1 Vector and tensor ANALYSIS
1.1 Cartesian coordinates in space E3, their transformations and invariants,
Einstein summation convention (opak.)
1.2 General curvilinear coordinates, covariant and contravariant coordinates
vectors (opak.)
1.3 Tensors in E3, their algebra, reduction of order tensor contractions
tensor invariants
1.4 Physical field as a scalar, vector or tensor function
argument vector in E3
1.5 Derivation of three-dimensional tensor fields, increase and decrease tensor
order derivatives
6.1 Differential operator "nabla" as gradient "grad" field
1.7 Differential divergence operator as a "wonder" field
8.1 Differential rotation operator as "rot" vector field
1.9 Laplace differential operator of second order "Delta"
1.10 Gauss divergence theorem the vector field
1.11 Stokes theorem on the rotation of the vector field
1.12 Directional and substancionální derivation, a generalized balance equation
(Continuity)
2. Differential Equations in Physics
2.1 Description of physical phenomena, methods of infinitesimal calculus, compilation
differential equations based on analysis of physical phenomena
2.2 Newton's equation of motion - movement in the field scalar potential
3.2 Newton's equation of motion - an oscillator, damped and forced oscillations
4.2 Diffusion equation
2.5 Heat equation
6.2 Euler's equation
2.7 Stokes equations
8.2 Laplace equation
2.9 Wave equation
2.10 Schödingerova wave equations - harmonic oscillator
3. FUNCTIONS as vectors in a Hilbert space
3.1 The development function in an infinite number of known elementary functions, Cauch and d'Alembertovo convergence criterion
3.2 Taylor expansion of functions
3.3 Fourier development functions, Fourier integral and Fourier transform
3.4 Geometric interpretation of the development - based on vector elementary functions
Hilbert space, symbolism Dirackova
3.5 Operators in Hilbert space commutation relations, the matrix elements
3.6 Eigenvalues and operator functions
1.1 Cartesian coordinates in space E3, their transformations and invariants,
Einstein summation convention (opak.)
1.2 General curvilinear coordinates, covariant and contravariant coordinates
vectors (opak.)
1.3 Tensors in E3, their algebra, reduction of order tensor contractions
tensor invariants
1.4 Physical field as a scalar, vector or tensor function
argument vector in E3
1.5 Derivation of three-dimensional tensor fields, increase and decrease tensor
order derivatives
6.1 Differential operator "nabla" as gradient "grad" field
1.7 Differential divergence operator as a "wonder" field
8.1 Differential rotation operator as "rot" vector field
1.9 Laplace differential operator of second order "Delta"
1.10 Gauss divergence theorem the vector field
1.11 Stokes theorem on the rotation of the vector field
1.12 Directional and substancionální derivation, a generalized balance equation
(Continuity)
2. Differential Equations in Physics
2.1 Description of physical phenomena, methods of infinitesimal calculus, compilation
differential equations based on analysis of physical phenomena
2.2 Newton's equation of motion - movement in the field scalar potential
3.2 Newton's equation of motion - an oscillator, damped and forced oscillations
4.2 Diffusion equation
2.5 Heat equation
6.2 Euler's equation
2.7 Stokes equations
8.2 Laplace equation
2.9 Wave equation
2.10 Schödingerova wave equations - harmonic oscillator
3. FUNCTIONS as vectors in a Hilbert space
3.1 The development function in an infinite number of known elementary functions, Cauch and d'Alembertovo convergence criterion
3.2 Taylor expansion of functions
3.3 Fourier development functions, Fourier integral and Fourier transform
3.4 Geometric interpretation of the development - based on vector elementary functions
Hilbert space, symbolism Dirackova
3.5 Operators in Hilbert space commutation relations, the matrix elements
3.6 Eigenvalues and operator functions