Functional Analysis

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Course Code: 
MTH3101
Course Credit Units: 
3
Semester: 
Semester 1
Year of Study: 
Year 3
Undergraduate or Graduate Level: 
Undergraduate Level
Department: 
Course Discipline: 
Course Description & Objectives: 

Functional analysis is the branch of mathematics concerned with the study of spaces of functions. This course is intended to introduce the student to the basic concepts and theorems of functional analysis and its applications.

Learning Outcomes: 

By the end of this course, students should be able to: 

  • describe properties of normed linear spaces and construct examples of such spaces
  • extend basic notions from calculus to metric spaces and normed vector spaces
  • state and prove theorems about finite dimensionality in normed vector spaces
  • state and prove the Cauchy-Swartz Inequality and apply it to the derivation of other inequalities
  • distinguish pointwise and uniform convergence
  • prove that a given space is a Hilbert spaces or a  Banach Spaces
  • describe the dual of a normed linear space
  • apply orthonormality to Fourier series expansions of functions
  • state and prove the Hahn-Banach theorem

 

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