**Differentiation**
- The Frechet derivative

**Measure and probability**

**Functional analysis**
- Why does uniform convergence
*really* matter? The properties of functions
- Differential equations
- Picard iteration

Calculus of variations -- in your study of calculus, you may have often wondered about problems like: given a curve in R^3, how do you find the surface with it as a boundary that minimises its area? Or, what function between two defined points minimises the surface area of its surface of revolution

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