Differential Forms: Basics and Applications

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Related lectures (31)

Page 3 of 4

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.

Linear Shell Theory: Equilibrium Equations

Covers the dimensional reduction of strain energy from 3D to 2D and linear shell theory equilibrium equations.

Meromorphic Functions & Differentials

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

General Manifolds and Topology

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

Christoffel Symbols and Gravity Before Einstein

Introduces Christoffel symbols and gravity concepts before Einstein, discussing mathematical tensors and the Nobel Prize in Physics.

Optimization on Manifolds

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

Riemannian connections: Proof sketch

Presents the fundamental theorem of Riemannian geometry and demonstrates the uniqueness of the Riemannian connection.

Riemannian connections: What they are and why we care

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

Symplectic Geometry

Covers the background on symplectic geometry, focusing on symplectic manifolds and canonical structures.

Manifolds and Tangent Space

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