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Functional Analysis
OVERVIEW
CEA CAPA Partner Institution: University of Galway
Location: Galway, Ireland
Primary Subject Area: Mathematics
Instruction in: English
Course Code: MA482
Transcript Source: Partner Institution
Course Details: Level 400
Recommended Semester Credits: 2.5
Contact Hours: 36
DESCRIPTION
This course introduces the theory of Linear Functional Analysis. Topics include Banach Spaces, Bounded Linear Operators, Dual Spaces, Hilbert Spaces, Orthogonal Complements and Direct Sums, Representation of Functionals on Hilbert Spaces and the Hilbert-Adjoint Operator.
Learning Outcomes
1. Understand the fundamentals in Normed Spaces, Linear Operators and Dual Spaces.
2. Understand the fundamentals of Inner Product Spaces, Direct Sums and Hilbert-Adjoint Operators.
3. Solve problems associated with Banach Spaces, Continuous Linear Operators, Normed Spaces of Operators and Dual Spaces.
4. Solve problems associated with Inner Product Spaces, Orthogonal Complements, Orthonormal Sets and Sequences, Functionals on Hilbert Spaces and the Hilbert-Adjoint Operator.
Learning Outcomes
1. Understand the fundamentals in Normed Spaces, Linear Operators and Dual Spaces.
2. Understand the fundamentals of Inner Product Spaces, Direct Sums and Hilbert-Adjoint Operators.
3. Solve problems associated with Banach Spaces, Continuous Linear Operators, Normed Spaces of Operators and Dual Spaces.
4. Solve problems associated with Inner Product Spaces, Orthogonal Complements, Orthonormal Sets and Sequences, Functionals on Hilbert Spaces and the Hilbert-Adjoint Operator.
