Lecture
Differentiating vector fields: Why do it?
Related lectures (53)
From embedded to general manifolds: Why?MOOC: Introduction to optimization on smooth manifolds: first order methods
Explores upgrading foundations from embedded to general manifolds in optimization, discussing smooth sets and tangent vectors.
Choosing a Step SizeMOOC: Introduction to optimization on smooth manifolds: first order methods
Explores choosing a step size in optimization on manifolds, including backtracking line-search and the Armijo method.
Computing the Newton Step: From GD to CGMOOC: Introduction to optimization on smooth manifolds: first order methods
Covers the transition from Gradient Descent to Conjugate Gradients, highlighting the efficiency of CG over GD in optimization on manifolds.
Differentiating Vector Fields: How Not to Do ItMOOC: Introduction to optimization on smooth manifolds: first order methods
Discusses the challenges in differentiating vector fields on submanifolds and the importance of choosing the right method.
Curve Integrals of Vector Fields
Explores curve integrals of vector fields, emphasizing energy considerations for motion against or with wind, and introduces unit tangent and unit normal vectors.
Gradient DescentMOOC: Introduction to optimization on smooth manifolds: first order methods
Explores gradient descent methods for optimizing functions on manifolds, emphasizing small gradient guarantees and global convergence.
Comparing Tangent Vectors: Parallel TransportMOOC: Introduction to optimization on smooth manifolds: first order methods
Explores comparing tangent vectors and parallel transport on manifolds.
Riemannian connections
Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.
Tangent vectors without embedding space: Equivalence classesMOOC: Introduction to optimization on smooth manifolds: first order methods
Delves into tangent vectors as equivalence classes on manifolds, highlighting their abstract nature and role in optimization.
General Manifolds and Topology
Covers manifolds, topology, smooth maps, and tangent vectors in detail.