- Classify given integral equations by type and properties.
- Transform differential equations into integral equations (and vice versa).
- Determine the adjoint of an integral operator.
- Apply solvability criteria (e.g., Fredholm theory).
- Analyze mapping properties (e.g., compactness, boundedness).
- Develop and implement numerical solution methods (e.g., collocation, Galerkin methods).
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- Definitions and types of integral equations (Fredholm/Volterra, first/second kind).
- Functional analytic foundations (e.g., Banach and Hilbert spaces, compactness of operators).
- Theoretical results on solvability (e.g., Fredholm alternative, existence and uniqueness conditions).
- Relationships between differential and integral equations (e.g., Green’s functions).
- Basics of linear operators and their adjoints.
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