| TATM85 |
Functional Analysis, 6 ECTS credits.
/Funktionalanalys/
For:
MMAT
Y
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Prel. scheduled
hours: 60
Rec. self-study hours: 100
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Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
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Advancement level
(G1, G2, A): A
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Aim:
To give familiarity with the fundamental concepts of functional analysis and to prepare the student for further studies in mathematics and related areas. After completing this course the student is able to:
- Describe the concepts of a metric space, vector space, subspace, normed space, Banach space, Hilbert space and dual space.
- Describe the logical connections between important concepts in the spaces mentioned above.
- Describe and apply central theorems in the theory of metric spaces, normed spaces, Banach spaces and Hilbert spaces.
- Apply Banach's fix point theorem in the theory of differential and integral equations.
- Describe the spectral theory for compact self adjoint operators
- Describe the Lebesgue integral and apply central theorems in the theory of the Lebesgue integral in order to solve problems.
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Linear Algebra,Calculus in one variable, Calculus in several variables, Real Analysis Honours Course, is a good preparation, but is not a prerequisite.
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
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Supplementary courses:
Partial differential equations, Fourier and Wavelet Analysis
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Organisation:
Lectures
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Course contents:
Elementary metric space theory. Normed spaces, Banach spaces, Hilbert spaces. Linear functionals, dual spaces. Linear operators. Aspects of the Lebesgue integral. Integral equations. Introduction to spectral theory for compact, symmetric operators.
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Course literature:
Kreysig, E: Introductory Functional Analysis with Applications. John Wiley & Sons, Inc. 1978.
Hand out material about integration theory.
Collection of problems published by the Department of Mathematics.
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Examination: |
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Assignements
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6 ECTS
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Course language is Swedish.
Department offering the course: MAI.
Director of Studies: Jesper Thorén
Examiner: Bengt Ove Turesson
Link to the course homepage at the department
Course Syllabus in Swedish
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