This is a course for those who hav had basic classical physics and mathematics up to multivariable calculus and some linear algebra (vectors and matrices).
Lesson 1: Review Material covers basic calculus up to ordinary differential equations, some linear algebra, and basic Newtonian mechanics.
Lesson 2:Vector Calculus covers linear mappings and the mathematics of scalar and vector fields.
Lesson 3:Newtonian Gravitational Fields covers the idea of the gravitational field from a vector calculus point of view and introduces the Poisson and Laplace equations.
Lesson 4:The Language of Tensors explores the use of tensors and other geometrical objects in classical mechanics.
Lesson 5:Maxwell's Equations covers the electric field, the magnetic field, electromagnetic induction, the derivation of the Maxwell equations, and the electromagnetic tensor.
Lesson 6:Applications of Maxwell's Equations covers how to use the equations.
Lesson 7:Basic Continuum Mechanics covers the ideas of deformation, strain, kinematics, stress, balance equations, constitutive equations, and symmetry groups.
Lesson 8:Basic Thermodynamics covers thermodynamic systems, thermodynamic laws, internal energy, heat and work, thermodynamic potentials, entropy, the ideal gas, energy balance, stress-strain-temperature coupling, and reversible and irreversible processes.
Lesson 9:Elastic Solids covers the equations of elasticity, equilibrium solutions, and elastic deformations.
Lesson 10: Fluid Dynamics covers the perfect fluid, steady flow, Newtonian fluids, the Navier-Stokes equation, dimensional analysis, and viscous flow.
Lesson 11: Waves in Deformable Media covers PDEs, ordinary waves, linearized waves, and shock waves.
Lesson 12: Introduction to Special Relativity covers the speed of light, spacetime, and the objects that live there.
Lesson 13: Introduction to Differential Geometry covers topology, manifolds, vectors, one-forms, and tensors from a mathematical point of view.
Lesson 14: More about Special Relativity covering worldline geometry, velocity addition, acceleration, observers, the Frenet-Serret frame, the Levi-Civita tensor in spacetime, decomposing 2-forms, and differentiation in spacetime.
Lesson 15: More About Special Relativity extends our understanding of topological groups, Lie groups and Lie algebras, the Lorentz group, one-parameter subgroups, and isometries.
Lesson 16: Classical Mechanics covers configuration space, the action principle, Lagrangian mechanics, symmetries and conservation laws, the action principle in spacetime, and Hamiltonian mechanics
Lesson 17: Dynamical Systems covers phase space, flows, autonomous systems, vector fields on phase space, fixed points, stability, linearization, Lyapunov functions and Lyapunov stability, periodic orbits, limit cycles, the Poincaré-Bendixson theorem, bifurcations, conservative vs dissipative systems, sensitivity to initial conditions, chaos, connections to physics.
Lesson 18: Fields in Terms of Special Relativity covers a general theory of fields in the language of special relativity in terms of Lagrangian mechanics, action in fields, relativistic fields, the relativistic Lagrangian, the scalar potential, the vector potential, and the electromagnetic field tensor.
Lesson 19: Particles and Fields covers how fields interact with particles, how particles interact with fields, the equations of motion in a field, gauge invariance, and the Lorentz force.
Lesson 20: Still More About Special Relativity explores physics in flat spacetime including the stress-energy tensor, four-momentum conservation, and matter in spacetime.
Lesson 21: Electromagnetic Radiation and Optics covers geometric optics as a mechanics problem, Liénard-Wiechert potentials, radiation energy, dipole radiation, plane waves, reflection and refraction, superposition, wave packets, and waves in conductors.
Lesson 22: Advanced Ideas of Special Relativity covers more physics in flat spacetime.
Lesson 23: Classical Statistical Mechanics covers the desire for a microscopic description, ensembles, Liouville's theorem, entropy, the postulate of a priori probabilities, temperature form the microcanonical ensemble, the Boltzmann factor, the partition function and the thermodynamic potentials, and ergodicity.
Lesson 24: Kinetic Theory covers ideal gases, molecular chaos, the distribution function, the Liouville equation and its reduction to the Boltzmann equation, the Maxwell-Boltzmann relation, pressure due to molecular collisions, mean free path, viscosity, thermal conductivity, diffusion, H-theorem, connection to thermodynamics and hydrodynamics, and the limitations.
Lesson 25: The Concept of Plasmas covers the particle kinetics approach to plasmas.
Lesson 26: Magnetohydrodynamics covers the theory of plasmas as a fluid.
Lesson 27: Astrophysics includes stellar structure, stellar evolution, interstellar medium, and galaxies.
Lesson 28: More Differential Geometry covers curved manifolds, tensor algebra in curved manifolds, commutators, one-parameter subgroups of diffeomorphisms, geodesics, parallel transport, covariant derivatives, and the geodesic equation.
Lesson 29: More Differential Geometry covers geodesic deviation, the Riemann curvature tensor, and Bianchi identities.
Lesson 30: More Differential Geometry covers local frames, proper frames, curvature, and differential forms.
Lesson 31: Physics in Curved Manifolds covers Poisson brackets, geodesics, curvature, thermodynamics, fluid dynamics, and electromagnetic fields.
Lesson 32: Introduction to General Relativity, covering the equivalence principle, fluid dynamics in a gravitational field, properties of covariant derivatives, factor ordering, the precession of equinoxes, the pendulum, Deriving the field equations by path 1.
Lesson 33: General Relativity, including the Newtonian limit, the linearized theory, the Schwarzschild solution, and post Newtonian theory.
Lesson 34: More General Relativity, including trajectories near a massive spherical body, Killing vectors and conservation laws, and asymptotic flatness.
Lesson 35: The Variational Approach introduces the Einstein-Hilbert action, general variance, more about the stress-energy tensor, the second path to the field equations, covariance and invariance, the tetrad, and the initial-value problem.
Lesson 36: Other approaches covers the Palatini formalism, the route from Lovelock's theorem, thermodynamic gravity, and the gauge theory of gravity.
Lesson 37: Quantum Mechanics covers the quantum of action, wave-particle duality, the de Broglie relation, the Schrödinger equation, the wave function, the probability interpretation and the Born rule, operators and observables, commutation relations and uncertainty, stationary states, the classical limit, simple solvable systems, phase space and Hilbert space, Poisson brackets, entanglement, decoherence, and the measurement problem.
Lesson 38: Statistical Mechanics covers the density operator and quantum ensembles, the quantum microcanonical ensemble, the density matrix for thermal states, the partition function, Bose-Einstein statistics, Fermi-Dirac statistics, Bose gases, Bose-Einstein condensation, Fermi gas, degeneracy pressure, blackbody radiation, the classical limit, lasers, and superconductivity.
Lesson 39: Quantum Field Theory covers the failure of quantum mechanics at relativity, scalar fields and the Klein-Gordon equation, canonical quantization of fields, creation and annihilation operators, particles as excitations, the vacuum state and zero-point energy, the Feynman propagator and causality, simple interacting theories, gauge fields and the photon, fermions and the Dirac field, Fock space, the Casimir effect, spontaneous emission, particle creation, renormalization, infinities, and the measurement problem in QFT.
Lesson 40: The Standard Model of Particle Physics covers quarks, leptons, generations, color, weak isospin, gauge bosons such as photons, W and Z, gluons, the Higgs boson, U(1) EM, SU(2) * U(1) Electroweak theory, QCD, the Higgs mechanism, Symmetry breaking, masses and mixing, Feynman rules, the hierarchy problem, neutrino masses, dark matter, baryogenesis, and grand unification.
Lesson 41: Nuclear Physics covers nuclear properties, nuclear forces and the strong interaction, the liquid drop model, the shell model, the collective model, radioactivity and decay processes, nuclear reactions, fission, fusion, nucleosynthesis, r-processes, s-processes, nuclear matter, exotic nuclei, the nuclear equation of state, and quark-gluon plasmas.
Lesson 42: Star death covers the endpoints of stellar evolution, supernovae, white dwarf stars, and neutron stars.
Lesson 43: Black Holes covers what is a black hole? what is gravitational collapse, black hole astrophysics, Schwarzschild black holes, Reissner-Nordstrom black holes, Kerr black holes, Kerr-Newman black holes, the physics of black holes.
Lesson 44: Black holes Physics includes singularities, horizons, the ergosphere, energy extraction, and Hawking radiation.
Lesson 45: High energy astrophysics covers relativistic particles, compact objects as engines, accretion disks, supernova remnants, gamma-ray bursts, AGNs and quasars, cosmic rays, synchrotron radiation, inverse Compton scattering, bremsstrahlung, pair production and annihilation, and neutrino astrophysics.
Lesson 46: Cosmology covers the cosmological principle, ,cosmological red shift, the evolution of the universe, and cosmic horizons, Friedmann universes, the cosmological constant, the hot big bang model, de Sitter space, blackbody radiation, CMBR, \[CapitalLambda]CDM model, and recent results from JWST.
Lesson 47: The Early Universe covers radiation and temperature, the scale factor, the radiation era, the isotropic CMB and the horizon, and anisotropies of the CMBR.
Lesson 48: History of the Universe covers condensation into galaxies, into stars, into atoms, into nuclei, and into nucleons.
Lesson 49: Frontiers of Cosmology includes inflation, inflation via scalar fields, structure formation, dark matter, and dark energy.
Lesson 50: Gravitational Waves include gravitational plane waves, sources of gravitational waves, LIGO and other detectors.
Talk presented by Christopher Winfield at the Midwest Relativity 2020 (a virtual conference) on a solid justification for the Cowling approximation using asymptotic and functional analysis methods is here.
Talk presented by George E. Hrabovsky at the Midwest Relativity 2020 (a virtual conference) on how to use Mathematica and xAct to derive the relativistic equations of motion for a viscous fluid is here, (the Mathematica notebook is here.)
Click here to visit the MAST web site.