Lectures related to Differential algebra

Geometrical Aspects of Differential Operators

Explores differential operators, regular curves, norms, and injective functions, addressing questions on curves' properties, norms, simplicity, and injectivity.

Meromorphic Functions & Differentials

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

Differential Operators: Vector Analysis

Covers differential operators, vector analysis, Fourier analysis, and potential fields with applications to gravity.

Differential Calculus: Applications and Reminders

Covers differential calculus applications and reminders, emphasizing the importance of differentiability in mathematical analysis.

Differential Forms on Manifolds

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

Differential Pair: Operation and Characteristics

Explains the differential operation of circuits and the immunity to common-mode noise.

Differential Forms Integration

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

Differential Operators: Gradient and Divergence

Introduces differential operators, gradient, and divergence in vector fields.

Introduction to Plasma Physics

Introduces the basics of plasma physics, covering collective behavior, Debye length, and plasma conditions.

Linear Approximation and Derivative Parametric

Covers linear approximation, parametric derivatives, and differentiability conditions on intervals.

Non-inertial Reference Frames & Constraints

Covers forces in non-inertial reference frames, constraints, and the use of pulleys and ropes.

Harmonic Forms: Main Theorem

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

Thermodynamics: Principles and Applications

Provides an overview of thermodynamic principles, focusing on the first principle and its applications in various systems.

Differential Operation: Circuit Invention and Noise Immunity

Explores the differential operation in high-performance analog circuits and its immunity to common-mode noise.

Transport Theorem: Hydro1_3

Covers the transport theorem, constitutive models, differential operators, and the continuity equation.

Distribution & Interpolation Spaces

Explores distribution and interpolation spaces, differential operators, Fourier transform, Schwartz space, fundamental solutions, Farrier transform, and uniform continuity.

Cohomology: Cross Product

Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.

Differential Operators: Theorems and Proofs

Covers the concept of differential operators and presents theorems and proofs related to scalar and vector fields.

Functions with Values in R^m

Explores functions with values in R^m, gradients, derivatives, and the Jacobian matrix in multiple dimensions.

Schur's Lemma and Representations

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.