Program Overview

Program Details

The Funktionalanalys course is a 7.5-credit advanced-level course, designated as M7010M. It is scheduled for VÕr 2027 and VÕr 2026.

Course Description

The course primarily focuses on vector spaces of infinite dimension, leading to various convergence problems where linear algebra meets analysis. It provides a solid theoretical foundation for formulating and analyzing linear problems. Key topics include:

• Metric, normed, and scalar product spaces, defined, described, and exemplified.
• Properties such as completeness and compactness are discussed in detail.
• Differences between weak and strong topology are analyzed.
• Fundamental theorems and their proofs, such as Hahn-Banach's theorem, the open mapping theorem, and Banach-Steinhaus's theorem, are emphasized.
• Applications, including Picard's theorem for the existence and uniqueness of ODE and examples of continuous functions for which the Fourier series does not converge, are explored.

Course Structure

• Period: Period 3 - 4, v. 3 2027 - v.
• Study Location: Ortsoberoende (Location-independent)
• Study Form: Dagtid 25% (Part-time, 25%)
• Language: Svenska (Swedish)
• Mandatory Meetings on Campus: 0
• Implementation: The course is conducted through self-study and examination assignments.

Admission Requirements

• Prerequisites: M0047M Differentialkalkyl 7.5 hp, M0048M Linjõr algebra och integralkalkyl 7.5 hp, M0049M Linjõr algebra och differentialekvationer 7.5 hp, M0055M Flervariabelanalys 7.5 hp, or equivalent. Proficiency in Swedish and English equivalent to basic eligibility for university studies, M7026M Analysens grunder 7.5 hp, or equivalent, is recommended but not required.
• Selection: The selection is based on 30-285 higher education credits.

Additional Information

• The course can be applied for as an elective by program students at LTU.
• It is also offered as a freestanding course.