Differential Equations, Extension and Oscillation Processes, Wave Theory Real part surface with edge of regression The non-integrabel pfaffian problem ydx - xdy + k dz = 0 Fresnel wave surface for optic uniaxial crystals Fresnel wave surface for optic uniaxial crystals Fresnel wave surface for optic biaxial crystals Fresnel wave surface for optic biaxial crystals Fresnel wave surface for optic biaxial crystals Heat conduction in a stick; single source Heat conduction in a stick; double source Periodic heat conduction in a stick 6 spheres with the + and - regions of the easiest spherical functions 6 spheres with the + and - regions of Lamé products Lissajous tuning fork curves. 18 stereo's with explanation 20 stereo's Lissajous curves Picked string (violin string) Picked string (violin string) Picked string Vibrating string Hammered string (Piano string) Hammered string (Piano string) Impulsion transversala d'une barre elastique appuyee aux extremites et heurtee Slide: Boundary value problem Slide: Boundary value problem Slide: Boundary value problem Slide: Boundary value problem Slide: Boundary value problem Slide: Boundary value problem Slide: Boundary value problem Slide: Mode of motion of the hammered string Slide: Mode of motion of the hammered string Slide: Picked strings Slide: Picked strings Slide: Hammered strings Slide: Hammered strings Slide: Bowed strings Slide: Bowed strings Slide: Bowed strings Slide: Hammered strings Slide: Singularities of a differential equation of 1. order Slide: Graphical integration of a differential equation Slide: Singularities of a differential equation of 1. order Slide: Singularities of a differential equation of 1. order Slide: Source functions of heat conduction Slide: Source functions of heat conduction, 1D Slide: Source functions of heat conduction, 2D Slide: Source functions of heat conduction, 3D Slide: The Bessel function Slide: The Bessel function Slide: Altitude chart of the Bessel function Slide: Relief of the Bessel function Slide: Partial derivative of the Bessel function Slide: Altitude chart of the Hankel function Slide: Relief of the Hankel function Slide: Relief of the Hankel function Slide: Altitude chart of the Hankel function Slide: Relief of the Hankel function Slide: Family of boundary-curves Slide: When have we to cumpute with the exceptional series? Slide: Bessel funcions of the order p=+-1/3 Slide: Sum and difference of two Bessel functions Slide: Relief of the function exp(i*cos(omega)) Slide: Relief of an exponential function Slide: The Lommel-Weber function Slide. Bessel function Slide: Bessel function against the plane p,x Slide: Bessel functions Slide: Bessel functions Slide: Bessel functions Slide: Bessel functions Slide: Zeros of Bessel functions Slide: Zeros of Bessel functions Slide: A function against the square of the half argument Slide: Zeros of Bessel functions Slide: Steepness at the zeros of Bessel functions of large order Slide: Extreme values of Bessel functions of larger order Slide: Position of the first function values for Bessel functions Slide: Bessel function x=p and x=p+1 Slide: Bessel functions of constant argument Slide: Bessel functions of constant argument Slide: Bessel functions of larger order than one Slide: The function Lambda(x) Slide: Bessel and Neumann function for x=p and x=p+1 Slide: Neumann function Slide: Neumann function Slide: Neumann function Slide: Hankel function H(1)(x) Slide: Zeros of the Neumann function Slide: Inversion of a function Slide: Inversion a function Slide: Inversion of a function Slide: Inversion of afunction Slide: Curves Slide: Bessel functions for pure imaginary argument Slide: Bessel functions for pure imaginary argument Slide: Bessel functions for fixed pure imaginary argument Slide: Bessel functions for fixed pure imaginary argument Slide: Hankel functions for pure imaginary argument Slide: Bessel function of order 0 Slide: Bessel function of order 0 Slide: Bessel function of order 1 Slide: Bessel function of order 1 Slide: Hankel function of order 0 Slide: Hankel function of order 0 Slide: H(1)(i1/2)=hi&eta Slide: H(1)(i1/2)=hi&eta Slide: The arrows (...) going out perpendicularly from the r-axis Slide: The arrows (...) going out perpendicularly from the r-axis Slide: J(r*sqrt(i))=b*i^beta Slide: J(r*sqrt(i))=b*i^beta Slide: J_0(r*sqrt(i))/J_1(r*sqrt(i)) Slide: H(1)_0(r*sqrt(i))/H(1)_1(r*sqrt(i)) Slide: The arrows (...) going out perpendicularly from the r-axis
Göttingen Collection of Mathematical Models and Instruments
Göttingen Collection of Mathematical Models and Instruments
Real part surface with edge of regression
The non-integrabel pfaffian problem ydx - xdy + k dz = 0
Fresnel wave surface for optic uniaxial crystals
Fresnel wave surface for optic uniaxial crystals
Fresnel wave surface for optic biaxial crystals
Fresnel wave surface for optic biaxial crystals
Fresnel wave surface for optic biaxial crystals
Heat conduction in a stick; single source
Heat conduction in a stick; double source
Periodic heat conduction in a stick
6 spheres with the + and - regions of the easiest spherical functions
6 spheres with the + and - regions of Lamé products
Lissajous tuning fork curves. 18 stereo's with explanation
20 stereo's Lissajous curves
Picked string (violin string)
Picked string (violin string)
Picked string
Vibrating string
Hammered string (Piano string)
Hammered string (Piano string)
Impulsion transversala d'une barre elastique appuyee aux extremites et heurtee
Slide: Boundary value problem
Slide: Boundary value problem
Slide: Boundary value problem
Slide: Boundary value problem
Slide: Boundary value problem
Slide: Boundary value problem
Slide: Boundary value problem
Slide: Mode of motion of the hammered string
Slide: Mode of motion of the hammered string
Slide: Picked strings
Slide: Picked strings
Slide: Hammered strings
Slide: Hammered strings
Slide: Bowed strings
Slide: Bowed strings
Slide: Bowed strings
Slide: Hammered strings
Slide: Singularities of a differential equation of 1. order
Slide: Graphical integration of a differential equation
Slide: Singularities of a differential equation of 1. order
Slide: Singularities of a differential equation of 1. order
Slide: Source functions of heat conduction
Slide: Source functions of heat conduction, 1D
Slide: Source functions of heat conduction, 2D
Slide: Source functions of heat conduction, 3D
Slide: The Bessel function
Slide: The Bessel function
Slide: Altitude chart of the Bessel function
Slide: Relief of the Bessel function
Slide: Partial derivative of the Bessel function
Slide: Altitude chart of the Hankel function
Slide: Relief of the Hankel function
Slide: Relief of the Hankel function
Slide: Altitude chart of the Hankel function
Slide: Relief of the Hankel function
Slide: Family of boundary-curves
Slide: When have we to cumpute with the exceptional series?
Slide: Bessel funcions of the order p=+-1/3
Slide: Sum and difference of two Bessel functions
Slide: Relief of the function exp(i*cos(omega))
Slide: Relief of an exponential function
Slide: The Lommel-Weber function
Slide. Bessel function 
Slide: Bessel function against the plane p,x
Slide: Bessel functions
Slide: Bessel functions
Slide: Bessel functions
Slide: Bessel functions
Slide: Zeros of Bessel functions
Slide: Zeros of Bessel functions
Slide: A function against the square of the half argument
Slide: Zeros of Bessel functions
Slide: Steepness at the zeros of Bessel functions of large order
Slide: Extreme values of Bessel functions of larger order
Slide: Position of the first function values for Bessel functions
Slide: Bessel function x=p and x=p+1
Slide: Bessel functions of constant argument
Slide: Bessel functions of constant argument
Slide: Bessel functions of larger order than one
Slide: The function Lambda(x)
Slide: Bessel and Neumann function for x=p and x=p+1
Slide: Neumann function
Slide: Neumann function
Slide: Neumann function
Slide: Hankel function H(1)(x)
Slide: Zeros of the Neumann function
Slide: Inversion of a function 
Slide: Inversion a function
Slide: Inversion of a function
Slide: Inversion of afunction
Slide: Curves
Slide: Bessel functions for pure imaginary argument
Slide: Bessel functions for pure imaginary argument
Slide: Bessel functions for fixed pure imaginary argument 
Slide: Bessel functions for fixed pure imaginary argument
Slide: Hankel functions for pure imaginary argument
Slide: Bessel function of order 0
Slide: Bessel function of order 0
Slide: Bessel function of order 1
Slide: Bessel function of order 1
Slide: Hankel function of order 0
Slide: Hankel function of order 0
Slide: H(1)(i1/2)=hi&eta
Slide: H(1)(i1/2)=hi&eta
Slide: The arrows (...) going out perpendicularly from the r-axis
Slide: The arrows (...) going out perpendicularly from the r-axis
Slide: J(r*sqrt(i))=b*i^beta
Slide: J(r*sqrt(i))=b*i^beta
Slide: J_0(r*sqrt(i))/J_1(r*sqrt(i))
Slide: H(1)_0(r*sqrt(i))/H(1)_1(r*sqrt(i))
Slide: The arrows (...) going out perpendicularly from the r-axis