# Re: accesible math resources

*From*: "Martin Slack" <m.g.slack@xxxxxxxxxxxx>*To*: <programmingblind@xxxxxxxxxxxxx>*Date*: Wed, 22 Apr 2009 07:49:46 +0100

Hi Tyler, The unix world has a number of command line utilities like bc, mathomatic, octave or singular, as well as libraries like lapack, GLPK and GMP. If you Google for terms like physics formulae you will find sites like: http://www.xs4all.nl/~johanw/contents.html of which the contents are: The table of contents from "Equations in Physics" is shown below. Physical Constants 1 1. Mechanics 2 1.1 Point-kinetics in a fixed coordinate system 2 1.1.1 Definitions 2 1.1.2 Polar coordinates 2 1.2 Relative motion 2 1.3 Point-dynamics in a fixed coordinate system 2 1.3.1 Force, (angular)momentum and energy 2 1.3.2 Conservative force fields 3 1.3.3 Gravitation 3 1.3.4 Orbital equations 3 Kepler's equations 4 1.3.5 The virial theorem 4 1.4 Point dynamics in a moving coordinate system 4 1.4.1 Apparent forces 4 1.4.2 Tensor notation 5 1.5 Dynamics of masspoint collections 5 1.5.1 The centre of mass 5 1.5.2 Collisions 6 1.6 Dynamics of rigid bodies 6 1.6.1 Moment of Inertia 6 1.6.2 Principal axes 6 1.6.3 Time dependence 6 1.7 Variational Calculus, Hamilton and Lagrange mechanics 7 1.7.1 Variational Calculus 7 1.7.2 Hamilton mechanics 7 1.7.3 Motion around an equilibrium, linearization 7 1.7.4 Phase space, Liouville's equation 8 1.7.5 Generating functions 8 2. Electricity & Magnetism 9 2.1 The Maxwell equations 9 2.2 Force and potential 9 2.3 Gauge transformations 10 2.4 Energy of the electromagnetic field 10 2.5 Electromagnetic waves 10 2.5.1 Electromagnetic waves in vacuum 10 2.5.2 Electromagnetic waves in matter 11 2.6 Multipoles 11 2.7 Electric currents 11 2.8 Depolarizing field 12 2.9 Mixtures of materials 12 3. Relativity 13 3.1 Special relativity 13 3.1.1 The Lorentz transformation 13 3.1.2 Red and blue shift 14 3.1.3 The stress-energy tensor and the field tensor 14 3.2 General relativity 14 3.2.1 Riemannian geometry, the Einstein tensor 14 3.2.2 The line element 15 3.2.3 Planetary orbits and the perihelion shift 16 3.2.4 The trajectory of a photon 17 3.2.5 Gravitational waves 17 3.2.6 Cosmology 17 4. Oscillations 18 4.1 Harmonic oscillations 18 4.2 Mechanic oscillations 18 4.3 Electric oscillations 19 4.4 Waves in long conductors 19 4.5 Coupled conductors and transformers 19 4.6 Pendulums 19 5. Waves 20 5.1 The wave equation 20 5.2 Solutions of the wave equation 20 5.2.1 Plane waves 20 5.2.2 Spherical waves 21 5.2.3 Cylindrical waves 21 5.2.4 The general solution in one dimension 21 5.3 The stationary phase method 21 5.4 Green functions for the initial-value problem 22 5.5 Waveguides and resonating cavities 22 5.6 Non-linear wave equations 23 6. Optics 24 6.1 The bending of light 24 6.2 Paraxial geometrical optics 24 6.2.1 Lenses 24 6.2.2 Mirrors 25 6.2.3 Principal planes 25 6.2.4 Magnification 25 6.3 Matrix methods 25 6.4 Aberrations 26 6.5 Reflection and transmission 26 6.6 Polarization 27 6.7 Prisms and dispersion 27 6.8 Diffraction 28 6.9 Special optical effects 28 6.10 The Fabry-Perot interferometer 29 7. Statistical physics 30 7.1 Degrees of freedom 30 7.2 The energy distribution function 30 7.3 Pressure on a wall 31 7.4 The equation of state 31 7.5 Collisions between molecules 32 7.6 Interaction between molecules 32 8. Thermodynamics 33 8.1 Mathematical introduction 33 8.2 Definitions 33 8.3 Thermal heat capacity 33 8.4 The laws of thermodynamics 34 8.5 State functions and Maxwell relations 34 8.6 Processes 35 8.7 Maximal work 36 8.8 Phase transitions 36 8.9 Thermodynamic potential 37 8.10 Ideal mixtures 37 8.11 Conditions for equilibrium 37 8.12 Statistical basis for thermodynamics 38 8.13 Application to other systems 38 9. Transport phenomena 39 9.1 Mathematical introduction 39 9.2 Conservation laws 39 9.3 Bernoulli's equations 41 9.4 Characterising of flows with dimensionless numbers 41 9.5 Tube flows 42 9.6 Potential theory 42 9.7 Boundary layers 43 9.7.1 Flow boundary layers 43 9.7.2 Temperature boundary layers 43 9.8 Heat conductance 44 9.9 Turbulence 44 9.10 Self organization 44 10. Quantum physics 45 10.1 Introduction to quantum physics 45 10.1.1 Black body radiation 45 10.1.2 The Compton effect 45 10.1.3 Electron diffraction 45 10.2 Wave functions 45 10.3 Operators in quantum physics 45 10.4 The uncertainty principle 46 10.5 The Schr\"odinger equation 46 10.6 Parity 46 10.7 The tunnel effect 47 10.8 The harmonic oscillator 47 10.9 Angular momentum 47 10.10 Spin 48 10.11 The Dirac formalism 48 10.12 Atomic physics 49 10.12.1 Solutions 49 10.12.2 Eigenvalue equations 49 10.12.3 Spin-orbit interaction 49 10.12.4 Selection rules 50 10.13 Interaction with electromagnetic fields 50 10.14 Perturbation theory 50 10.14.1 Time-independent perturbation theory 50 10.14.2 Time-dependent perturbation theory 51 10.15 N-particle systems 51 10.15.1 General 51 10.15.2 Molecules 52 10.16 Quantum statistics 52 11. Plasma physics 54 11.1 Introduction 54 11.2 Transport 54 11.3 Elastic collisions 55 11.3.1 General 55 11.3.2 The Coulomb interaction 56 11.3.3 The induced dipole interaction 56 11.3.4 The centre of mass system 56 11.3.5 Scattering of light 56 11.4 Thermodynamic equilibrium and reversibility 57 11.5 Inelastic collisions 57 11.5.1 Types of collisions 57 11.5.2 Cross sections 58 11.6 Radiation 58 11.7 The Boltzmann transport equation 59 11.8 Collision-radiative models 60 11.9 Waves in plasma's 60 12. Solid state physics 62 12.1 Crystal structure 62 12.2 Crystal binding 62 12.3 Crystal vibrations 63 12.3.1 A lattice with one kind of atoms 63 12.3.2 A lattice with two kinds of atoms 63 12.3.3 Phonons 63 12.3.4 Thermal heat capacity 64 12.4 Magnetic field in the solid state 65 12.4.1 Dielectrics 65 12.4.2 Paramagnetism 65 12.4.3 Ferromagnetism 65 12.5 Free electron Fermi gas 66 12.5.1 Thermal heat capacity 66 12.5.2 Electric conductance 66 12.5.3 The Hall-effect 66 12.5.4 Thermal heat conductivity 67 12.6 Energy bands 67 12.7 Semiconductors 67 12.8 Superconductivity 68 12.8.1 Description 68 12.8.2 The Josephson effect 69 12.8.3 Flux quantisation in a superconducting ring 69 12.8.4 Macroscopic quantum interference 69 12.8.5 The London equation 70 12.8.6 The BCS model 70 13. Theory of groups 71 13.1 Introduction 71 13.1.1 Definition of a group 71 13.1.2 The Cayley table 71 13.1.3 Conjugated elements, subgroups and classes 71 13.1.4 Isomorfism and homomorfism; representations 72 13.1.5 Reducible and irreducible representations 72 13.2 The fundamental orthogonality theorem 72 13.2.1 Schur's lemma 72 13.2.2 The fundamental orthogonality theorem 72 13.2.3 Character 72 13.3 The relation with quantum mechanics 73 13.3.1 Representations, energy levels and degeneracy 73 13.3.2 Breaking of degeneracy with a perturbation 73 13.3.3 The construction of a basefunction 73 13.3.4 The direct product of representations 74 13.3.5 Clebsch-Gordan coefficients 74 13.3.6 Symmetric transformations of operators, irreducible tensor operators 74 13.3.7 The Wigner-Eckart theorem 75 13.4 Continuous groups 75 13.4.1 The 3-dimensional translation group 75 13.4.2 The 3-dimensional rotation group 76 13.4.3 Properties of continuous groups 76 13.5 The group SO(3) 77 13.6 Applications to quantum mechanics 78 13.6.1 Vectormodel for the addition of angular momentum 78 13.6.2 Irreducible tensoroperators, matrixelements and selection rules 78 Some examples of the behaviour of operators under SO(3) 78 Selection rules for dipole transitions 79 Land\'e -equation for the anomalous Zeeman splitting 79 13.7 Applications to particle physics 79 14. Nuclear physics 81 14.1 Nuclear forces 81 14.2 The shape of the nucleus 82 14.3 Radioactive decay 82 14.4 Scattering and nuclear reactions 83 14.4.1 Kinetic model 83 14.4.2 Quantum mechanical model for n-p scattering 83 14.4.3 Conservation of energy and momentum in nuclear reactions 84 14.5 Radiation dosimetry 84 15. Quantum field theory & Particle physics 85 15.1 Creation and annihilation operators 85 15.2 Classical and quantum fields 85 15.3 The interaction picture 86 15.4 Real scalar field in the interaction picture 86 15.5 Charged spin-0 particles, conservation of charge 87 15.6 Field functions for 1/2-particles 87 15.7 Quantization of spin-1/2 fields 88 15.8 Quantization of the electromagnetic field 89 15.9 Interacting fields and the S-matrix 89 15.10 Divergences and renormalization 90 15.11 Classification of elementary particles 90 15.12 P and CP-violation 92 15.13 The standard model 93 15.13.1 The electroweak theory 93 15.13.2 Spontaneous symmetry breaking: the Higgs mechanism 94 15.13.3 Quantumchromodynamics 94 15.14 Pathintegrals 95 15.15 Unification and quantum gravity 95 16. Astrophysics 96 16.1 Determination of distances 96 16.2 Brightness and magnitudes 96 16.3 Radiation and stellar atmospheres 97 16.4 Composition and evolution of stars 97 16.5 Energy production in stars 98 The Nabla operator 99 The SI units 100 but this particular download is a pdf file so I don't know how accessible it will be. I haven't used any of these resources myself, so caveat emptor. hth Martin

`----- Original Message -----`

`From: "Tyler Littlefield" <tyler@xxxxxxxxxxxxx>`

To: <programmingblind@xxxxxxxxxxxxx> Sent: Wednesday, April 22, 2009 5:07 AM Subject: accesible math resources Hello all, I wanted to get in to some design with physics, building simulations, etc. I had some ideas for some fun games, though I have a problem. I want to learn about vectors, trig, calc, etc. Are there any accessible math resources you guys used? I do great if I can sit down and teach myself, or if I can understand the problem, it's just getting everything that's the issue. Second, would someone happen to have a list of formulas for physics calculations? I'd like to play around with some of those. I'd also like to find a decent calculator (preferably software) that will do what I set it to, using variables and etc. I heard about matlab, but I believe that costs. I just want to play around with it, so investing cash isn't an option at this point. It might, if I had the cash to invest, but that just opens up a whole new set of doors(problems) Last, I'd like to learn how algos work such as compression and encryption. All the info on these I've found are decent, but they tend to show their formulas in graphics, which is no help at all. Thanks, Tyler Littlefield Web: tysdomain.com email: tyler@xxxxxxxxxxxxx My programs don't have bugs, they're called randomly added features. __________

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**Follow-Ups**:**Re: accesible math resources***From:*black ares

**References**:**accesible math resources***From:*Tyler Littlefield

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- » Re: accesible math resources - Zach
- » Re: accesible math resources - Tyler Littlefield
- » Re: accesible math resources - Zach