Non-analytic Smooth Functions

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (51)

Riemannian connections Log in to Mediaspace to watch this video

Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.

General Manifolds and Topology Log in to Mediaspace to watch this video

Covers manifolds, topology, smooth maps, and tangent vectors in detail.

Smooth maps on manifolds and differentials Log in to Mediaspace to watch this video

Covers smooth maps on manifolds, defining functions, tangent spaces, and differentials.

Linear Lie Groups: Definitions and Theorems Log in to Mediaspace to watch this video

Discusses linear Lie groups, their definitions, properties, and the relationship between integral curves and vector fields.

Manopt: Optimization Toolbox for Manifolds Log in to Mediaspace to watch this video

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

All things Riemannian: metrics, (sub)manifolds and gradients Log in to Mediaspace to watch this video

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

Manifolds: Charts and Compatibility Log in to Mediaspace to watch this video

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

Differential Forms and Invariant Measures Log in to Mediaspace to watch this video

Covers differential forms, invariant measures, and integration on manifolds with examples and illustrations.

Laurent Series and Convergence: Complex Analysis Fundamentals Log in to Mediaspace to watch this video

Introduces Laurent series in complex analysis, focusing on convergence and analytic functions.

Total Differential: Definition and Integrals Log in to Mediaspace to watch this video

Explores the definition of total differential and its applications in integral calculus.

The Conjugate Gradients Method (CG)Log in to Mediaspace to watch this video

Covers the Conjugate Gradients method for solving linear systems iteratively with quadratic convergence and emphasizes the importance of linear independence among conjugate directions.

Equidistribution of CM Points Log in to Mediaspace to watch this video

Covers the joint equidistribution of CM points and explores convergence in multiple variables.

Effective Version of the Explicit Formula Log in to Mediaspace to watch this video

Explores the effective version of the explicit formula in Number Theory, focusing on smooth functions and integral calculations.

Harmonic Forms and Riemann Surfaces Log in to Mediaspace to watch this video

Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.

Optimization Techniques: Gradient Descent and Convex Functions Log in to Mediaspace to watch this video

Provides an overview of optimization techniques, focusing on gradient descent and properties of convex functions in machine learning.

Riemannian Gradient Descent: Convergence Theorem and Line Search Method Log in to Mediaspace to watch this video

Covers the convergence theorem of Riemannian Gradient Descent and the line search method.

Distributions and Laplace Transform: Key Concepts Log in to Mediaspace to watch this video

Discusses distributions, the Laplace transform, and their applications in mathematical analysis.

Complex Manifolds: GAGA Principle Log in to Mediaspace to watch this video

Covers the GAGA principle, stating that any morphism on projective varieties is constant.

Derivatives of Entire Functions Log in to Mediaspace to watch this video

Explores derivatives of entire functions and the use of Taylor series for function representation.

Differential Geometry: Surfaces Log in to Mediaspace to watch this video

Explores the differential geometry of parametric surfaces, covering tangent space, normal curvature, principal curvatures, and asymptotic curves.

Page 2 of 3