The first part (van Gaans) of Linear Analysis consists of functional analysis, a discipline which is concerned with ubiquitous fundamental abstract structures in analysis. Understanding the language of functional analysis is, in fact, indispensable for various parts of both analysis and stochastics. Covered in the first part are the basic theory of Hilbert and Banach spaces and their operators, thus providing the functional analytic vocabulary which is also necessary for other disciplines. It also contains the prerequisites (!) for the national master course Functional Analysis, intended for students who want to continue in this direction in the following year.
The second part (de Jeu) is an introduction to partial differential equations, which are the basic ingredient in many models, and knowledge of which is important in a variety of applications. The national master course Partial Differential Equations has no formal prerequisites, but it has nevertheless proven to be rather tough without a previous introduction.
It is strongly recommended that students with an interest in analysis follow Linear Analysis in their third year. For other students this course may also be a valuable addition in later years
Prerequisite
Rather limited. For the functional analysis part, basic knowledge of linear algebra (hardly beyond the notion of abstract vector spaces and linear maps) and elementary topology (metric spaces) are required. For the PDE part, basic calculus at the level of Analysis 1 and 2 is sufficient.
Literature
Compulsory: “Linear Functional Analysis” by Rynne and Youngson, 1st ed., Springer, 2000, ISBN: 978-1-85233-257-0. A second edition is in the making which may or may not be available in September. Both editions are suitable. For the PDE-part of the course a handout will be available
Methods of instruction
2 lecture hours per week
Examination
Handing in assignments.
Blackboard
Enrollment is compulsory.
Remarks
It is strongly recommended that students with an interest in analysis or stochastics follow Linear Analysis in their third year, as well as Measure Theory. For other students these courses may also be a valuable addition in later years.
Possible sequels: Graduation in analysis or stochastics, national courses on functional analysis, PDE or stochastics.