Eleonoraagostinelli
Op deze pagina vind je alle documenten, voordeelbundels en oefenvragen die worden aangeboden door verkoper eleonoraagostinelli.
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11 items

Mathematical Methods for PDEs
The package starts showing the solution of important PDEs, then it focuses on ODEs and how to find series solutions, to then go back to PDEs and focus on how to solve PDEs using separation of variables and reducing them to ODEs that can be easily solved. Finally it show how integral transforms can be used to solved PDEs
- Voordeelbundel
- • 4 items •
- Integral Transforms 2022/23 • College aantekeningen
- General approach to solve separation of variables problems • College aantekeningen
- Orthogonality and eigenvalue problems • College aantekeningen
- Series solutions to ODEs: the Frobenius method • College aantekeningen
The package starts showing the solution of important PDEs, then it focuses on ODEs and how to find series solutions, to then go back to PDEs and focus on how to solve PDEs using separation of variables and reducing them to ODEs that can be easily solved. Finally it show how integral transforms can be used to solved PDEs

Introduction to PDEs and separation of variables
This chapter introduces important PDEs such as the heat equation, wave equation, Laplace equation and Helmholtz equation and gives examples of how to solve them using separation of variables. Then it introduces the 3 coordinate systems of polars, cylindrical polars and spherical, showing how to go from one system to another. Finally it shows how separation of variables can be used to to solve some important types of equation such as the Euler-type equation, the Bessel's equation and the Legendr...
- College aantekeningen
- • 5 pagina's •
This chapter introduces important PDEs such as the heat equation, wave equation, Laplace equation and Helmholtz equation and gives examples of how to solve them using separation of variables. Then it introduces the 3 coordinate systems of polars, cylindrical polars and spherical, showing how to go from one system to another. Finally it shows how separation of variables can be used to to solve some important types of equation such as the Euler-type equation, the Bessel's equation and the Legendr...

Series solutions to ODEs: the Frobenius method
This chapter focuses on ODEs, which are essential when solving PDEs. In particular it show how to solve ordinary differential equation using the Frobenius method, i.e. finding a series solution to the ODE.
- Voordeelbundel
- College aantekeningen
- • 13 pagina's •
This chapter focuses on ODEs, which are essential when solving PDEs. In particular it show how to solve ordinary differential equation using the Frobenius method, i.e. finding a series solution to the ODE.

Orthogonality and eigenvalue problems
This document introduces to Sturm-Liouville eigenvalue problems, regular, singular and periodic, to find eigenvalues and eigenfunctions of partial differential equations. In introduces the concept of orthogonality of eigenfunctions. Then it focuses on how to generate the generalised Fourier series expansion of a function, and in particular the Fourier-Bessel and Fourier-Legendre series. Finally, it introduces inhomogeneous problems and how to solve them.
- Voordeelbundel
- College aantekeningen
- • 10 pagina's •
This document introduces to Sturm-Liouville eigenvalue problems, regular, singular and periodic, to find eigenvalues and eigenfunctions of partial differential equations. In introduces the concept of orthogonality of eigenfunctions. Then it focuses on how to generate the generalised Fourier series expansion of a function, and in particular the Fourier-Bessel and Fourier-Legendre series. Finally, it introduces inhomogeneous problems and how to solve them.

General approach to solve separation of variables problems
Providing a general approach to solve problems involving partial differential equations using the separation of variables method
- Voordeelbundel
- College aantekeningen
- • 7 pagina's •
Providing a general approach to solve problems involving partial differential equations using the separation of variables method

Integral Transforms 2022/23
Introduction to Fourier and Laplace transforms and their reverse transform and their use to solve partial differential equations
- Voordeelbundel
- College aantekeningen
- • 13 pagina's •
Introduction to Fourier and Laplace transforms and their reverse transform and their use to solve partial differential equations

Introduction to Applied stochastic methods
This package gives an introduction to applied stochastic methods: starting with the Brownian process, stochastic calculus and SDEs, to exploring the connection from PDEs and SDEs and finding methods to approximate complex systems of SDEs to simpler and solvable ones. Finally it introduces linear response theory, to predict the response of a system
- Voordeelbundel
- • 4 items •
- Stochastic differential equations • College aantekeningen
- Approximation methods for stochastic differential equations • College aantekeningen
- From SDEs to PDEs and back • College aantekeningen
- Linear response theory • College aantekeningen
This package gives an introduction to applied stochastic methods: starting with the Brownian process, stochastic calculus and SDEs, to exploring the connection from PDEs and SDEs and finding methods to approximate complex systems of SDEs to simpler and solvable ones. Finally it introduces linear response theory, to predict the response of a system

Linear response theory
Providing methods to use the known past behaviour of a stochastic process in order to predict its response to a perturbation
- Voordeelbundel
- College aantekeningen
- • 4 pagina's •
Providing methods to use the known past behaviour of a stochastic process in order to predict its response to a perturbation

From SDEs to PDEs and back
Investigating the connection between stochastic differential equations and partial differential equations in order to use PDEs to solve or find characteristics of the SDE and viceversa
- Voordeelbundel
- College aantekeningen
- • 18 pagina's •
Investigating the connection between stochastic differential equations and partial differential equations in order to use PDEs to solve or find characteristics of the SDE and viceversa

Approximation methods for stochastic differential equations
Providing methods to approximate complex systems of stochastic differential equations to simpler ones that can be solved
- Voordeelbundel
- College aantekeningen
- • 15 pagina's •
Providing methods to approximate complex systems of stochastic differential equations to simpler ones that can be solved