MATHEMATICAL PHYSICS

BASIC ELECTRICAL ENGINEERING

RCL circuit - Physics Lab FISI 3014 -march 2008

Fourier sine transform

Power at the load using Complex Fortran

AC circuits under steady state from Schaum's Basic Electrical Engineering prob 3.8 using FORTRAN complex code

Average power at the load

COMPLEX NUMBERS RCL CIRCUIT

FORTRAN-Use of complex numbers in Impedance and Admittance

The Catenary

Schaum's BEE prob 6.13

Schaum's Basic Electrical Engineering, prob 5.11 - Mutual Inductance

Schaum's BEE prob 15.7 -Automobile suspension

Coupled circuits oct. 17 2006

Surge analysis (oct 15 2006)

EXAMPLE OF FINITE ELEMENT METHOD

Solution of Laplace Equation by Iterations (semi circle problem)

Potential in a semi circle (sept 22 , 2006)

Plot of equipotentials in a semi circle

Control Criteria - Schaum's BEE problem 17.8

A square pulse applied to an RC circuit

Schaum's Outline BEE problem 3.7

Schaum's Outline BEE problem 4.19

Percent overshoot of a capacitor-Schaum's BEE problem 4.10

delx(del(phi))=0 , del*(delxA)=0

Schaum's Outline BEE problem 4.3

Schaum's Outline BEE problem 5.4

Schaum's Outline of Basic Electrical Engineering-problem 5.13

FORCED RCL circuit

Driven RLC Circuit

Fourier coefficients

RCL CIRCUIT

RCL circuit with a delta function voltage imput

RC Circuit-part2

RC CIRCUIT - part 1

Circuit Analysis-Schaum's BEE prob 6.10

Schaum's Outline-Basic Electrical Engineering prob 6.10

Schaum's Outline-Basic Electrical Engineering prob 6.11

CLASSICAL MECHANICS / MECHANICAL ENGINEERING

The lengthening pendulum

Dominant Eigenvalue of a Matrix

Green?s Function of the String Problem (V1)

The Duffing equation-MATLAB

Solution of d^2y/dt^2 = -y + (1/6) y^3 +2 sin(3wt)

The Poynting - Robertson effect (meteoritic dust)

Planetary orbits in cartesian coordinates

Harmonic oscillator

Solution of mdv/dt = -mg -bv

Isynchronous motion example 1

Force Free Motion of a Symmetric Top

Beam deflection equation-example 1

Spectral Resolution of the Double Pendulum

A Problem of Dynamic System Modeling

QUANTUM PHYSICS

NEON ONE PARAMETER VARIATIONAL CALCULATION

Electron repulsion ?Vee- one parameter approximations

Plot of exchange energy term K1s2s

Approximation to the exchange energy term K1s2s

Total energy of lithium in the Hartree approximation

Total energy of lithium with a single variational parameter

Ground state of the modified -a/x2 potential ( part 3)

Ground state of the modified -a/x2 potential ( part 2)

Ground state of the modified -a/x2 potential ( part 1)

Energy Levels of the -1/x^(1/2) Potential

Polynomial fit of the solution to the Thomas-Fermi Equation

Kinetic energy in the Thomas-Fermi model

White dwarf stars equation

The Thomas-Fermi equation V2

The JWKB Method applied to string vibrations

The Variational Principle with a Difference Equation

Electron - electron repulsion by Monte Carlo Method

The Ising Model in One Dimension

Linear Chain of Atoms

The Kronig Penney model

Muonic atom 2P energy level with a finite size nucleus

Muonic atom 2S energy level with a finite size nucleus

Muonic atom with finite size nuclei

Dirac delta function potential

Deep well with a single energy level

THE WKB APPROXIMATION

Energy eigenvalues of a quartic oscillator

Bound states in weak attractive potentials

QUARK CONFINEMENT (u quark) part 1

Barrier reflection for E < V0 (version 2.)

Barrier reflection for E > V0 (a numerical treatment)

Potential barrier

Carbon ground state total energy

Boron ground state total energy

Beryllium ground state total energy

Lithium Total Energy

Lithium Ionization Potential

THE BREIT PAULI EQUATION

Momentum space wave functions (no.1)

Morse Potential- H2 vibrational energy levels

The Stark effect in one dimensional hydrogen

Vibrational energy levels for the hydrogen molecule

The H2+ molecule ion

The X-alpha method -helium atom

Total energies for the 1s2s - 1S state of heliumlike ions

Eigenvalues via Asymptotic Solutions

Nonorthogonal Hartree - Fock

THE ROOTHAAN EQUATIONS

The Linear Variational Method - two STO basis set

Neon atom- a density functional calculation

Lithium atom ,a semi Hartree-Fock calculation

Beryllium - a density functional calculation

Effective potential for lithium

Schrodinger's equation-harmonic oscillator

DIRAC EQUATION-NUMERICAL SOLUTION

Klein Gordon equation

THE HYDROGEN MOLECULE

Effective repulsive potential in Helium

HYDROGENIC ATOMS

QUANTUM OSCILLATOR

THE EXCHANGE INTEGRAL K(1s,2s)

Carbon atom - a density functional calculation

INFINITE AND SEMI INFINITE WELL POTENTIAL

Variational calculation in momentum space

DEUTERON

Double square well potential

SQUARE WELL POTENTIALS

One Dimensional Lithium

One Dimensional Hydrogenic Atom ( Variational treatment)

Neutron energy eigenvalues s and p states

One dimensional helium - part 3

Chemical Kinetics example 1

CALCULUS

LECTURE 1 - The Derivative Algorithm

LECTURE 2 - Derivative of a polynomial and derivative of a product

LECTURE 3 Derivative the sine function and cosine functions

THE SPECIAL THEORY OF RELATIVITY

Lecture 2

Lecture 3

Lecture 4

Lecture 5

GENERAL THEORY OF RELATIVITY -six lectures

Trajectory of a light ray in the Schwarschild Field

Cosmological solutions-part 1

White dwarf stars equation

NUMERICAL ANALYSIS

Applications of the Cayley ?Hamilton Theorem

Solution of the equation d2x/dt2 +c1(dx/dt) +c2 x = c3 sgn(dx/dt)

Dominant Eigenvalue of a Matrix

White dwarf stars equation

Green?s Function of the String Problem (V1)

Fourier sine transform of step function of width b

Fourier sine transform

Numerical solution of the Differential Equation x**2(d2y/dx2)-3.*x(dy/dx) -5.*y=0

Differential Equation of the First Order and Second Degree V 3.0

Differential Equation of the First Order and Second Degree V 2.0

Differential Equation of the First Order and Second Degree

Clairaut Equation V.1

Random number generator (dec 2007)

The Laguerre Equation

Volume of a sphere's octant by Monte Carlo method

Pair of total differential equations in three variables

The Riccati equation

The Binomial Distribution

Linear Pursuit

The Logistic Curve

Calculation of the elliptic function F(phi,k),with phi fixed, k variable

The Elliptic Functions F(phi,k) and E(phi,k)

The Gauss Equation

Cauchy - Euler equidimensional differential equation

Simultaneous Linear differential equations

Planetary orbits -Cartesian coordinates

Associated Legendre Functions

Legendre polynomials

Max-Min with constraint

Max-Min Algorithm

Muonic atom with finite size nuclei

Dirac delta function potential

Deep well with a single energy level

Period formula for the cubic oscillator

Harmonic oscillator with centripetal barrier, the classical and quantum case

Numerical integration of the classical oscillator period formula

HOCB-Harmonic oscillator with centripetal barrier , classical case

Energy eigenvalues of a quartic oscillator

Isotonic oscillator

Projectile motion with air resistance quadratic in speed

Isynchronous motion example 1

PREDATOR PREY POPULATION aug. 2007

Fresnel Integrals (Analytical)

Fresnel integral sin(x**2)

Chebyshev polynomials of the second kind

Chebyshev polynomials of the first kind

Chebyshev Polynomial T2

Definite integral of trigonometric functions// I= $dtheta/(1+a sin(theta) ) , from 0 to 2pi

Improper integrals involving trigonometric functions//Integral of cos(x)dx/(x**2+1.)**2 from -infinity to infinty

Force Free Motion of a Symmetric Top

Two end point problem:The solution of y''+xy'+y=2x that passes through the points (0,1) and (1,0)...

Two-end-point problem y =0 , y''=0 at x= 0;y=0 y'=0 at x=L

Pendulum with linear damping
d^2y/dt^2=-a dy/dt- b sin(y)

Parabolic approximation to the heat equation, T(x,0)=50 (example 2)

Parabolic approximation to the heat equation

Determinant of a Matrix

Three dimensional max-min optimization

Optimization in two dimensions

Optimization of f(x1,x2)=x1**3 + x2**3-2.*x1**2+3.*x2**2-8.

Optimization of f= (x1-sin(x1+x2))**2 +(x2-cos(x1-x2))**2

MATLAB CODES SECTION

Approximation to the exchange energy term K1s2s

The First Painlev項quation

The Second Painlev項quation

The Linear Pursuit Problem

The Logistic Curve

The Duffing equation-MATLAB

Solution of d^2y/dt^2 = -y + (1/6) y^3 +2 sin(3wt)

The Gauss Equation

Alternation of decay and growth

Decay or growth with oscillations

Hermite differential equation : Hermite polynomials

Cauchy Linear Differential Equation (version 1)

Legendre Polynomials (MATLAB version)

Gravitational problem in one dimension

Function with saddle point

The catenary

The cable deflection problem

Eigenvalues of fourth order matrix

Eigenvalues and eigenvectors

Laplace equation

The Predator-Prey Population Equation

The infection equation , dy/dt= k*y(m- y)

Ritz method in one dimension , solution of d^2y/dx^2= - x^2

Fourth order DE , d^4y/dx^4= 24

Second order boundary value problem d2 y/dx2 =(1./8.){32.+2x3 -y*(dy/dx ) }

One dimensional boundary value problem, y''= - x**2 version 3 (solution by iteration)

One dimensional boundary value problem, y''= - x**2

Chemical kinetics (nov 21)

Boltzmann distribution -part 1

THE FOUCALT PENDULUM

Van der Pol equation (nov 18 2006)

RCL with a sinusoidal source

RCL circuit nov14

Stiff Differential equation ,y'=-100y +99 exp(-x)

Stiff differential equation dy/dt= ay**2-by**3

RC circuit example 1

Simple pendulum

Periodic force

Coupled Oscillators

The hydrogen molecule-ion

Gravitational potential

Coupled Oscillators

The Hydrogen Atom-asymptotic method

Schroginger's equation -infinite well

Power method

The heat equation (diffusion equation)

Classic oscillator

Equation of motion , mdv/dt= -mg +kv**2

Damped Oscillator

Gravitational orbits

Complex Variables - a synopsis

COMPLEX VARIABLES

Complex variables (synopsis)

Integral cos^3(3x)dx/((5.-4.*cos(2x))

Definite integral of trigonometric functions// I= $dtheta/(1+a sin(theta) ) , from 0 to 2pi

Improper integrals involving trigonometric functions//Integral of cos(x)dx/(x**2+1.)**2 from -infinity to infinty

Integral of tan(z)dz

Integration of (exp(iz)/z) dz

Integration of dz(5z-2)/( z(z-1))

Complex variable integration of (2x**2- 1) /( x**4+5*x**2+4) dx