Analysis

Differentiation
  1. The Frechet derivative
Measure and probability
Functional analysis
  1. Why does uniform convergence really matter? The properties of functions
  2. Differential equations
  3. 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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