Course: Nonlinear Functional Analysis

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Course title Nonlinear Functional Analysis
Course code KMA/NLFA
Organizational form of instruction Lecture + Exercise
Level of course Master
Year of study not specified
Semester Summer
Number of ECTS credits 4
Language of instruction Czech
Status of course Compulsory, Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Pastor Karel, doc. Mgr. Ph.D.
  • Dvorská Marie, Mgr.
Course content
1.The Banach algebra 2.Spectrum in the Banach algebra 3.The Fréchet, the Gâteaux derivative, strict differentiability. 4.Derivative of a composition of two functions. Mean value theorem. 5.Inverse fuction theorem. Implicit fuction theorem. 6.Convex and the Clarke subdifferential. 7.The class of functions with locally Lipschitz gradient. 8.Monotone operators. 9.Differentiability of convex functions, Asplund spaces. 10.Applications of subdifferential calculus.

Learning activities and teaching methods
Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
  • Attendace - 39 hours per semester
  • Homework for Teaching - 30 hours per semester
  • Preparation for the Exam - 50 hours per semester
Learning outcomes
Understand differential calculus of nonsmooth functions.
Comprehension differential calculus of nonsmooth functions.
Prerequisites
Knowledge of basic notions of functional analysis.
KMA/FA2N

Assessment methods and criteria
Oral exam, Dialog

Credit: active participation, homework solving. Exam: the student has to understand the subject and be able to prove the principal results.
Recommended literature
  • F.H. Clarke. (1983). Optimization and nonsmooth analysis. J.Wiley New York.
  • J. Lukeš. (2001). Zápisky z funkcionální analýzy. MatFyzPress.
  • V. M. Aleksejev, V. M. Tichomirov, S. V. Fomin. (1991). Matematická teorie optimálních procesů. Academia, Praha.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Applied Mathematics (2014) Mathematics courses 1 Summer