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Lecturer(s)
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Staněk Svatoslav, prof. RNDr. CSc.
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Tomeček Jan, doc. RNDr. Ph.D.
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Course content
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Functional spaces. Basic principles of linear functional analysis. Operators (continuous, linear, compact, completely continuous, adjoint, closed). General forms of linear continuous functionls. Fredholm theorems. Spectral theory for linear operators. Fixed point theorems (Schauder and its corollaries, theorems based on degree of mapping, theorems in ordered spaces). Derivative of operators.
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Learning activities and teaching methods
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Dialogic Lecture (Discussion, Dialog, Brainstorming), Work with Text (with Book, Textbook)
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Learning outcomes
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Master methods and tools of linear functional analysis and tools of nonlinear functional analysis.
Comprehension Understand the theory of linear and nonlinear operators in functional spaces.
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Prerequisites
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Master's degree in mathematics.
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Assessment methods and criteria
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Oral exam
Exam: to know and to understand the subject.
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Recommended literature
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A. E. Taylor. (1977). Funkcionální analýza. Academia Praha.
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Conway, J. B. (1990). A course in functional analysis. Springer.
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J. Lukeš. (2001). Zápisky z funkcionální analýzy. MatFyzPress.
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K. Deimling. (1985). Nonlinear functional analysis. Springer.
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K. Najzar. (1988). Funkcionální analýza. SPN, Praha.
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M. Fabian a kol. (2001). Functional Analysis and Infinite-Dimensional Geometry. Springer, Berlin.
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S. Fučík, A. Kufner. (1978). Nelineární diferenciální rovnice. SNTL Praha.
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