Many online courses on mathematics can be found here! (More than you need)
Natural number: 1, 2, 3, …
Integers: …, -2,-1, 0, 1, 2, …
Score:
Real number: sqrt (2) =1.4142135 ..., PI = 3. 14 159265 ..., e = 2.71. ......
Complex numbers: 2+3i, eia = cos a+i sin a, ... They are very important!
Set theory: open set, compact space, topology.
You may find it strange that they are really useful in physics.
Dave e Joyce's trigonometric function course.
This is a must: Professor James Binney's complex course
(Almost) Everything on it is here! Kubota, Kentucky. You can also read Chris Pope's handout: Method 1-CH 1 Method 1-CH2.
Complex plane. Cauchy theorem and contour integral (G. Cain, Atlanta)
Algebraic equation. Approximate method. Series expansion: Talylor series. Solve complex equations. Trigonometric function: sin(2x)=2sin x cos x, and so on.
Infinitely small. Difference. Find the differential of the basic function (sin, cos, exp).
Integral, if possible, the integral of the basic function.
Differential equation system. linear system of equations
Fourier transform. The use of plural numbers. Convergence of series.
Complex plane. Cauchy theorem and contour integral method (very interesting now).
Gamma function (enjoy learning his properties).
Gaussian integral. Probability theory.
System of partial differential equations. Dirichlet and Neumann boundary conditions.
These are for beginners. Some content can be used as a complete lecture course. Most of these contents are essential in physical theory. You don't need to finish all these courses when you start to learn the rest, but remember to come back and finish the course you missed the first time.
A very good set of lectures from Harvard;
More explanations of Lagrange and Hamilton equations
Lectures on Louro Optics
Alfred Huan's textbook Statistical Mechanics
Lectures on thermodynamics by Professor Donald B. melrose.
Classical mechanics: statics (force, stress); Hydrostatics. Newton's law.
Elliptic orbits of planets. Many-body problem.
Action principle. Hamilton equation. Lagrange (don't skip it, it's extremely important! )
Harmonic oscillator swings.
Poisson bracket.
Wave equation. Liquid and gas. Viscosity. Naville-Stokes equation. Viscosity and friction.
Optics: refraction and reflection. Lens and mirror. Telescope and microscope. Introduction to wave propagation. Doppler effect. Huygens wave superposition principle. Wavefront caustics
Statistical mechanics and thermodynamics: the first, second and third laws of thermodynamics.
Boltzmann distribution.
Carnot cycle. Entropy. heat engine
Phase transition. Thermodynamic model.
Ising model (the technology of solving two-dimensional Ising model is put behind).
Planck's radiation law (as a prelude to quantum mechanics)
(just some very basic) electronics: circuits. Ohm's law capacitance, inductance, use complex numbers to calculate their influence. Transistors, diodes (you will learn how they work later).
Mathematics for Science Students, james kelly Angus McKinnon, Computational Physics.
W. Spencer, electromagnetism
Botide "EM field theory text (advanced)
Jackson's book has done exercises, set 1/set 2.
Introduction to Quantum Mechanics and Special Relativity: Michael Fowler
Alternative introduction
Lecture Notes of Niels Valit's Lecture Course on Quality Management (Manchester)
Even the purest theorist may be interested in some aspects of computational physics.
Maxwell's electromagnetic theory. Maxwell's law (uniform and non-uniform)
Maxwell's law in media. Boundary. Solve the equation under the following conditions:
Vacuum and homogeneous medium (electromagnetic wave);
In the box (waveguide);
On the boundary (refraction and reflection);
(non-relativistic) quantum mechanics. Bohr atom
De Broglie relation (energy-frequency, momentum-wave number)
Schrodinger equation (with electric potential and magnetic field)
Allen Feister Li Ming
A particle in the box
Hydrogen atom, the detailed solution process is given. Zeeman effect stark effect.
Quantum harmonic oscillator.
Operators: energy, momentum, angular momentum, production and elimination operators.
The reciprocal relationship between them.
Introduction to scattering theory of quantum mechanics. S matrix. Radioactive decay.
Atoms and molecules. Chemical bonding. Orbit. Atomic and molecular spectra. Emission and absorption of light. The law of quantum selection. Magnetic moment.
Solid State Physics: Notes by Chetan Nayak (UCLA)
Solid state physics. Crystal. Bragg reflection. Crystal group. Dielectric constant and permeability resistance. Bloch spectrum. Fermi level. Conductors, semiconductors and insulators. Specific heat electrons and holes. Transistors. Superconducting. Hall effect.
Nuclear physics. Isotope. Radioactive fission and fusion. Water drop model. Quantum number of nucleus. Magic number kernel. Isospin yukawa theory.
Plasma physics: magnetohydrodynamics, Alvin wave.
See John Hein Birkel, Virginia.
See Chr. Pope: Method 2
G. Hooft: Li Qun, practicing in Holland.
Special functions and polynomials (you don't need to remember these, just understand them).
Advanced Mathematics: Group Theory and Linear Representation of Groups. Lie group theory. Vector and tensor.
More skills in solving (partial) differential equations and integral equations.
Extreme value principle and approximation skills based on extreme value principle.
Difference equation. Generating function. Hilbert space.
Introduction to functional integration.
Peter Dunsby's lecture on tensor and special relativity
Michigan Notes (Advanced) Quantum Mechanics
Special relativity. Lorentz transformation. Lorentz contraction, time expansion. E = mc2. Four-dimensional vector and four-dimensional tensor. Transformation rules of Maxwell's equation. Relativistic Doppler effect.
Higher quantum mechanics: Hilbert space. Atomic transition. Emission and absorption of light. Stimulated emission. Density matrix. The explanation of quantum mechanics. Bell inequality. Transition to relativistic quantum mechanics: Dirac equation, fine structure. Electrons and positrons. BCS theory of superconductivity. Quantum hall effect. Advanced scattering theory. Decentralize the relationship. Disturbance expansion. WKB approximation. Extreme value principle. Bose-Einstein condensation. Superfluid liquid helium.
More phenomenological theory: subatomic particles (mesons, baryons, photons, leptons, quarks) and cosmic rays; Material characteristics and chemistry; Isotopes of atomic nuclei; Phase transition; Astrophysics (planetary systems, stars, galaxies, redshifts, supernovae); Cosmology (cosmological model, skyrocketing universe theory, microwave background radiation); Detection technology.
G.T. Hooft's Introduction+Practice
Alternative: Sean M Carroll's speech on GR
Pierre van Baer's Notes on QFT
General relativity. Normative tensor curvature of spacetime. Einstein's equation of gravity. Schwartzchild black hole; Lisnell-Naustrom black hole. Perihelion moves. Gravitational lens. A model of the universe. Gravity radiation
Quantum field theory. Classical fields: scalar field, Dirac-spinor field and Yang-Mills vector field.
Interaction, perturbation expansion. Spontaneous symmetry breaking, GoldSi Tong module. Higgs mechanism.
Particles and fields: fokker space. Antiparticles. Fei Enman's law. The gherman-Levi Sigma model of mesons and nuclei is derived. Circle chart. Monopositivity, causality and deviation. Renormalization (Pauli-Villar; Dimension renormalization). Quantum gauge theory: gauge fixation, Dief-popov determinant, Slavov identity, BRST symmetry. The renormalization group is asymptotically free.
Lonely person, son of the sky. Magnetic monopoles and instantons. Quark confinement mechanism. 1/N extension. Product development of operators. Beta-Sabbetta equation. Establishment of standard model. P and CP are damaged. The connection between spin and statistics of CPT theorem. Supersymmetry.
Introduction+practice
A more general superstring website
Superstring theory.
More online handouts can be found here.
Books. There are many books on various topics of theoretical physics.
Here are some books:
H.Margenau and G.M. Murphy, Mathematics of Physics and Chemistry, D. v.Nostrand Comp.
R. Baker, Linear Algebra, Linton Press
Modern Course of Length Statistical Physics, 2nd Edition.
R.K. Pathria: statistical mechanics
M (short for meter) Plieske & ampb. Bergson: Balanced Statistical Physics.
Length landau law firm. Statistical physics, part 1
Nanma, Statistical Mechanics, World Science
J.D. Jackson, Classical Electrodynamics, 3rd Edition. Willie law firm. Sons.
A.Das & amp quantum mechanics, Gordon & violation
Davydov, quantum mechanics. Pegamon publishing house
E. Maze Bachel, quantum mechanics, Willie & son.
R.Shankar, Principles of Quantum Mechanics, Plenary Session
Sakurai, advanced quantum mechanics, Addison Wesley
B. Dewit & ampj. Smith, Field Theory in Particle Physics, North Holland.
Acheson Company Hey, gauge theory in particle physics, Adam Hilge.
Ryder, Quantum Field Theory, Cambridge University Press.
C itzykson & quantum field theory, McGraw-hill.
Green, Schwartz & Witten, Superstring Theory, Vols. I&II, Cambridge University Press.
J. Polczynski, String Theory, Volume 1. Second, Cambridge University Press
Other useful lists of textbooks can be found here: math and physics (many of them are for recreation, not for understanding the basic reading materials of the world).
There have been some responses. I want to thank Rob Vanlinden, Robert Thun, Ruan Hui, Tina Witham, Jerry Blair, Jonathan Martin and others.
Last revision date: 20 February 2003