Concept

Exact solutions in general relativity

Related lectures (30)

General Solutions of Differential Equations

Explores general solutions of differential equations with a focus on x

Linear Differential Equations of Higher Order

Revises linear differential equations with constant coefficients of higher order and their geometric interpretation.

General Solutions of Differential Equations

Covers general solutions of differential equations, focusing on particular and homogeneous solutions.

Linear Second Order ODEs

Covers the solution of linear second order ODEs with constant coefficients and explores the method of variation of parameters.

General Solutions of Differential Equations

Explores general solutions of differential equations, emphasizing homogeneous and inhomogeneous equations and the process of finding solutions.

Differential Equations: General Solutions and Methods

Covers solving linear inhomogeneous differential equations and finding their general solutions using the method of variation of constants.

Method of Undetermined Coefficients

Explores the method of undetermined coefficients for solving non-homogeneous linear differential equations with constant coefficients.

Characteristic Polynomials: Solutions and Roots

Covers characteristic polynomials, their solutions, and roots for different types of polynomials.

Cauchy-Towalewski Theorem

Discusses the Cauchy-Towalewski theorem and the classification of solutions.

Electromagnetic Plane Waves

Covers the general solution for electromagnetic potentials, energy conservation, and the electric field.

General Solution of Inhomogeneous ED

Covers the general solution of inhomogeneous differential equations and explores linear dependence, uniqueness theorems, and second-order equations.

Method of variation of constants

Covers the method of variation of constants for solving differential equations.

Variation of Constants in Differential Equations

Explains the method of variation of constants in differential equations and its application in finding particular solutions.

Optical Bloch Equations

Covers the derivation and solutions of Optical Bloch Equations for a two-level quantum system.

Quantum Chaos and Scrambling

Explores the concept of scrambling in quantum chaotic systems, connecting classical chaos to quantum chaos and emphasizing sensitivity to initial conditions.

Characteristic Polynomials: Roots and Solutions

Covers characteristic polynomials, roots, solutions, and general solutions for differential equations.

Coupled Oscillators: General Solutions

Explores general solutions for coupled oscillators, focusing on single and N harmonic oscillators, eigenmodes, and initial conditions.

Separable Differential Equations

Covers separable differential equations of order 1, defining separable equations and providing examples.

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Linear Differential Equations: Homogeneous and Separable

Covers linear differential equations of order 1, focusing on homogeneous and separable equations.