Non-analytic Smooth Functions

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Related lectures (32)

Page 3 of 4

Holomorphic Functions: Taylor Series Expansion

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Taylor expansions: second order

Explores Taylor expansions and retractions on Riemannian manifolds, emphasizing second-order approximations and covariant derivatives.

Riemannian connections: What they are and why we care

Covers Riemannian connections, emphasizing their properties and significance in geometry.

Differentiating Vector Fields: Definition

Introduces differentiating vector fields along curves on manifolds with connections and the unique operator satisfying specific properties.

Differentiating vector fields: Why do it?

Explores the importance of differentiating vector fields and the correct methodology to achieve it, emphasizing the significance of going beyond the first order.

Tangent to Graph of a Function

Explores finding the equation of the tangent line to a function's graph at a point.

Optimality conditions: second order

Explores necessary and sufficient optimality conditions for local minima on manifolds, focusing on second-order critical points.

Manifolds: Charts and Compatibility

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.

Manopt: Optimization Toolbox for Manifolds

Introduces Manopt, a toolbox for optimization on manifolds, focusing on solving optimization problems on smooth manifolds using the Matlab version.

Retractions: second order

Covers second-order retractions in optimization on manifolds, focusing on smooth curves and their relation to the gradient and Hessian of a function.