Single-Course English 5 ECTS

Advanced Topics in Applied Functional Analysis

Overall Course Objectives

The primary goal is to utilize and apply fundamental notions, abstractions, and principles of functional analysis towards solving concrete mathematical problems arising in engineering and natural sciences. In addition we aim at strengthening students’ analytical, logical reasoning, and problem solving abilities.

Learning Objectives

  • Identify functional analytic abstractions in statements of concrete model problems
  • Interpret model problems in functional analytic terms and formally verify prerequisites for such interpretations
  • Utilize and apply fundamental functional analytic principles towards analyzing and solving model problems
  • Interpret certain computational algorithms in functional analytic terms
  • Follow and apply logical strategies of formal mathematical arguments
  • Establish the validity mathematical statements about models by constructing and providing formal arguments
  • Know and master the relevant mathematical language and be able to communicate abstract and precise mathematical statements and reasoning orally and in writing.
  • Know and master advanced topics in functional analysis such as the spectral theorem for compact operators, compact embeddings and the Lax-Milgram Theorem.

Course Content

The course concerns functional analytic methods for integral and/or partial differential equations. Some specific keywords include: compact sets and operators, Sobolev spaces, elliptic boundary value problems, fixed point theorems, Galerkin method and FEM, and optimization in Hilbert and Banach spaces.

Recommended prerequisites

01715/01418, Basic knowledge of partial differential equations and functional analysis

Teaching Method

Lectures, practical exercises, and oral presentations by the students


Limited number of seats

Minimum: 10.

Please be aware that this course will only be held if the required minimum number of participants is met. You will be informed 8 days before the start of the course, whether the course will be held.

See course in the course database.





13 weeks




DTU Lyngby Campus

Course code 01716
Course type Candidate
Semester start Week 5
Semester end Week 19
Days Tues 8-12

7.500,00 DKK

Please note that this course has participants limitation. Read more