial differential equation.
Syllabus
  • Modern methods
  • 1) Sobolev spaces of generalized functions
  • 2) Linear seccond-order elliptic equations:
  • - Weak formulation of elliptic problems
  • - Lax-Milgram lemma and existence of solutions
  • - Regularity
  • - Maximum principle
  • 3) Linear parabolic and hyperbolic equations:
  • - Ritz-Galerkin method
  • - Regularity
  • - Semigroup theory
Literature
  • Partial differential equations. Edited by Jürgen Jost. New York: Springer-Verlag, 2002, xi, 325. ISBN 0387954287. info
  • GILBARG, David and Neil S. TRUDINGER. Elliptic partial differential equations of second order. Berlin: Springer-Verlag, 1997, x, 401 s. ISBN 3-540-08007-4-. info
  • BASSANINI, Piero and Alan R. ELCRAT. Theory and applications of partial differential equations. New York: Plenum Press, 1997, ix, 439 s. ISBN 0-306-45640-0. info
  • RENARDY, Michael and Robert ROGERS. An introduction to partial differential equations. New York: Springer-Verlag, 1992, vii, 428. ISBN 0387979522. info
Teaching methods
Lectures,class exercises;
Assessment methods
Oral examination.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Spring 2005, Spring 2007, Spring 2009.

M9150 Partial Differential Equations - Modern Methods

Faculty of Science
Spring 2012

The course is not taught in Spring 2012

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M8110 Partial Diff. Equations
Calculus of several variables, basic methods of solving ordinary and partial differential equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
The course is a continuation of the course "Partial differential equations - classical methods".
Students will acquire techniques necessary for formulating and solving problems using partial differential equations in modern setting.
At the end of this course, students will be able to understand concepts of weak solution of second-order linear elliptic and evolutionary partial differential equation.
Syllabus
  • Modern methods
  • 1) Sobolev spaces of generalized functions
  • 2) Linear seccond-order elliptic equations:
  • - Weak formulation of elliptic problems
  • - Lax-Milgram lemma and existence of solutions
  • - Regularity
  • - Maximum principle
  • 3) Linear parabolic and hyperbolic equations:
  • - Ritz-Galerkin method
  • - Regularity
  • - Semigroup theory
Literature
  • Partial differential equations. Edited by Jürgen Jost. New York: Springer-Verlag, 2002, xi, 325. ISBN 0387954287. info
  • GILBARG, David and Neil S. TRUDINGER. Elliptic partial differential equations of second order. Berlin: Springer-Verlag, 1997, x, 401 s. ISBN 3-540-08007-4-. info
  • BASSANINI, Piero and Alan R. ELCRAT. Theory and applications of partial differential equations. New York: Plenum Press, 1997, ix, 439 s. ISBN 0-306-45640-0. info
  • RENARDY, Michael and Robert ROGERS. An introduction to partial differential equations. New York: Springer-Verlag, 1992, vii, 428. ISBN 0387979522. info
Teaching methods
Lectures,class exercises;
Assessment methods
Oral examination.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Spring 2005, Spring 2007, Spring 2009.

M9150 Partial Differential Equations - Modern Methods

Faculty of Science
Spring 2011

The course is not taught in Spring 2011

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M8110 Partial Diff. Equations
Calculus of several variables, basic methods of solving ordinary and partial differential equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
The course is a continuation of the course "Partial differential equations - classical methods".
Students will acquire techniques necessary for formulating and solving problems using partial differential equations in modern setting.
At the end of this course, students will be able to understand concepts of weak solution of second-order linear elliptic and evolutionary partial differential equation.
Syllabus
  • Modern methods
  • 1) Sobolev spaces of generalized functions
  • 2) Linear seccond-order elliptic equations:
  • - Weak formulation of elliptic problems
  • - Lax-Milgram lemma and existence of solutions
  • - Regularity
  • - Maximum principle
  • 3) Linear parabolic and hyperbolic equations:
  • - Ritz-Galerkin method
  • - Regularity
  • - Semigroup theory
Literature
  • Partial differential equations. Edited by Jürgen Jost. New York: Springer-Verlag, 2002, xi, 325. ISBN 0387954287. info
  • GILBARG, David and Neil S. TRUDINGER. Elliptic partial differential equations of second order. Berlin: Springer-Verlag, 1997, x, 401 s. ISBN 3-540-08007-4-. info
  • BASSANINI, Piero and Alan R. ELCRAT. Theory and applications of partial differential equations. New York: Plenum Press, 1997, ix, 439 s. ISBN 0-306-45640-0. info
  • RENARDY, Michael and Robert ROGERS. An introduction to partial differential equations. New York: Springer-Verlag, 1992, vii, 428. ISBN 0387979522. info
Teaching methods
Lectures,class exercises;
Assessment methods
Oral examination.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Spring 2005, Spring 2007, Spring 2009.

M9150 Partial Differential Equations - Modern Methods

Faculty of Science
Spring 2010

The course is not taught in Spring 2010

Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M8110 Part. Diff. Eq. - Class. Meth.
Calculus of several variables, basic methods of solving ordinary and partial differential equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
The course is a continuation of the course "Partial differential equations - classical methods".
Students will acquire techniques necessary for formulating and solving problems using partial differential equations in modern setting.
At the end of this course, students will be able to understand concepts of weak solution of second-order linear elliptic and evolutionary partial differential equation.
Syllabus
  • Modern methods
  • 1) Sobolev spaces of generalized functions
  • 2) Linear seccond-order elliptic equations:
  • - Weak formulation of elliptic problems
  • - Lax-Milgram lemma and existence of solutions
  • - Regularity
  • - Maximum principle
  • 3) Linear parabolic and hyperbolic equations:
  • - Ritz-Galerkin method
  • - Regularity
  • - Semigroup theory
Literature
  • Partial differential equations. Edited by Jürgen Jost. New York: Springer-Verlag, 2002, xi, 325. ISBN 0387954287. info
  • GILBARG, David and Neil S. TRUDINGER. Elliptic partial differential equations of second order. Berlin: Springer-Verlag, 1997, x, 401 s. ISBN 3-540-08007-4-. info
  • BASSANINI, Piero and Alan R. ELCRAT. Theory and applications of partial differential equations. New York: Plenum Press, 1997, ix, 439 s. ISBN 0-306-45640-0. info
  • RENARDY, Michael and Robert ROGERS. An introduction to partial differential equations. New York: Springer-Verlag, 1992, vii, 428. ISBN 0387979522. info
Teaching methods
Lectures,class exercises;
Assessment methods
Oral examination.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Spring 2005, Spring 2007, Spring 2009.

M9150 Partial Differential Equations II

Faculty of Science
Spring 2008

The course is not taught in Spring 2008

Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Guaranteed by
doc. RNDr. Ladislav Adamec, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M8110 Partial Differential Equations I
Calculus of several variables, basic methods of solving ordinary and partial differential equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
This course is a continuation of Partial differential equations I. The aim of the first part is to give a broader view on solutions of pde's and their properties, using modern methods. The main tools are functional and Fourier analysis. The aim of the second part is to show on the example of Navier-Stokes equations some techniques for analysis of nonlinear equations and their systems.
Syllabus
  • 1. Modern methods - Sobolev spaces of generalized functions - Weak formulation of elliptic problems - Lax-Milgram lemma and existence of solutions - Variational formulation of elliptical problems - Ritz-Galerkin method - Monotone operators 2. Navier-Stokes equations - Examples of exact solutions - Vorticity, vorticity equation - Leray's formulation - Properties of 2-D flows - Beltrami flow
Literature
  • ARSENIN, Vasilij Jakovlevič. Metody matematičeskoj fiziki i special'nyje funkcii. 2. perer. i dop. izd. Moskva: Nauka, 1984, 382 s. info
Assessment methods (in Czech)
Typ výuky - přednáška a cvičení, zkouška - ústní
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Spring 2005, Spring 2007, Spring 2009.

M9150 Partial Differential Equations II

Faculty of Science
Spring 2006

The course is not taught in Spring 2006

Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
doc. RNDr. Ladislav Adamec, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Ladislav Adamec, CSc.
Prerequisites
M8110 Partial Differential Equations I
Calculus of several variables, basic methods of solving ordinary and partial differential equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
This course is a continuation of Partial differential equations I. The aim of the first part is to give a broader view on solutions of pde's and their properties, using modern methods. The main tools are functional and Fourier analysis. The aim of the second part is to show on the example of Navier-Stokes equations some techniques for analysis of nonlinear equations and their systems.
Syllabus
  • 1. Modern methods - Sobolev spaces of generalized functions - Weak formulation of elliptic problems - Lax-Milgram lemma and existence of solutions - Variational formulation of elliptical problems - Ritz-Galerkin method - Monotone operators 2. Navier-Stokes equations - Examples of exact solutions - Vorticity, vorticity equation - Leray's formulation - Properties of 2-D flows - Beltrami flow
Literature
  • ARSENIN, Vasilij Jakovlevič. Metody matematičeskoj fiziki i special'nyje funkcii. 2. perer. i dop. izd. Moskva: Nauka, 1984, 382 s. info
Assessment methods (in Czech)
Typ výuky - přednáška a cvičení, zkouška - ústní
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Spring 2005, Spring 2007, Spring 2009.

M9150 Partial Differential Equations - Modern Methods

Faculty of Science
spring 2012 - acreditation

The course is not taught in spring 2012 - acreditation

The information about the term spring 2012 - acreditation is not made public

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M8110 Partial Diff. Equations
Calculus of several variables, basic methods of solving ordinary and partial differential equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
The course is a continuation of the course "Partial differential equations - classical methods".
Students will acquire techniques necessary for formulating and solving problems using partial differential equations in modern setting.
At the end of this course, students will be able to understand concepts of weak solution of second-order linear elliptic and evolutionary partial differential equation.
Syllabus
  • Modern methods
  • 1) Sobolev spaces of generalized functions
  • 2) Linear seccond-order elliptic equations:
  • - Weak formulation of elliptic problems
  • - Lax-Milgram lemma and existence of solutions
  • - Regularity
  • - Maximum principle
  • 3) Linear parabolic and hyperbolic equations:
  • - Ritz-Galerkin method
  • - Regularity
  • - Semigroup theory
Literature
  • Partial differential equations. Edited by Jürgen Jost. New York: Springer-Verlag, 2002, xi, 325. ISBN 0387954287. info
  • GILBARG, David and Neil S. TRUDINGER. Elliptic partial differential equations of second order. Berlin: Springer-Verlag, 1997, x, 401 s. ISBN 3-540-08007-4-. info
  • BASSANINI, Piero and Alan R. ELCRAT. Theory and applications of partial differential equations. New York: Plenum Press, 1997, ix, 439 s. ISBN 0-306-45640-0. info
  • RENARDY, Michael and Robert ROGERS. An introduction to partial differential equations. New York: Springer-Verlag, 1992, vii, 428. ISBN 0387979522. info
Teaching methods
Lectures,class exercises;
Assessment methods
Oral examination.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Spring 2005, Spring 2007, Spring 2009.

M9150 Partial Differential Equations - Modern Methods

Faculty of Science
Spring 2011 - only for the accreditation

The course is not taught in Spring 2011 - only for the accreditation

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M8110 Partial Differential Equations I
Calculus of several variables, basic methods of solving ordinary and partial differential equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
The course is a continuation of the course "Partial differential equations - classical methods".
Students will acquire techniques necessary for formulating and solving problems using partial differential equations in modern setting.
At the end of this course, students will be able to understand concepts of weak solution of second-order linear elliptic and evolutionary partial differential equation.
Syllabus
  • Modern methods
  • 1) Sobolev spaces of generalized functions
  • 2) Linear seccond-order elliptic equations:
  • - Weak formulation of elliptic problems
  • - Lax-Milgram lemma and existence of solutions
  • - Regularity
  • - Maximum principle
  • 3) Linear parabolic and hyperbolic equations:
  • - Ritz-Galerkin method
  • - Regularity
  • - Semigroup theory
Literature
  • Partial differential equations. Edited by Jürgen Jost. New York: Springer-Verlag, 2002, xi, 325. ISBN 0387954287. info
  • GILBARG, David and Neil S. TRUDINGER. Elliptic partial differential equations of second order. Berlin: Springer-Verlag, 1997, x, 401 s. ISBN 3-540-08007-4-. info
  • BASSANINI, Piero and Alan R. ELCRAT. Theory and applications of partial differential equations. New York: Plenum Press, 1997, ix, 439 s. ISBN 0-306-45640-0. info
  • RENARDY, Michael and Robert ROGERS. An introduction to partial differential equations. New York: Springer-Verlag, 1992, vii, 428. ISBN 0387979522. info
Teaching methods
Lectures,class exercises;
Assessment methods
Oral examination.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Spring 2005, Spring 2007, Spring 2009.

M9150 Partial Differential Equations II

Faculty of Science
Spring 2008 - for the purpose of the accreditation

The course is not taught in Spring 2008 - for the purpose of the accreditation

Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
doc. RNDr. Ladislav Adamec, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Ladislav Adamec, CSc.
Prerequisites
M8110 Partial Differential Equations I
Calculus of several variables, basic methods of solving ordinary and partial differential equations.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
This course is a continuation of Partial differential equations I. The aim of the first part is to give a broader view on solutions of pde's and their properties, using modern methods. The main tools are functional and Fourier analysis. The aim of the second part is to show on the example of Navier-Stokes equations some techniques for analysis of nonlinear equations and their systems.
Syllabus
  • 1. Modern methods - Sobolev spaces of generalized functions - Weak formulation of elliptic problems - Lax-Milgram lemma and existence of solutions - Variational formulation of elliptical problems - Ritz-Galerkin method - Monotone operators 2. Navier-Stokes equations - Examples of exact solutions - Vorticity, vorticity equation - Leray's formulation - Properties of 2-D flows - Beltrami flow
Literature
  • ARSENIN, Vasilij Jakovlevič. Metody matematičeskoj fiziki i special'nyje funkcii. 2. perer. i dop. izd. Moskva: Nauka, 1984, 382 s. info
Assessment methods (in Czech)
Typ výuky - přednáška a cvičení, zkouška - ústní
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Spring 2005, Spring 2007, Spring 2009.
  • Enrolment Statistics (recent)