Lectures related to Objective function, Differentiability, The second order

Explores properties of functions with continuous partial derivatives in open subsets of Rn.

Covers methods of demonstrations and differential calculus of functions of several variables.

Introduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.

Covers functions with values in R^m, discussing limits, partial derivatives, and differentiability.

Covers linear and membrane theories of pressure vessels, differential geometry of surfaces, and the reduction of dimensionality from 3D to 2D.