Course overview
The advances in mathematics and theoretical physics from the start of the twentieth century brought about a need for a more general abstract framework for the study of differential operators, and the functional spaces where these operator act. While Lebesgues theory of integration gave us a precise description of the functions to be studied, it was the development of Hilbert spaces and Banach spaces that gave us the correct setting for the study of operators. In this course we will study Hilbert and Banach spaces, the various notions of convergence on those spaces, and the behaviour of bounded and unbounded operators defined therein. Connections to differential equations will be shown in examples.
- Normed Linear Spaces
Course learning outcomes
- Distinguish between different notions of convergence in normed linear spaces;
- Work with bases on a Hilbert space;
- Apply the three main theorems (Hahn-Banach, Uniform boundedness, Closed Graph) to a variety of situations
- Write proofs at an appropriate level
- Communicate results clearly
Availability
Class details
Adelaide City Campus East
Class number 52328
Section FR01
Size 25
Available 25
Class number 52329
Section WS01
Size 25
Available 25
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