Lectures related to Grassmann manifold and Retractions

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

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.

Optimization on Manifolds

Covers optimization on manifolds, focusing on smooth manifolds and functions, and the process of gradient descent.

Differentiability of Functions of Several Variables

Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.

All things Riemannian: metrics, (sub)manifolds and gradients

Covers the definition of retraction, open submanifolds, local defining functions, tangent spaces, and Riemannian metrics.

Manifolds and Tangent Space

Introduces manifolds, charts, atlases, tangent space, tensors, and the metric in curved spaces.

Tangent to Graph of a Function

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

Riemannian metrics and gradients: Computing gradients from extensions

Explores computing gradients on Riemannian manifolds through extensions and retractions, emphasizing orthogonal projectors and smooth extensions.

Hands on with Manopt: Optimization on Manifolds

Introduces Manopt, a toolbox for optimization on smooth manifolds with a Riemannian structure, covering cost functions, different types of manifolds, and optimization principles.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Tangent spaces to submanifolds

Introduces tangent spaces to submanifolds and their properties in optimization on manifolds.

Riemannian metrics and gradients: Examples and Riemannian submanifolds

Explores Riemannian metrics on manifolds and the concept of Riemannian submanifolds in Euclidean spaces.

Derivatives and Functions: Definitions and Interpretations

Covers the definition of derivative functions and their interpretation, focusing on differentiability, velocity, and curve lengths.

Differentiability and Tangent Planes in Multivariable Functions

Explains differentiability in multivariable functions and the geometric interpretation of tangent planes.

Euclidean Spaces: Properties and Concepts

Covers the properties of Euclidean spaces, focusing on R^n and its applications in analysis.

Real Functions: Definitions and Properties

Explores real functions, covering parity, periodicity, and polynomial functions.

Taylor Series: Convergence and Applications

Explores Taylor series convergence and applications in approximating functions and solving mathematical problems.

Derivatives and Continuity

Explores derivatives, reciprocal functions, and continuity of functions with examples and formulas.

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Differentiability and Tangent Planes in Multivariable Functions

Covers differentiability in multivariable functions and the existence of tangent planes, emphasizing geometric interpretations and practical applications.