M9150 Partial Differential Equations II
Faculty of ScienceSpring 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:
- 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.
M9150 Partial Differential Equations II
Faculty of ScienceSpring 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:
- 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.
M9150 Partial Differential Equations II
Faculty of ScienceSpring 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:
- 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.
M9150 Partial Differential Equations II
Faculty of ScienceAutumn 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.
M9150 Partial Differential Equations II
Faculty of ScienceAutumn 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.
M9150 Partial Differential Equations II
Faculty of ScienceAutumn 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.
M9150 Partial Differential Equations II
Faculty of ScienceAutumn 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.
M9150 Partial Differential Equations II
Faculty of ScienceAutumn 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.
M9150 Partial Differential Equations - Modern Methods
Faculty of ScienceSpring 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.
M9150 Partial Differential Equations - Modern Methods
Faculty of ScienceSpring 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.
M9150 Partial Differential Equations - Modern Methods
Faculty of ScienceSpring 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.
M9150 Partial Differential Equations - Modern Methods
Faculty of ScienceSpring 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.
M9150 Partial Differential Equations - Modern Methods
Faculty of ScienceSpring 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.
M9150 Partial Differential Equations - Modern Methods
Faculty of ScienceSpring 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.
M9150 Partial Differential Equations - Modern Methods
Faculty of ScienceSpring 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.
M9150 Partial Differential Equations II
Faculty of ScienceSpring 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.
M9150 Partial Differential Equations II
Faculty of ScienceSpring 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.
M9150 Partial Differential Equations - Modern Methods
Faculty of Sciencespring 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.
M9150 Partial Differential Equations - Modern Methods
Faculty of ScienceSpring 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.
M9150 Partial Differential Equations II
Faculty of ScienceSpring 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.
- Enrolment Statistics (recent)