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College of Arts & Sciences
Advanced Solutions Group


Lecture Videos for Lie Algebra

Lecture 1 (22:40) - Classical Mechanics and The Harmonic Oscillator

Lecture 2 (22:35) - Homogeneous and Inhomogeneous Solutions and Conservative Forces

Lecture 3 (22:15) - Systems of Particles and Lagranges Equations

Lecture 4 (24:45) - Lagranges Equations, Hamilton's Equations, and Variational Principles

Lecture 5 (23:55) - Poisson Brackets, Work, and The Electromagnetic Field

Lecture 6 (23:05) - Maxwells Equations and Lorentz Force

Lecture 7 (24:00) - Electromagnetic Waves and The Theory of Relativity

Lecture 8 (22:05) - Lorentz Transformation, Relativistic Scalars, Vectors, and Tensors

Lecture 9 (21:45) - Lorentz Contraction, Time Dialation, Covariant Vectors, and Tensors

Lecture 10 (23:05) - Relativistic Energy, Momentum, Particles, and Electromagnetic Theory

Lecture 11 (23:42) - Maxwells Equations, Four-Vector Potential, and Magnetic Monopoles

Lecture 12 (23:45) - Maxwells Equations, Traditional Fields, and Newtons Covariant Eqs.

Lecture 13 (23:05) - Gauge Invariance, General Relativity, Lie Groups, and Lie Algebras

Lecture 14 (23:50) - Dirac Notation, Lie Groups, and Lie Algebras

Lecture 15 (23:57) - Lie Algebras, Lie Groups, and Representation Space

Lecture 16 (23:55) - The Heisenberg Lie Algebra

Lecture 17 (23:25) - The Heisenberg Lie Algebra

Lecture 18 (22:45) - The Heisenberg Lie Group and The Harmonic Oscillator Lie Algebra

Lecture 19 (24:40) - The Harmonic Oscillator Lie Algebra

Lecture 20 (24:00) - The Harmonic Oscillator Lie Algebra and Harmonic Oscillator Lie Group

Lecture 21 (24:00) - Angular Momentum Lie Algebra and Cartan Subalgebra

Lecture 22 (23:17) - O3 Lie Algebra Eigenvalue Spectra

Lecture 23 (24:07) - O3 Spherical Harmonics

Lecture 24 (25:40) - Heisenberg LA with Spin, Relativistic Heisenberg Algebra, & Lorentz LA

Lecture 25 (22:40) - Relativistic Heisenberg Algebra, and Lorentz Lie Algebra

Lecture 26 (23:15) - XPIM - Lie Group - Rotations and Lorentz Transformations

Lecture 27 (24:36) - Lorentz Lie Algebra and Irreducible Tensor Operators

Lecture 28 (23:47) - Irreducible Tensor Operators and The XPIM Lie Algebra

Lecture 29 (25:40) - XPIM- Lie Algebra - Particle Representation

Lecture 30 (22:15) - Markov-type Lie Groups and Lie Algebra

Lecture 31 (23:15) - The General Linear Group and Properties of the M(n R) Algebra

Lecture 32 (22:57) - Properties of the M(n R) Lie Algebra and Markov Lie Algebra

Lecture 33 (23:50) - Fibonacci Numbers, The Golden Numbers, and Generation of e^-tL

Supplemental Video Lectures:

Markov Processes (54:44)

QRECT: A New System for Continuous Real Time Educational Assessment (1:02:28)

A New Type of Game Theory (28:20)

The Retention of Information in Systems with Entropy (27:33)

40 Years in Research at USC (1:01:34)

A New Kind of Number (56:37)

 

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