Lectures related to Modeling Heat Equation

Quantum Mechanics: Jacobi Identity and Gauge Invariance

Explores Jacobi identity, gauge invariance, and conservation laws in quantum mechanics and classical physics.

Hamiltonian Formalism: Harmonic Oscillator

Explores the Hamiltonian formalism for the harmonic oscillator, focusing on deriving Lagrangian and Hamiltonian, isolating the system, and generating new conserved quantities.

Canonical Transformations: Existence and Equations

Explores canonical transformations, focusing on existence, equations, simplicity, and differential equations' theory.

Differential Calculus: Applications and Reminders

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

Differential Functions: Derivability and Gradient

Explores differentiability in functions and the role of gradients in directional derivatives.

Functions with Values in R^m

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

Partial Derivatives: Gradient and Theorem of Mean Value

Introduces the gradient concept and the Theorem of Mean Value for functions in several variables.

Derivable Functions: Partial Derivatives and Jacobian Matrix Log in to Mediaspace to watch this video

Covers derivable functions, partial derivatives, Jacobian matrix, and rule of composition.

Partial Derivatives and Differential Equations Log in to Mediaspace to watch this video

Covers partial derivatives, differentiability, differential equations, sets properties, and local extrema verification.

Partial Derivatives and Functions Log in to Mediaspace to watch this video

Explores partial derivatives and functions in multivariable calculus, emphasizing their importance and practical applications.

Derivatives and Tangent Planes Log in to Mediaspace to watch this video

Covers derivatives, differentiability, and tangent planes for functions of one and two variables.

Fourier Analysis and PDEs Log in to Mediaspace to watch this video

Explores Fourier analysis, PDEs, historical context, heat equation, Laplace equation, and periodic boundary conditions.

Laplacian in Polar and Spherical Coordinates: Derivatives Log in to Mediaspace to watch this video

Covers the Laplacian operator in polar and spherical coordinates, focusing on derivatives and integral calculations.

Partial Differential Equations Log in to Mediaspace to watch this video

Introduces partial differential equations, covering derivatives, special cases, transformations, and the Jacobian matrix.

Convolution and Fourier Transform Log in to Mediaspace to watch this video

Explores convolution properties, heat equation application, and Fourier transform on tempered distributions.

Functions of Class C^p Log in to Mediaspace to watch this video

Explores functions of class C^p, emphasizing continuity and differentiability properties.

Heat Equation: Separation of Variables Log in to Mediaspace to watch this video

Covers the application of separation of variables method to solve the heat equation.

Derivatives and Continuity in Multivariable Functions Log in to Mediaspace to watch this video

Covers derivatives and continuity in multivariable functions, emphasizing the importance of partial derivatives.

Differentiation and Coordinate Changes in Multivariable Functions Log in to Mediaspace to watch this video

Discusses differentiation of multivariable functions and coordinate transformations, including polar and cylindrical coordinates, along with the Laplacian operator and its applications.

Partial Differential Equations: Basics and Classification Log in to Mediaspace to watch this video

Introduces the basics and classification of partial differential equations, including notation, definitions, and examples.