Talks:
First order equations, Cauchy problem, characteristic equations.
Cauchy problem for equations of higher degrees.
Classification equations of the second order.
Formulation of the classical equations given by physical phenomenon (formulation boundary and initial conditions) like: heat eq., diffusion eq., wave eq., Laplace and Poisson eq., etc.
Solution by method of characteristic.
Solution by Fourier method.
Solution by integral transformations.
Solution by Green function.
Maximal principle and uniqueness of solution.
Solution by method of potentials.
Seminars:
Examples of solutions of the classical partial differential equations, compare PDE and ODE.
Classification of the equations, reduction to the canonical form.
Formulation of the classical type eq and their boundary and initial conditions.
Solution of several eq. by characteristic method.
Solution of several eq. by Fourier method.
Solution of several eq. by Green functions.
Application of the Green function.
Solution of the uniqueness problem of the eq.
Solution of several eq. using potentials.
Solution of several eq. by using mathematical software.
Projects:
Students will solve standard problems based on typical equations and their applications.
First order equations, Cauchy problem, characteristic equations.
Cauchy problem for equations of higher degrees.
Classification equations of the second order.
Formulation of the classical equations given by physical phenomenon (formulation boundary and initial conditions) like: heat eq., diffusion eq., wave eq., Laplace and Poisson eq., etc.
Solution by method of characteristic.
Solution by Fourier method.
Solution by integral transformations.
Solution by Green function.
Maximal principle and uniqueness of solution.
Solution by method of potentials.
Seminars:
Examples of solutions of the classical partial differential equations, compare PDE and ODE.
Classification of the equations, reduction to the canonical form.
Formulation of the classical type eq and their boundary and initial conditions.
Solution of several eq. by characteristic method.
Solution of several eq. by Fourier method.
Solution of several eq. by Green functions.
Application of the Green function.
Solution of the uniqueness problem of the eq.
Solution of several eq. using potentials.
Solution of several eq. by using mathematical software.
Projects:
Students will solve standard problems based on typical equations and their applications.