Re: accesible math resources

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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