M8180 Nonlinear Functional Analysis

Faculty of Science
Spring 2010
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 18:00–19:50 MS2,01022
Prerequisites
M6150 Linear Functional Analysis I
Differential and integral calculus, Linear functional analysis I and II, Linear algebra.
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
Nonlinear functional analysis belongs to advanced parts of university courses in mathematics. It is utilized in many applications. The aim of the course is to introduce the bases of nonlinear functional analysis, namely differential and integral calculus in normed spaces and their applications. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • 1. Differential calculus in normed spaces. Freschet and Gateaux differentials. Integral calculus in normed spaces. Newton-Leibnitz formula. Higher order derivatives. Taylor formula. 2. Application of differential calculus. 3. Degree theory.
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • ZEIDLER, Eberhard. Nonlinear functional analysis and its applications. Translated by Leo F. Boron. New York: Springer-Verlag, 1990, xv, 469-12. ISBN 354097167X. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
  • KRASNOSEL‘SKIJ, Mark Aleksandrovič. Topologičeskijje metody v teorii nelinejnych integral'nych uravnenij. Moskva: Techniko teoretičeskoj literatury, 1956, 392 s. info
Teaching methods
lectures and class exercises
Assessment methods
Teaching: lecture 2 hours a week, seminar 1 hours a week. Examination: written and oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008.

M8180 Nonlinear Functional Analysis

Faculty of Science
Spring 2008
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 8:00–9:50 UP2
  • Timetable of Seminar Groups:
M8180/01: Mon 10:00–10:50 UP2, A. Lomtatidze
Prerequisites
M6150 Linear Functional Analysis I
Differential and integral calculus, Linear functional analysis I and II, Linear algebra.
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 aim of the course is to introduce the bases of nonlinear functional analysis, namely differential and integral calculus in normed spaces and their applications. At the end of this course, students should be able to: understand and explain basic notions of nonlinear functional analysis and relations between them.
Syllabus
  • 1. Differential calculus in normed spaces. Freschet and Gateaux differentials. Integral calculus in normed spaces. Newton-Leibnitz formula. Higher order derivatives. Taylor formula. 2. Application of differential calculus. 3. Degree theory.
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
Assessment methods
Teaching: lecture 3 hours a week, seminar 1 hours a week. Examination: written and oral.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2010.

M8180 Nonlinear Functional Analysis

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)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. Alexander Lomtatidze, DrSc.
Timetable
Mon 15:00–16:50 U1
  • Timetable of Seminar Groups:
M8180/01: Mon 17:00–17:50 U1, A. Lomtatidze
Prerequisites (in Czech)
M6150 Linear Functional Analysis 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 (in Czech)
Cílem předmětu je seznámit posluchače se základy nelineární funkcionální analýzy, zejména s diferenciálním počtem v normovaných prostorech a aplikacemi.
Syllabus (in Czech)
  • 1. Diferenciální počet v normovaných prostorech 1.1. Silný diferenciál (Freschetův diferenciál) 1.2. Slabý diferenciál (Gateauxův diferenciál) 1.3. Integrál 1.4. Newton-Leibnitzův vzorec 1.5. Derivace vyšších řádů 1.6. Taylorův vzorec 2. Aplikace v extrémálních úlohach 3. Věta o implicitní funkci 3.1. Věta o implicitní funkci 3.2. Věta o lokální inverzi
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2008, Spring 2010.

M8180 Nonlinear Functional Analysis

Faculty of Science
Spring 2006
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. Alexander Lomtatidze, DrSc.
Timetable
Tue 8:00–9:50 UM
  • Timetable of Seminar Groups:
M8180/01: Tue 10:00–10:50 UM, A. Lomtatidze
Prerequisites (in Czech)
M6150 Linear Functional Analysis 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 (in Czech)
Cílem předmětu je seznámit posluchače se základy nelineární funkcionální analýzy, zejména s diferenciálním počtem v normovaných prostorech a aplikacemi.
Syllabus (in Czech)
  • 1. Diferenciální počet v normovaných prostorech 1.1. Silný diferenciál (Freschetův diferenciál) 1.2. Slabý diferenciál (Gateauxův diferenciál) 1.3. Integrál 1.4. Newton-Leibnitzův vzorec 1.5. Derivace vyšších řádů 1.6. Taylorův vzorec 2. Aplikace v extrémálních úlohach 3. Věta o implicitní funkci 3.1. Věta o implicitní funkci 3.2. Věta o lokální inverzi
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2007, Spring 2008, Spring 2010.

M8180 Nonlinear Functional Analysis

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)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. Alexander Lomtatidze, DrSc.
Timetable
Tue 10:00–11:50 UP2
  • Timetable of Seminar Groups:
M8180/01: Tue 12:00–12:50 UP2, A. Lomtatidze
Prerequisites (in Czech)
M6150 Linear Functional Analysis 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 (in Czech)
Cílem předmětu je seznámit posluchače se základy nelineární funkcionální analýzy, zejména s diferenciálním počtem v normovaných prostorech a aplikacemi.
Syllabus (in Czech)
  • 1. Diferenciální počet v normovaných prostorech 1.1. Silný diferenciál (Freschetův diferenciál) 1.2. Slabý diferenciál (Gateauxův diferenciál) 1.3. Integrál 1.4. Newton-Leibnitzův vzorec 1.5. Derivace vyšších řádů 1.6. Taylorův vzorec 2. Aplikace v extrémálních úlohach 3. Věta o implicitní funkci 3.1. Věta o implicitní funkci 3.2. Věta o lokální inverzi
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2006, Spring 2007, Spring 2008, Spring 2010.

M8180 Nonlinear Functional Analysis

Faculty of Science
Spring 2004
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. Alexander Lomtatidze, DrSc.
Timetable
Mon 15:00–16:50 UK
  • Timetable of Seminar Groups:
M8180/01: Mon 17:00–17:50 UK
Prerequisites (in Czech)
M6150 Linear Functional Analysis 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 (in Czech)
Cílem předmětu je seznámit posluchače se základy nelineární funkcionální analýzy, zejména s diferenciálním počtem v normovaných prostorech a aplikacemi.
Syllabus (in Czech)
  • 1. Diferenciální počet v normovaných prostorech 1.1. Silný diferenciál (Freschetův diferenciál) 1.2. Slabý diferenciál (Gateauxův diferenciál) 1.3. Integrál 1.4. Newton-Leibnitzův vzorec 1.5. Derivace vyšších řádů 1.6. Taylorův vzorec 2. Aplikace v extrémálních úlohach 3. Věta o implicitní funkci 3.1. Věta o implicitní funkci 3.2. Věta o lokální inverzi
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010.

M8180 Nonlinear Functional Analysis

Faculty of Science
Spring 2003
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. Alexander Lomtatidze, DrSc.
Timetable of Seminar Groups
M8180/01: No timetable has been entered into IS. A. Lomtatidze
Prerequisites (in Czech)
M6150 Linear Functional Analysis 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 (in Czech)
Cílem předmětu je seznámit posluchače se základy nelineární funkcionální analýzy, zejména s diferenciálním počtem v normovaných prostorech a aplikacemi.
Syllabus (in Czech)
  • 1. Diferenciální počet v normovaných prostorech 1.1. Silný diferenciál (Freschetův diferenciál) 1.2. Slabý diferenciál (Gateauxův diferenciál) 1.3. Integrál 1.4. Newton-Leibnitzův vzorec 1.5. Derivace vyšších řádů 1.6. Taylorův vzorec 2. Aplikace v extrémálních úlohach 3. Věta o implicitní funkci 3.1. Věta o implicitní funkci 3.2. Věta o lokální inverzi
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010.

M8180 Nonlinear Functional Analysis

Faculty of Science
Spring 2002
Extent and Intensity
2/1/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. Alexander Lomtatidze, DrSc.
Prerequisites (in Czech)
M6150 Linear Functional Analysis 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 (in Czech)
1.Základy diferenciálního počtu v normovaných prostorech - Základní pojmy - Základní věty - Taylorova formule 2.Věta o implicitní funkci a věta o lokální inversi - Věta o implicitní funkci - Věta o lokální inversi - Tečný prostor, Ljusternikova věta 3.Diferencování speciálních operátorů - Operátory Němyckého - Integrální operátory - Aplikace v extrémálních úlohách (variační počet)
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 Spring 2008 - for the purpose of the accreditation, Spring 2000, Spring 2001, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010.

M8180 Nonlinear Functional Analysis

Faculty of Science
Spring 2001
Extent and Intensity
2/1/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. Alexander Lomtatidze, DrSc.
Prerequisites (in Czech)
M6150 Linear Functional Analysis 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 (in Czech)
1.Základy diferenciálního počtu v normovaných prostorech - Základní pojmy - Základní věty - Taylorova formule 2.Věta o implicitní funkci a věta o lokální inversi - Věta o implicitní funkci - Věta o lokální inversi - Tečný prostor, Ljusternikova věta 3.Diferencování speciálních operátorů - Operátory Němyckého - Integrální operátory - Aplikace v extrémálních úlohách (variační počet)
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 Spring 2008 - for the purpose of the accreditation, Spring 2000, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010.

M8180 Nonlinear Functional Analysis

Faculty of Science
Spring 2000
Extent and Intensity
2/1/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Erich Barvínek, CSc. (lecturer)
Guaranteed by
doc. RNDr. Erich Barvínek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Erich Barvínek, CSc.
Prerequisites (in Czech)
M6150 Linear Functional Analysis 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 (in Czech)
  • 1.Základy diferenciálního počtu v normovaných prostorech - Základní pojmy - Základní věty - Taylorova formule 2.Věta o implicitní funkci a věta o lokální inversi - Věta o implicitní funkci - Věta o lokální inversi - Tečný prostor, Ljusternikova věta 3.Diferencování speciálních operátorů - Operátory Němyckého - Integrální operátory - Aplikace v extrémálních úlohách (variační počet)
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 Spring 2008 - for the purpose of the accreditation, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010.

M8180 Nonlinear Functional Analysis

Faculty of Science
Spring 2019

The course is not taught in Spring 2019

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. Alexander Lomtatidze, 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
M6150 Functional Analysis I
Differential and integral calculus, Linear functional analysis I and II, Linear algebra.
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
Nonlinear functional analysis belongs to advanced parts of university courses in mathematics. It is utilized in many applications. The aim of the course is to introduce the bases of nonlinear functional analysis, namely differential and integral calculus in normed spaces and their applications. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • 1. Differential calculus in normed spaces. Freschet and Gateaux differentials. Integral calculus in normed spaces. Newton-Leibnitz formula. Higher order derivatives. Taylor formula. 2. Application of differential calculus. 3. Degree theory.
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • ZEIDLER, Eberhard. Nonlinear functional analysis and its applications. Translated by Leo F. Boron. New York: Springer-Verlag, 1990, xv, 469-12. ISBN 354097167X. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
  • KRASNOSEL‘SKIJ, Mark Aleksandrovič. Topologičeskijje metody v teorii nelinejnych integral'nych uravnenij. Moskva: Techniko teoretičeskoj literatury, 1956, 392 s. info
Teaching methods
lectures and class exercises
Assessment methods
Teaching: lecture 2 hours a week, seminar 1 hours a week. Examination: written and oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010.

M8180 Nonlinear Functional Analysis

Faculty of Science
spring 2018

The course is not taught in spring 2018

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. Alexander Lomtatidze, 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
M6150 Functional Analysis I
Differential and integral calculus, Linear functional analysis I and II, Linear algebra.
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
Nonlinear functional analysis belongs to advanced parts of university courses in mathematics. It is utilized in many applications. The aim of the course is to introduce the bases of nonlinear functional analysis, namely differential and integral calculus in normed spaces and their applications. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • 1. Differential calculus in normed spaces. Freschet and Gateaux differentials. Integral calculus in normed spaces. Newton-Leibnitz formula. Higher order derivatives. Taylor formula. 2. Application of differential calculus. 3. Degree theory.
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • ZEIDLER, Eberhard. Nonlinear functional analysis and its applications. Translated by Leo F. Boron. New York: Springer-Verlag, 1990, xv, 469-12. ISBN 354097167X. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
  • KRASNOSEL‘SKIJ, Mark Aleksandrovič. Topologičeskijje metody v teorii nelinejnych integral'nych uravnenij. Moskva: Techniko teoretičeskoj literatury, 1956, 392 s. info
Teaching methods
lectures and class exercises
Assessment methods
Teaching: lecture 2 hours a week, seminar 1 hours a week. Examination: written and oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010.

M8180 Nonlinear Functional Analysis

Faculty of Science
Spring 2017

The course is not taught in Spring 2017

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. Alexander Lomtatidze, 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
M6150 Functional Analysis I
Differential and integral calculus, Linear functional analysis I and II, Linear algebra.
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
Nonlinear functional analysis belongs to advanced parts of university courses in mathematics. It is utilized in many applications. The aim of the course is to introduce the bases of nonlinear functional analysis, namely differential and integral calculus in normed spaces and their applications. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • 1. Differential calculus in normed spaces. Freschet and Gateaux differentials. Integral calculus in normed spaces. Newton-Leibnitz formula. Higher order derivatives. Taylor formula. 2. Application of differential calculus. 3. Degree theory.
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • ZEIDLER, Eberhard. Nonlinear functional analysis and its applications. Translated by Leo F. Boron. New York: Springer-Verlag, 1990, xv, 469-12. ISBN 354097167X. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
  • KRASNOSEL‘SKIJ, Mark Aleksandrovič. Topologičeskijje metody v teorii nelinejnych integral'nych uravnenij. Moskva: Techniko teoretičeskoj literatury, 1956, 392 s. info
Teaching methods
lectures and class exercises
Assessment methods
Teaching: lecture 2 hours a week, seminar 1 hours a week. Examination: written and oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010.

M8180 Nonlinear Functional Analysis

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. Alexander Lomtatidze, 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
M6150 Functional Analysis I
Differential and integral calculus, Linear functional analysis I and II, Linear algebra.
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
Nonlinear functional analysis belongs to advanced parts of university courses in mathematics. It is utilized in many applications. The aim of the course is to introduce the bases of nonlinear functional analysis, namely differential and integral calculus in normed spaces and their applications. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • 1. Differential calculus in normed spaces. Freschet and Gateaux differentials. Integral calculus in normed spaces. Newton-Leibnitz formula. Higher order derivatives. Taylor formula. 2. Application of differential calculus. 3. Degree theory.
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • ZEIDLER, Eberhard. Nonlinear functional analysis and its applications. Translated by Leo F. Boron. New York: Springer-Verlag, 1990, xv, 469-12. ISBN 354097167X. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
  • KRASNOSEL‘SKIJ, Mark Aleksandrovič. Topologičeskijje metody v teorii nelinejnych integral'nych uravnenij. Moskva: Techniko teoretičeskoj literatury, 1956, 392 s. info
Teaching methods
lectures and class exercises
Assessment methods
Teaching: lecture 2 hours a week, seminar 1 hours a week. Examination: written and oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010.

M8180 Nonlinear Functional Analysis

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. Alexander Lomtatidze, 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
M6150 Functional Analysis I
Differential and integral calculus, Linear functional analysis I and II, Linear algebra.
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
Nonlinear functional analysis belongs to advanced parts of university courses in mathematics. It is utilized in many applications. The aim of the course is to introduce the bases of nonlinear functional analysis, namely differential and integral calculus in normed spaces and their applications. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • 1. Differential calculus in normed spaces. Freschet and Gateaux differentials. Integral calculus in normed spaces. Newton-Leibnitz formula. Higher order derivatives. Taylor formula. 2. Application of differential calculus. 3. Degree theory.
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • ZEIDLER, Eberhard. Nonlinear functional analysis and its applications. Translated by Leo F. Boron. New York: Springer-Verlag, 1990, xv, 469-12. ISBN 354097167X. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
  • KRASNOSEL‘SKIJ, Mark Aleksandrovič. Topologičeskijje metody v teorii nelinejnych integral'nych uravnenij. Moskva: Techniko teoretičeskoj literatury, 1956, 392 s. info
Teaching methods
lectures and class exercises
Assessment methods
Teaching: lecture 2 hours a week, seminar 1 hours a week. Examination: written and oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010.

M8180 Nonlinear Functional Analysis

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. Alexander Lomtatidze, 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
M6150 Functional Analysis I
Differential and integral calculus, Linear functional analysis I and II, Linear algebra.
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
Nonlinear functional analysis belongs to advanced parts of university courses in mathematics. It is utilized in many applications. The aim of the course is to introduce the bases of nonlinear functional analysis, namely differential and integral calculus in normed spaces and their applications. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • 1. Differential calculus in normed spaces. Freschet and Gateaux differentials. Integral calculus in normed spaces. Newton-Leibnitz formula. Higher order derivatives. Taylor formula. 2. Application of differential calculus. 3. Degree theory.
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • ZEIDLER, Eberhard. Nonlinear functional analysis and its applications. Translated by Leo F. Boron. New York: Springer-Verlag, 1990, xv, 469-12. ISBN 354097167X. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
  • KRASNOSEL‘SKIJ, Mark Aleksandrovič. Topologičeskijje metody v teorii nelinejnych integral'nych uravnenij. Moskva: Techniko teoretičeskoj literatury, 1956, 392 s. info
Teaching methods
lectures and class exercises
Assessment methods
Teaching: lecture 2 hours a week, seminar 1 hours a week. Examination: written and oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010.

M8180 Nonlinear Functional Analysis

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)
prof. Alexander Lomtatidze, DrSc. (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
M6150 Functional Analysis I
Differential and integral calculus, Linear functional analysis I and II, Linear algebra.
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
Nonlinear functional analysis belongs to advanced parts of university courses in mathematics. It is utilized in many applications. The aim of the course is to introduce the bases of nonlinear functional analysis, namely differential and integral calculus in normed spaces and their applications. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • 1. Differential calculus in normed spaces. Freschet and Gateaux differentials. Integral calculus in normed spaces. Newton-Leibnitz formula. Higher order derivatives. Taylor formula. 2. Application of differential calculus. 3. Degree theory.
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • ZEIDLER, Eberhard. Nonlinear functional analysis and its applications. Translated by Leo F. Boron. New York: Springer-Verlag, 1990, xv, 469-12. ISBN 354097167X. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
  • KRASNOSEL‘SKIJ, Mark Aleksandrovič. Topologičeskijje metody v teorii nelinejnych integral'nych uravnenij. Moskva: Techniko teoretičeskoj literatury, 1956, 392 s. info
Teaching methods
lectures and class exercises
Assessment methods
Teaching: lecture 2 hours a week, seminar 1 hours a week. Examination: written and oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010.

M8180 Nonlinear Functional Analysis

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)
prof. Alexander Lomtatidze, DrSc. (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
M6150 Functional Analysis I
Differential and integral calculus, Linear functional analysis I and II, Linear algebra.
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
Nonlinear functional analysis belongs to advanced parts of university courses in mathematics. It is utilized in many applications. The aim of the course is to introduce the bases of nonlinear functional analysis, namely differential and integral calculus in normed spaces and their applications. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • 1. Differential calculus in normed spaces. Freschet and Gateaux differentials. Integral calculus in normed spaces. Newton-Leibnitz formula. Higher order derivatives. Taylor formula. 2. Application of differential calculus. 3. Degree theory.
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • ZEIDLER, Eberhard. Nonlinear functional analysis and its applications. Translated by Leo F. Boron. New York: Springer-Verlag, 1990, xv, 469-12. ISBN 354097167X. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
  • KRASNOSEL‘SKIJ, Mark Aleksandrovič. Topologičeskijje metody v teorii nelinejnych integral'nych uravnenij. Moskva: Techniko teoretičeskoj literatury, 1956, 392 s. info
Teaching methods
lectures and class exercises
Assessment methods
Teaching: lecture 2 hours a week, seminar 1 hours a week. Examination: written and oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010.

M8180 Nonlinear Functional Analysis

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)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M6150 Functional Analysis I
Differential and integral calculus, Linear functional analysis I and II, Linear algebra.
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
Nonlinear functional analysis belongs to advanced parts of university courses in mathematics. It is utilized in many applications. The aim of the course is to introduce the bases of nonlinear functional analysis, namely differential and integral calculus in normed spaces and their applications. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • 1. Differential calculus in normed spaces. Freschet and Gateaux differentials. Integral calculus in normed spaces. Newton-Leibnitz formula. Higher order derivatives. Taylor formula. 2. Application of differential calculus. 3. Degree theory.
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • ZEIDLER, Eberhard. Nonlinear functional analysis and its applications. Translated by Leo F. Boron. New York: Springer-Verlag, 1990, xv, 469-12. ISBN 354097167X. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
  • KRASNOSEL‘SKIJ, Mark Aleksandrovič. Topologičeskijje metody v teorii nelinejnych integral'nych uravnenij. Moskva: Techniko teoretičeskoj literatury, 1956, 392 s. info
Teaching methods
lectures and class exercises
Assessment methods
Teaching: lecture 2 hours a week, seminar 1 hours a week. Examination: written and oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010.

M8180 Nonlinear Functional Analysis

Faculty of Science
Spring 2009

The course is not taught in Spring 2009

Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M6150 Linear Functional Analysis I
Differential and integral calculus, Linear functional analysis I and II, Linear algebra.
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
Nonlinear functional analysis belongs to advanced parts of university courses in mathematics. It is utilized in many applications. The aim of the course is to introduce the bases of nonlinear functional analysis, namely differential and integral calculus in normed spaces and their applications. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • 1. Differential calculus in normed spaces. Freschet and Gateaux differentials. Integral calculus in normed spaces. Newton-Leibnitz formula. Higher order derivatives. Taylor formula. 2. Application of differential calculus. 3. Degree theory.
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • ZEIDLER, Eberhard. Nonlinear functional analysis and its applications. Translated by Leo F. Boron. New York: Springer-Verlag, 1990, xv, 469-12. ISBN 354097167X. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
  • KRASNOSEL‘SKIJ, Mark Aleksandrovič. Topologičeskijje metody v teorii nelinejnych integral'nych uravnenij. Moskva: Techniko teoretičeskoj literatury, 1956, 392 s. info
Teaching methods
lectures and class exercises
Assessment methods
Teaching: lecture 2 hours a week, seminar 1 hours a week. Examination: written and oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010.

M8180 Nonlinear Functional Analysis

Faculty of Science
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)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. Alexander Lomtatidze, DrSc.
Prerequisites (in Czech)
M6150 Linear Functional Analysis 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 (in Czech)
Cílem předmětu je seznámit posluchače se základy nelineární funkcionální analýzy, zejména s diferenciálním počtem v normovaných prostorech a aplikacemi.
Syllabus (in Czech)
  • 1. Diferenciální počet v normovaných prostorech 1.1. Silný diferenciál (Freschetův diferenciál) 1.2. Slabý diferenciál (Gateauxův diferenciál) 1.3. Integrál 1.4. Newton-Leibnitzův vzorec 1.5. Derivace vyšších řádů 1.6. Taylorův vzorec 2. Aplikace v extrémálních úlohach 3. Věta o implicitní funkci 3.1. Věta o implicitní funkci 3.2. Věta o lokální inverzi
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 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 Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010.

M8180 Nonlinear Functional Analysis

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)
prof. Alexander Lomtatidze, DrSc. (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
M6150 Functional Analysis I
Differential and integral calculus, Linear functional analysis I and II, Linear algebra.
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
Nonlinear functional analysis belongs to advanced parts of university courses in mathematics. It is utilized in many applications. The aim of the course is to introduce the bases of nonlinear functional analysis, namely differential and integral calculus in normed spaces and their applications. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • 1. Differential calculus in normed spaces. Freschet and Gateaux differentials. Integral calculus in normed spaces. Newton-Leibnitz formula. Higher order derivatives. Taylor formula. 2. Application of differential calculus. 3. Degree theory.
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • ZEIDLER, Eberhard. Nonlinear functional analysis and its applications. Translated by Leo F. Boron. New York: Springer-Verlag, 1990, xv, 469-12. ISBN 354097167X. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
  • KRASNOSEL‘SKIJ, Mark Aleksandrovič. Topologičeskijje metody v teorii nelinejnych integral'nych uravnenij. Moskva: Techniko teoretičeskoj literatury, 1956, 392 s. info
Teaching methods
lectures and class exercises
Assessment methods
Teaching: lecture 2 hours a week, seminar 1 hours a week. Examination: written and oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010.

M8180 Nonlinear Functional Analysis

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)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites (in Czech)
M6150 Functional Analysis 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)
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 Spring 2008 - for the purpose of the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010.
  • Enrolment Statistics (recent)