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ByDr. Talat Nazir

Functional Analysis

MTH 327

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Vector Spaces Normed Spaces

Lecture # 1

MTH 327

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Lecture’s outline

• Vector Spaces

• Some Examples of Vector Spaces

• Normed Spaces

• Some Examples of Normed Spaces

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Functional Analysis

Functional analysis is an abstract branch of mathematics that originated from classical analysis. The impetus came from applications: problems related to ordinary and partial di erential equations, numerical analysis, calculus of ffvariations, approximation theory, integral equations, and so on. In ordinary calculus, one dealt with limiting processes in finite-dimensional vector spaces (R or Rn), but problems arising in the above applications required a calculus in spaces of functions (which are infinite-dimensional vector spaces).

Vector Space

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Examples:

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More Examples:

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Normed Spaces

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More Examples of Normed Spaces:

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Some Problems:

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