Lectures related to Closed and exact differential forms

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Differential Forms on Manifolds

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

Harmonic Forms and Riemann Surfaces

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

Magnetostatics: Magnetic Field and Force

Covers magnetic fields, Ampère's law, and magnetic dipoles with examples and illustrations.

Differential Forms and Invariant Measures

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

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Hodge Duality and Covariant Derivatives

Introduces Hodge duality, covariant derivatives, and key concepts in differential geometry.

Meromorphic Functions & Differentials

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

Differential Forms: Basics and Applications

Introduces the concept of differential forms and their applications in n-dimensional manifolds, including the Levi-Civita tensor and volume form.

Riemann Surfaces: Complex Manifolds

Covers Riemann surfaces as complex manifolds of dimension 1, including transition maps and holomorphic functions.

Conformal Transformations: Theory and Applications

Explores the theory and applications of conformal transformations, covering special conformal transformations and isomorphic transformations.

Vector Calculus Review: Maxwell Equations

Covers a review of vector calculus and the Maxwell equations in electromagnetism.

Total Differential: Definition and Integrals

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

Lyapunov Functions: Construction and Properties

Explores Lyapunov functions, Chetaev's theorem, and differential forms classification.

Mathematical Complements: df or δf

Explores mathematical tools for differentials of functions of multiple variables and their practical applications in thermodynamics and real-life scenarios.

Ampère's Law and Applications

Explores Ampère's law in magnetostatics, demonstrating its application in calculating magnetic fields from current-carrying wires and solenoids.

Electric Field Calculation using Gauss's Law

Explains how to calculate the electric field around a point charge using Gauss's law.

Green Functions: Theory and Applications

Explores the theory and applications of Green functions in classical electrodynamics, emphasizing the importance of choosing the right function based on boundary conditions.

Geometric Property: Spectral Side

Covers the derivation of geometric properties from spectral side functions.

Applications of Gauss's law: Electric Field Calculations Simplified

Simplifies electric field calculations using Gauss's law and symmetry arguments.