##### Department of Mathematics,

University of California San Diego

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### Food for Thought

## Evangelos ``Vaki'' Nikitopoulos

#### UCSD

## Infinite-Dimensional Calculus I: The Derivative

##### Abstract:

Calculus in normed vector spaces is the basis for several areas of mathematics and physics, but it is not a topic that is often covered with very much care or detail. This talk's focus is the theory of differentiation in normed vector spaces, more specifically the Gateaux and Fr\'{e}chet derivatives. Towards the end, we shall cover an infinite-dimensional Taylor's Theorem, and we shall likely get to discuss some applications. Plus, there will be plenty of examples throughout! This talk is Part I of a (likely) three- or four-part series, with future topics including integration and complex analysis.

### October 11, 2019

### 12:00 PM

### AP&M 5402

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