Lectures in course PHYS-216: Mathematical methods (for SPH)

Covers the study of a vibrating string, wave equations, sinusoidal waves, and eigenvalue problems.

Mathematical Methods: Collision Dynamics and Energy Transfer

Covers mathematical methods for analyzing collision dynamics and energy transfer in physics.

Mathematical Methods: Oscillations and Energy Transfer

Discusses oscillations, energy transfer, and the Green function in physics.

Mathematical Methods for Physicists: Differential Equations and Special Functions

Covers solving differential equations and special functions essential for physicists, emphasizing practical problem-solving skills.

Eigenvectors and 1D Wave Equation

Covers eigenvectors, eigenvalues, and the solution to the 1D wave equation on a bounded system.

Electrostatics and Green's Functions: Mathematical Methods

Discusses electrostatics, Green's functions, and the application of complex analysis in deriving potentials.

Eigenfunctions and Continuous Bounded 1D Wave Equation

Explores eigenfunctions, harmonic oscillators, and the solution to linear differential equations using a basis of eigenvectors.

Gamma Function and Stirling's Approximation: Mathematical Methods

Discusses the gamma function, its properties, and Stirling's approximation for large factorials, emphasizing their significance in mathematical methods for physics.

Linear Algebra Concepts: Motivation for Studying Eigenmodes in Physical Systems

Explores the motivation for studying linear algebra concepts in eigenmodes of physical systems and their central role in quantum mechanics.

Variational Methods: Shortest Time Path Problem

Covers variational methods to find the shortest time path for a particle under gravity.

Random Walks: Return Probabilities in Lattice Dimensions

Covers random walks on a lattice, focusing on return probabilities and their dependence on dimensionality.

Function Spaces and Hilbert Spaces

Introduces function spaces and Hilbert spaces, discussing inner product spaces and the importance of completeness in Hilbert spaces.

Random Walks: Return Probabilities in Multiple Dimensions

Covers the analysis of random walks and their return probabilities in multiple dimensions.

Orthogonal/Orthonormal Bases and Polynomials

Explores orthogonal and orthonormal bases, Gram-Schmidt process, and orthogonal polynomials in physics.

Orthogonal Polynomials in Physics

Covers important orthogonal polynomials in physics used to represent angular and radial dependencies in fields and quantum systems.

Fourier Transforms in Tomography: Inversion Techniques

Covers the application of Fourier transforms in tomography, focusing on the Radon transform and its inversion techniques.

Linear Operators: Motivation in Quantum Mechanics

Explores the motivation for studying linear operators in Quantum Mechanics, emphasizing their essential role and practical applications.

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Adjoint of Linear Operators on Inner Product Spaces

Explores the adjoint of linear operators on inner product spaces, including self-adjoint, unitary, and normal operators.