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| Tekst źródłowy (English) | Tekst docelowy (English) |
|---|---|
| In order to help the reading of the next chapters, a quick classification of various mathematical problems encountered in the modelization of physical phenomena is proposed in the present chapter. | To help with the reading of the next chapters, this chapter provides a quick classification of various mathematical problems encountered in the modeling of physical phenomena. |
| More precisely, the problems considered in this chapter are those that can be reduced to the finding of the solution of a partial differential equation (PDE). | More precisely, the problems considered in this chapter are those that can be reduced to finding the solution of a partial deifferential equation(PDE). |
| Indeed, for many physicists, to provide a model of a phenomenon means to provide a PDE describing this phenomenon. | In fact, for many physicists, providing a model of a phenomenon means providing an EDP that describes that phenomenom. |
| They can be boundary problems, spectral problems, evolution problems. | They can be boundary, spectral problems, evolution problems. |
| General ideas about the methods of exact and approximate solving of those PDE is also proposed[1]. | General ideas about exact and approximate resolution methods for these PDs[1] are also proposed. |
| This chapter contains numerous references to the "physical" part of this book which justify the interest given to those mathematical problems. | This chapter contains numerous references to the "physics" part of this book which justify the interest given to these mathematical problems. |
| In classical books about PDE, equations are usually classified into three categories: hyperbolic, parabolic and elliptic equation. | In classic EDP textbooks, equations are generally classified into three categories: hiperbolic, parabolic and elliptic equations. |
| This classification is connected to the proof of existence and unicity of the solutions rather than to the actual way of obtaining the solution. | This classification is more linked to the proof of the existence and uniqueness of the solutions than to the actual way of obtaining the solution. |
| We present here another classification connected to the way one obtains the solutions: we distinguish mainly boundary problems and evolution problems. | Here we present another classification linked to the way in wich solutions are obtained: we distinguish mainly between boundary problems and evolution problems. |
| In order to help the reading of the next chapters, a quick classification of various mathematical problems encountered in the modelization of physical phenomena is proposed in the present chapter. | To help with the reading of the next chapters, this chapter provides a quick classification of various mathematical problems encountered in the modeling of physical phenomena. |
| More precisely, the problems considered in this chapter are those that can be reduced to the finding of the solution of a partial differential equation (PDE). | More precisely, the problems considered in this chapter are those that can be reduced to finding the solution of a partial deifferential equation(PDE). |
| Indeed, for many physicists, to provide a model of a phenomenon means to provide a PDE describing this phenomenon. | In fact, for many physicists, providing a model of a phenomenon means providing an EDP that describes that phenomenom. |
| They can be boundary problems, spectral problems, evolution problems. | They can be boundary, spectral problems, evolution problems. |
| General ideas about the methods of exact and approximate solving of those PDE is also proposed[1]. | General ideas about exact and approximate resolution methods for these PDs[1] are also proposed. |
| This chapter contains numerous references to the "physical" part of this book which justify the interest given to those mathematical problems. | This chapter contains numerous references to the "physics" part of this book which justify the interest given to these mathematical problems. |
| In classical books about PDE, equations are usually classified into three categories: hyperbolic, parabolic and elliptic equation. | In classic EDP textbooks, equations are generally classified into three categories: hiperbolic, parabolic and elliptic equations. |
| This classification is connected to the proof of existence and unicity of the solutions rather than to the actual way of obtaining the solution. | This classification is more linked to the proof of the existence and uniqueness of the solutions than to the actual way of obtaining the solution. |
| We present here another classification connected to the way one obtains the solutions: we distinguish mainly boundary problems and evolution problems. | Here we present another classification linked to the way in wich solutions are obtained: we distinguish mainly between boundary problems and evolution problems. |
| In order to help the reading of the next chapters, a quick classification of various mathematical problems encountered in the modelization of physical phenomena is proposed in the present chapter. | To help with the reading of the next chapters, this chapter provides a quick classification of various mathematical problems encountered in the modeling of physical phenomena. |
| More precisely, the problems considered in this chapter are those that can be reduced to the finding of the solution of a partial differential equation (PDE). | More precisely, the problems considered in this chapter are those that can be reduced to finding the solution of a partial deifferential equation(PDE). |
| Indeed, for many physicists, to provide a model of a phenomenon means to provide a PDE describing this phenomenon. | In fact, for many physicists, providing a model of a phenomenon means providing an EDP that describes that phenomenom. |
| They can be boundary problems, spectral problems, evolution problems. | They can be boundary, spectral problems, evolution problems. |
| General ideas about the methods of exact and approximate solving of those PDE is also proposed[1]. | General ideas about exact and approximate resolution methods for these PDs[1] are also proposed. |
| This chapter contains numerous references to the "physical" part of this book which justify the interest given to those mathematical problems. | This chapter contains numerous references to the "physics" part of this book which justify the interest given to these mathematical problems. |
| In classical books about PDE, equations are usually classified into three categories: hyperbolic, parabolic and elliptic equation. | In classic EDP textbooks, equations are generally classified into three categories: hiperbolic, parabolic and elliptic equations. |
| This classification is connected to the proof of existence and unicity of the solutions rather than to the actual way of obtaining the solution. | This classification is more linked to the proof of the existence and uniqueness of the solutions than to the actual way of obtaining the solution. |
| We present here another classification connected to the way one obtains the solutions: we distinguish mainly boundary problems and evolution problems. | Here we present another classification linked to the way in wich solutions are obtained: we distinguish mainly between boundary problems and evolution problems. |
| In order to help the reading of the next chapters, a quick classification of various mathematical problems encountered in the modelization of physical phenomena is proposed in the present chapter. | To help with the reading of the next chapters, this chapter provides a quick classification of various mathematical problems encountered in the modeling of physical phenomena. |
| More precisely, the problems considered in this chapter are those that can be reduced to the finding of the solution of a partial differential equation (PDE). | More precisely, the problems considered in this chapter are those that can be reduced to finding the solution of a partial deifferential equation(PDE). |
| Indeed, for many physicists, to provide a model of a phenomenon means to provide a PDE describing this phenomenon. | In fact, for many physicists, providing a model of a phenomenon means providing an EDP that describes that phenomenom. |
| They can be boundary problems, spectral problems, evolution problems. | They can be boundary, spectral problems, evolution problems. |
| General ideas about the methods of exact and approximate solving of those PDE is also proposed[1]. | General ideas about exact and approximate resolution methods for these PDs[1] are also proposed. |
| This chapter contains numerous references to the "physical" part of this book which justify the interest given to those mathematical problems. | This chapter contains numerous references to the "physics" part of this book which justify the interest given to these mathematical problems. |
| In classical books about PDE, equations are usually classified into three categories: hyperbolic, parabolic and elliptic equation. | In classic EDP textbooks, equations are generally classified into three categories: hiperbolic, parabolic and elliptic equations. |
| This classification is connected to the proof of existence and unicity of the solutions rather than to the actual way of obtaining the solution. | This classification is more linked to the proof of the existence and uniqueness of the solutions than to the actual way of obtaining the solution. |
| We present here another classification connected to the way one obtains the solutions: we distinguish mainly boundary problems and evolution problems. | Here we present another classification linked to the way in wich solutions are obtained: we distinguish mainly between boundary problems and evolution problems. |
| In order to help the reading of the next chapters, a quick classification of various mathematical problems encountered in the modelization of physical phenomena is proposed in the present chapter. | To help with the reading of the next chapters, this chapter provides a quick classification of various mathematical problems encountered in the modeling of physical phenomena. |
| More precisely, the problems considered in this chapter are those that can be reduced to the finding of the solution of a partial differential equation (PDE). | More precisely, the problems considered in this chapter are those that can be reduced to finding the solution of a partial deifferential equation(PDE). |
| Indeed, for many physicists, to provide a model of a phenomenon means to provide a PDE describing this phenomenon. | In fact, for many physicists, providing a model of a phenomenon means providing an EDP that describes that phenomenom. |
| They can be boundary problems, spectral problems, evolution problems. | They can be boundary, spectral problems, evolution problems. |
| General ideas about the methods of exact and approximate solving of those PDE is also proposed[1]. | General ideas about exact and approximate resolution methods for these PDs[1] are also proposed. |
| This chapter contains numerous references to the "physical" part of this book which justify the interest given to those mathematical problems. | This chapter contains numerous references to the "physics" part of this book which justify the interest given to these mathematical problems. |
| In classical books about PDE, equations are usually classified into three categories: hyperbolic, parabolic and elliptic equation. | In classic EDP textbooks, equations are generally classified into three categories: hiperbolic, parabolic and elliptic equations. |
| This classification is connected to the proof of existence and unicity of the solutions rather than to the actual way of obtaining the solution. | This classification is more linked to the proof of the existence and uniqueness of the solutions than to the actual way of obtaining the solution. |
| We present here another classification connected to the way one obtains the solutions: we distinguish mainly boundary problems and evolution problems. | Here we present another classification linked to the way in wich solutions are obtained: we distinguish mainly between boundary problems and evolution problems. |
| In order to help the reading of the next chapters, a quick classification of various mathematical problems encountered in the modelization of physical phenomena is proposed in the present chapter. | To help with the reading of the next chapters, this chapter provides a quick classification of various mathematical problems encountered in the modeling of physical phenomena. |
| More precisely, the problems considered in this chapter are those that can be reduced to the finding of the solution of a partial differential equation (PDE). | More precisely, the problems considered in this chapter are those that can be reduced to finding the solution of a partial deifferential equation(PDE). |
| Indeed, for many physicists, to provide a model of a phenomenon means to provide a PDE describing this phenomenon. | In fact, for many physicists, providing a model of a phenomenon means providing an EDP that describes that phenomenom. |
| They can be boundary problems, spectral problems, evolution problems. | They can be boundary, spectral problems, evolution problems. |
| General ideas about the methods of exact and approximate solving of those PDE is also proposed[1]. | General ideas about exact and approximate resolution methods for these PDs[1] are also proposed. |
| This chapter contains numerous references to the "physical" part of this book which justify the interest given to those mathematical problems. | This chapter contains numerous references to the "physics" part of this book which justify the interest given to these mathematical problems. |
| In classical books about PDE, equations are usually classified into three categories: hyperbolic, parabolic and elliptic equation. | In classic EDP textbooks, equations are generally classified into three categories: hiperbolic, parabolic and elliptic equations. |
| This classification is connected to the proof of existence and unicity of the solutions rather than to the actual way of obtaining the solution. | This classification is more linked to the proof of the existence and uniqueness of the solutions than to the actual way of obtaining the solution. |
| We present here another classification connected to the way one obtains the solutions: we distinguish mainly boundary problems and evolution problems. | Here we present another classification linked to the way in wich solutions are obtained: we distinguish mainly between boundary problems and evolution problems. |
| In order to help the reading of the next chapters, a quick classification of various mathematical problems encountered in the modelization of physical phenomena is proposed in the present chapter. | To help with the reading of the next chapters, this chapter provides a quick classification of various mathematical problems encountered in the modeling of physical phenomena. |
| More precisely, the problems considered in this chapter are those that can be reduced to the finding of the solution of a partial differential equation (PDE). | More precisely, the problems considered in this chapter are those that can be reduced to finding the solution of a partial deifferential equation(PDE). |
| Indeed, for many physicists, to provide a model of a phenomenon means to provide a PDE describing this phenomenon. | In fact, for many physicists, providing a model of a phenomenon means providing an EDP that describes that phenomenom. |
| They can be boundary problems, spectral problems, evolution problems. | They can be boundary, spectral problems, evolution problems. |
| General ideas about the methods of exact and approximate solving of those PDE is also proposed[1]. | General ideas about exact and approximate resolution methods for these PDs[1] are also proposed. |
| This chapter contains numerous references to the "physical" part of this book which justify the interest given to those mathematical problems. | This chapter contains numerous references to the "physics" part of this book which justify the interest given to these mathematical problems. |
| In classical books about PDE, equations are usually classified into three categories: hyperbolic, parabolic and elliptic equation. | In classic EDP textbooks, equations are generally classified into three categories: hiperbolic, parabolic and elliptic equations. |
| This classification is connected to the proof of existence and unicity of the solutions rather than to the actual way of obtaining the solution. | This classification is more linked to the proof of the existence and uniqueness of the solutions than to the actual way of obtaining the solution. |
| We present here another classification connected to the way one obtains the solutions: we distinguish mainly boundary problems and evolution problems. | Here we present another classification linked to the way in wich solutions are obtained: we distinguish mainly between boundary problems and evolution problems. |
| In order to help the reading of the next chapters, a quick classification of various mathematical problems encountered in the modelization of physical phenomena is proposed in the present chapter. | To help with the reading of the next chapters, this chapter provides a quick classification of various mathematical problems encountered in the modeling of physical phenomena. |
| More precisely, the problems considered in this chapter are those that can be reduced to the finding of the solution of a partial differential equation (PDE). | More precisely, the problems considered in this chapter are those that can be reduced to finding the solution of a partial deifferential equation(PDE). |
| Indeed, for many physicists, to provide a model of a phenomenon means to provide a PDE describing this phenomenon. | In fact, for many physicists, providing a model of a phenomenon means providing an EDP that describes that phenomenom. |
| They can be boundary problems, spectral problems, evolution problems. | They can be boundary, spectral problems, evolution problems. |
| General ideas about the methods of exact and approximate solving of those PDE is also proposed[1]. | General ideas about exact and approximate resolution methods for these PDs[1] are also proposed. |
| This chapter contains numerous references to the "physical" part of this book which justify the interest given to those mathematical problems. | This chapter contains numerous references to the "physics" part of this book which justify the interest given to these mathematical problems. |
| In classical books about PDE, equations are usually classified into three categories: hyperbolic, parabolic and elliptic equation. | In classic EDP textbooks, equations are generally classified into three categories: hiperbolic, parabolic and elliptic equations. |
| This classification is connected to the proof of existence and unicity of the solutions rather than to the actual way of obtaining the solution. | This classification is more linked to the proof of the existence and uniqueness of the solutions than to the actual way of obtaining the solution. |
| We present here another classification connected to the way one obtains the solutions: we distinguish mainly boundary problems and evolution problems. | Here we present another classification linked to the way in wich solutions are obtained: we distinguish mainly between boundary problems and evolution problems. |
| In order to help the reading of the next chapters, a quick classification of various mathematical problems encountered in the modelization of physical phenomena is proposed in the present chapter. | To help with the reading of the next chapters, this chapter provides a quick classification of various mathematical problems encountered in the modeling of physical phenomena. |
| More precisely, the problems considered in this chapter are those that can be reduced to the finding of the solution of a partial differential equation (PDE). | More precisely, the problems considered in this chapter are those that can be reduced to finding the solution of a partial deifferential equation(PDE). |
| Indeed, for many physicists, to provide a model of a phenomenon means to provide a PDE describing this phenomenon. | In fact, for many physicists, providing a model of a phenomenon means providing an EDP that describes that phenomenom. |
| They can be boundary problems, spectral problems, evolution problems. | They can be boundary, spectral problems, evolution problems. |
| General ideas about the methods of exact and approximate solving of those PDE is also proposed[1]. | General ideas about exact and approximate resolution methods for these PDs[1] are also proposed. |
| This chapter contains numerous references to the "physical" part of this book which justify the interest given to those mathematical problems. | This chapter contains numerous references to the "physics" part of this book which justify the interest given to these mathematical problems. |
| In classical books about PDE, equations are usually classified into three categories: hyperbolic, parabolic and elliptic equation. | In classic EDP textbooks, equations are generally classified into three categories: hiperbolic, parabolic and elliptic equations. |
| This classification is connected to the proof of existence and unicity of the solutions rather than to the actual way of obtaining the solution. | This classification is more linked to the proof of the existence and uniqueness of the solutions than to the actual way of obtaining the solution. |
| We present here another classification connected to the way one obtains the solutions: we distinguish mainly boundary problems and evolution problems. | Here we present another classification linked to the way in wich solutions are obtained: we distinguish mainly between boundary problems and evolution problems. |
| In order to help the reading of the next chapters, a quick classification of various mathematical problems encountered in the modelization of physical phenomena is proposed in the present chapter. | To help with the reading of the next chapters, this chapter provides a quick classification of various mathematical problems encountered in the modeling of physical phenomena. |
| More precisely, the problems considered in this chapter are those that can be reduced to the finding of the solution of a partial differential equation (PDE). | More precisely, the problems considered in this chapter are those that can be reduced to finding the solution of a partial deifferential equation(PDE). |
| Indeed, for many physicists, to provide a model of a phenomenon means to provide a PDE describing this phenomenon. | In fact, for many physicists, providing a model of a phenomenon means providing an EDP that describes that phenomenom. |
| They can be boundary problems, spectral problems, evolution problems. | They can be boundary, spectral problems, evolution problems. |
| General ideas about the methods of exact and approximate solving of those PDE is also proposed[1]. | General ideas about exact and approximate resolution methods for these PDs[1] are also proposed. |
| This chapter contains numerous references to the "physical" part of this book which justify the interest given to those mathematical problems. | This chapter contains numerous references to the "physics" part of this book which justify the interest given to these mathematical problems. |
| In classical books about PDE, equations are usually classified into three categories: hyperbolic, parabolic and elliptic equation. | In classic EDP textbooks, equations are generally classified into three categories: hiperbolic, parabolic and elliptic equations. |
| This classification is connected to the proof of existence and unicity of the solutions rather than to the actual way of obtaining the solution. | This classification is more linked to the proof of the existence and uniqueness of the solutions than to the actual way of obtaining the solution. |
| We present here another classification connected to the way one obtains the solutions: we distinguish mainly boundary problems and evolution problems. | Here we present another classification linked to the way in wich solutions are obtained: we distinguish mainly between boundary problems and evolution problems. |
| In order to help the reading of the next chapters, a quick classification of various mathematical problems encountered in the modelization of physical phenomena is proposed in the present chapter. | To help with the reading of the next chapters, this chapter provides a quick classification of various mathematical problems encountered in the modeling of physical phenomena. |
| More precisely, the problems considered in this chapter are those that can be reduced to the finding of the solution of a partial differential equation (PDE). | More precisely, the problems considered in this chapter are those that can be reduced to finding the solution of a partial deifferential equation(PDE). |
| Indeed, for many physicists, to provide a model of a phenomenon means to provide a PDE describing this phenomenon. | In fact, for many physicists, providing a model of a phenomenon means providing an EDP that describes that phenomenom. |
| They can be boundary problems, spectral problems, evolution problems. | They can be boundary, spectral problems, evolution problems. |
| General ideas about the methods of exact and approximate solving of those PDE is also proposed[1]. | General ideas about exact and approximate resolution methods for these PDs[1] are also proposed. |
| This chapter contains numerous references to the "physical" part of this book which justify the interest given to those mathematical problems. | This chapter contains numerous references to the "physics" part of this book which justify the interest given to these mathematical problems. |
| In classical books about PDE, equations are usually classified into three categories: hyperbolic, parabolic and elliptic equation. | In classic EDP textbooks, equations are generally classified into three categories: hiperbolic, parabolic and elliptic equations. |
| This classification is connected to the proof of existence and unicity of the solutions rather than to the actual way of obtaining the solution. | This classification is more linked to the proof of the existence and uniqueness of the solutions than to the actual way of obtaining the solution. |
| We present here another classification connected to the way one obtains the solutions: we distinguish mainly boundary problems and evolution problems. | Here we present another classification linked to the way in wich solutions are obtained: we distinguish mainly between boundary problems and evolution problems. |
| In order to help the reading of the next chapters, a quick classification of various mathematical problems encountered in the modelization of physical phenomena is proposed in the present chapter. | To help with the reading of the next chapters, this chapter provides a quick classification of various mathematical problems encountered in the modeling of physical phenomena. |
| More precisely, the problems considered in this chapter are those that can be reduced to the finding of the solution of a partial differential equation (PDE). | More precisely, the problems considered in this chapter are those that can be reduced to finding the solution of a partial deifferential equation(PDE). |
| Indeed, for many physicists, to provide a model of a phenomenon means to provide a PDE describing this phenomenon. | In fact, for many physicists, providing a model of a phenomenon means providing an EDP that describes that phenomenom. |
| They can be boundary problems, spectral problems, evolution problems. | They can be boundary, spectral problems, evolution problems. |
| General ideas about the methods of exact and approximate solving of those PDE is also proposed[1]. | General ideas about exact and approximate resolution methods for these PDs[1] are also proposed. |
| This chapter contains numerous references to the "physical" part of this book which justify the interest given to those mathematical problems. | This chapter contains numerous references to the "physics" part of this book which justify the interest given to these mathematical problems. |
| In classical books about PDE, equations are usually classified into three categories: hyperbolic, parabolic and elliptic equation. | In classic EDP textbooks, equations are generally classified into three categories: hiperbolic, parabolic and elliptic equations. |
| This classification is connected to the proof of existence and unicity of the solutions rather than to the actual way of obtaining the solution. | This classification is more linked to the proof of the existence and uniqueness of the solutions than to the actual way of obtaining the solution. |
| We present here another classification connected to the way one obtains the solutions: we distinguish mainly boundary problems and evolution problems. | Here we present another classification linked to the way in wich solutions are obtained: we distinguish mainly between boundary problems and evolution problems. |
| In order to help the reading of the next chapters, a quick classification of various mathematical problems encountered in the modelization of physical phenomena is proposed in the present chapter. | To help with the reading of the next chapters, this chapter provides a quick classification of various mathematical problems encountered in the modeling of physical phenomena. |
| More precisely, the problems considered in this chapter are those that can be reduced to the finding of the solution of a partial differential equation (PDE). | More precisely, the problems considered in this chapter are those that can be reduced to finding the solution of a partial deifferential equation(PDE). |
| Indeed, for many physicists, to provide a model of a phenomenon means to provide a PDE describing this phenomenon. | In fact, for many physicists, providing a model of a phenomenon means providing an EDP that describes that phenomenom. |
| They can be boundary problems, spectral problems, evolution problems. | They can be boundary, spectral problems, evolution problems. |
| General ideas about the methods of exact and approximate solving of those PDE is also proposed[1]. | General ideas about exact and approximate resolution methods for these PDs[1] are also proposed. |
| This chapter contains numerous references to the "physical" part of this book which justify the interest given to those mathematical problems. | This chapter contains numerous references to the "physics" part of this book which justify the interest given to these mathematical problems. |
| In classical books about PDE, equations are usually classified into three categories: hyperbolic, parabolic and elliptic equation. | In classic EDP textbooks, equations are generally classified into three categories: hiperbolic, parabolic and elliptic equations. |
| This classification is connected to the proof of existence and unicity of the solutions rather than to the actual way of obtaining the solution. | This classification is more linked to the proof of the existence and uniqueness of the solutions than to the actual way of obtaining the solution. |
| We present here another classification connected to the way one obtains the solutions: we distinguish mainly boundary problems and evolution problems. | Here we present another classification linked to the way in wich solutions are obtained: we distinguish mainly between boundary problems and evolution problems. |
| In order to help the reading of the next chapters, a quick classification of various mathematical problems encountered in the modelization of physical phenomena is proposed in the present chapter. | To help with the reading of the next chapters, this chapter provides a quick classification of various mathematical problems encountered in the modeling of physical phenomena. |
| More precisely, the problems considered in this chapter are those that can be reduced to the finding of the solution of a partial differential equation (PDE). | More precisely, the problems considered in this chapter are those that can be reduced to finding the solution of a partial deifferential equation(PDE). |
| Indeed, for many physicists, to provide a model of a phenomenon means to provide a PDE describing this phenomenon. | In fact, for many physicists, providing a model of a phenomenon means providing an EDP that describes that phenomenom. |
| They can be boundary problems, spectral problems, evolution problems. | They can be boundary, spectral problems, evolution problems. |
| General ideas about the methods of exact and approximate solving of those PDE is also proposed[1]. | General ideas about exact and approximate resolution methods for these PDs[1] are also proposed. |
| This chapter contains numerous references to the "physical" part of this book which justify the interest given to those mathematical problems. | This chapter contains numerous references to the "physics" part of this book which justify the interest given to these mathematical problems. |
| In classical books about PDE, equations are usually classified into three categories: hyperbolic, parabolic and elliptic equation. | In classic EDP textbooks, equations are generally classified into three categories: hiperbolic, parabolic and elliptic equations. |
| This classification is connected to the proof of existence and unicity of the solutions rather than to the actual way of obtaining the solution. | This classification is more linked to the proof of the existence and uniqueness of the solutions than to the actual way of obtaining the solution. |
| We present here another classification connected to the way one obtains the solutions: we distinguish mainly boundary problems and evolution problems. | Here we present another classification linked to the way in wich solutions are obtained: we distinguish mainly between boundary problems and evolution problems. |
| In order to help the reading of the next chapters, a quick classification of various mathematical problems encountered in the modelization of physical phenomena is proposed in the present chapter. | To help with the reading of the next chapters, this chapter provides a quick classification of various mathematical problems encountered in the modeling of physical phenomena. |
| More precisely, the problems considered in this chapter are those that can be reduced to the finding of the solution of a partial differential equation (PDE). | More precisely, the problems considered in this chapter are those that can be reduced to finding the solution of a partial deifferential equation(PDE). |
| Indeed, for many physicists, to provide a model of a phenomenon means to provide a PDE describing this phenomenon. | In fact, for many physicists, providing a model of a phenomenon means providing an EDP that describes that phenomenom. |
| They can be boundary problems, spectral problems, evolution problems. | They can be boundary, spectral problems, evolution problems. |
| General ideas about the methods of exact and approximate solving of those PDE is also proposed[1]. | General ideas about exact and approximate resolution methods for these PDs[1] are also proposed. |
| This chapter contains numerous references to the "physical" part of this book which justify the interest given to those mathematical problems. | This chapter contains numerous references to the "physics" part of this book which justify the interest given to these mathematical problems. |
| In classical books about PDE, equations are usually classified into three categories: hyperbolic, parabolic and elliptic equation. | In classic EDP textbooks, equations are generally classified into three categories: hiperbolic, parabolic and elliptic equations. |
| This classification is connected to the proof of existence and unicity of the solutions rather than to the actual way of obtaining the solution. | This classification is more linked to the proof of the existence and uniqueness of the solutions than to the actual way of obtaining the solution. |
| We present here another classification connected to the way one obtains the solutions: we distinguish mainly boundary problems and evolution problems. | Here we present another classification linked to the way in wich solutions are obtained: we distinguish mainly between boundary problems and evolution problems. |
| In order to help the reading of the next chapters, a quick classification of various mathematical problems encountered in the modelization of physical phenomena is proposed in the present chapter. | To help with the reading of the next chapters, this chapter provides a quick classification of various mathematical problems encountered in the modeling of physical phenomena. |
| More precisely, the problems considered in this chapter are those that can be reduced to the finding of the solution of a partial differential equation (PDE). | More precisely, the problems considered in this chapter are those that can be reduced to finding the solution of a partial deifferential equation(PDE). |
| Indeed, for many physicists, to provide a model of a phenomenon means to provide a PDE describing this phenomenon. | In fact, for many physicists, providing a model of a phenomenon means providing an EDP that describes that phenomenom. |
| They can be boundary problems, spectral problems, evolution problems. | They can be boundary, spectral problems, evolution problems. |
| General ideas about the methods of exact and approximate solving of those PDE is also proposed[1]. | General ideas about exact and approximate resolution methods for these PDs[1] are also proposed. |
| This chapter contains numerous references to the "physical" part of this book which justify the interest given to those mathematical problems. | This chapter contains numerous references to the "physics" part of this book which justify the interest given to these mathematical problems. |
| In classical books about PDE, equations are usually classified into three categories: hyperbolic, parabolic and elliptic equation. | In classic EDP textbooks, equations are generally classified into three categories: hiperbolic, parabolic and elliptic equations. |
| This classification is connected to the proof of existence and unicity of the solutions rather than to the actual way of obtaining the solution. | This classification is more linked to the proof of the existence and uniqueness of the solutions than to the actual way of obtaining the solution. |
| We present here another classification connected to the way one obtains the solutions: we distinguish mainly boundary problems and evolution problems. | Here we present another classification linked to the way in wich solutions are obtained: we distinguish mainly between boundary problems and evolution problems. |
| In order to help the reading of the next chapters, a quick classification of various mathematical problems encountered in the modelization of physical phenomena is proposed in the present chapter. | To help with the reading of the next chapters, this chapter provides a quick classification of various mathematical problems encountered in the modeling of physical phenomena. |
| More precisely, the problems considered in this chapter are those that can be reduced to the finding of the solution of a partial differential equation (PDE). | More precisely, the problems considered in this chapter are those that can be reduced to finding the solution of a partial deifferential equation(PDE). |
| Indeed, for many physicists, to provide a model of a phenomenon means to provide a PDE describing this phenomenon. | In fact, for many physicists, providing a model of a phenomenon means providing an EDP that describes that phenomenom. |
| They can be boundary problems, spectral problems, evolution problems. | They can be boundary, spectral problems, evolution problems. |
| General ideas about the methods of exact and approximate solving of those PDE is also proposed[1]. | General ideas about exact and approximate resolution methods for these PDs[1] are also proposed. |
| This chapter contains numerous references to the "physical" part of this book which justify the interest given to those mathematical problems. | This chapter contains numerous references to the "physics" part of this book which justify the interest given to these mathematical problems. |
| In classical books about PDE, equations are usually classified into three categories: hyperbolic, parabolic and elliptic equation. | In classic EDP textbooks, equations are generally classified into three categories: hiperbolic, parabolic and elliptic equations. |
| This classification is connected to the proof of existence and unicity of the solutions rather than to the actual way of obtaining the solution. | This classification is more linked to the proof of the existence and uniqueness of the solutions than to the actual way of obtaining the solution. |
| We present here another classification connected to the way one obtains the solutions: we distinguish mainly boundary problems and evolution problems. | Here we present another classification linked to the way in wich solutions are obtained: we distinguish mainly between boundary problems and evolution problems. |
| In order to help the reading of the next chapters, a quick classification of various mathematical problems encountered in the modelization of physical phenomena is proposed in the present chapter. | To help with the reading of the next chapters, this chapter provides a quick classification of various mathematical problems encountered in the modeling of physical phenomena. |
| More precisely, the problems considered in this chapter are those that can be reduced to the finding of the solution of a partial differential equation (PDE). | More precisely, the problems considered in this chapter are those that can be reduced to finding the solution of a partial deifferential equation(PDE). |
| Indeed, for many physicists, to provide a model of a phenomenon means to provide a PDE describing this phenomenon. | In fact, for many physicists, providing a model of a phenomenon means providing an EDP that describes that phenomenom. |
| They can be boundary problems, spectral problems, evolution problems. | They can be boundary, spectral problems, evolution problems. |
| General ideas about the methods of exact and approximate solving of those PDE is also proposed[1]. | General ideas about exact and approximate resolution methods for these PDs[1] are also proposed. |
| This chapter contains numerous references to the "physical" part of this book which justify the interest given to those mathematical problems. | This chapter contains numerous references to the "physics" part of this book which justify the interest given to these mathematical problems. |
| In classical books about PDE, equations are usually classified into three categories: hyperbolic, parabolic and elliptic equation. | In classic EDP textbooks, equations are generally classified into three categories: hiperbolic, parabolic and elliptic equations. |
| This classification is connected to the proof of existence and unicity of the solutions rather than to the actual way of obtaining the solution. | This classification is more linked to the proof of the existence and uniqueness of the solutions than to the actual way of obtaining the solution. |
| We present here another classification connected to the way one obtains the solutions: we distinguish mainly boundary problems and evolution problems. | Here we present another classification linked to the way in wich solutions are obtained: we distinguish mainly between boundary problems and evolution problems. |
| In order to help the reading of the next chapters, a quick classification of various mathematical problems encountered in the modelization of physical phenomena is proposed in the present chapter. | To help with the reading of the next chapters, this chapter provides a quick classification of various mathematical problems encountered in the modeling of physical phenomena. |
| More precisely, the problems considered in this chapter are those that can be reduced to the finding of the solution of a partial differential equation (PDE). | More precisely, the problems considered in this chapter are those that can be reduced to finding the solution of a partial deifferential equation(PDE). |
| Indeed, for many physicists, to provide a model of a phenomenon means to provide a PDE describing this phenomenon. | In fact, for many physicists, providing a model of a phenomenon means providing an EDP that describes that phenomenom. |
| They can be boundary problems, spectral problems, evolution problems. | They can be boundary, spectral problems, evolution problems. |
| General ideas about the methods of exact and approximate solving of those PDE is also proposed[1]. | General ideas about exact and approximate resolution methods for these PDs[1] are also proposed. |
| This chapter contains numerous references to the "physical" part of this book which justify the interest given to those mathematical problems. | This chapter contains numerous references to the "physics" part of this book which justify the interest given to these mathematical problems. |
| In classical books about PDE, equations are usually classified into three categories: hyperbolic, parabolic and elliptic equation. | In classic EDP textbooks, equations are generally classified into three categories: hiperbolic, parabolic and elliptic equations. |
| This classification is connected to the proof of existence and unicity of the solutions rather than to the actual way of obtaining the solution. | This classification is more linked to the proof of the existence and uniqueness of the solutions than to the actual way of obtaining the solution. |
| We present here another classification connected to the way one obtains the solutions: we distinguish mainly boundary problems and evolution problems. | Here we present another classification linked to the way in wich solutions are obtained: we distinguish mainly between boundary problems and evolution problems. |
| In order to help the reading of the next chapters, a quick classification of various mathematical problems encountered in the modelization of physical phenomena is proposed in the present chapter. | To help with the reading of the next chapters, this chapter provides a quick classification of various mathematical problems encountered in the modeling of physical phenomena. |
| More precisely, the problems considered in this chapter are those that can be reduced to the finding of the solution of a partial differential equation (PDE). | More precisely, the problems considered in this chapter are those that can be reduced to finding the solution of a partial deifferential equation(PDE). |
| Indeed, for many physicists, to provide a model of a phenomenon means to provide a PDE describing this phenomenon. | In fact, for many physicists, providing a model of a phenomenon means providing an EDP that describes that phenomenom. |
| They can be boundary problems, spectral problems, evolution problems. | They can be boundary, spectral problems, evolution problems. |
| General ideas about the methods of exact and approximate solving of those PDE is also proposed[1]. | General ideas about exact and approximate resolution methods for these PDs[1] are also proposed. |
| This chapter contains numerous references to the "physical" part of this book which justify the interest given to those mathematical problems. | This chapter contains numerous references to the "physics" part of this book which justify the interest given to these mathematical problems. |
| In classical books about PDE, equations are usually classified into three categories: hyperbolic, parabolic and elliptic equation. | In classic EDP textbooks, equations are generally classified into three categories: hiperbolic, parabolic and elliptic equations. |
| This classification is connected to the proof of existence and unicity of the solutions rather than to the actual way of obtaining the solution. | This classification is more linked to the proof of the existence and uniqueness of the solutions than to the actual way of obtaining the solution. |
| We present here another classification connected to the way one obtains the solutions: we distinguish mainly boundary problems and evolution problems. | Here we present another classification linked to the way in wich solutions are obtained: we distinguish mainly between boundary problems and evolution problems. |
| In order to help the reading of the next chapters, a quick classification of various mathematical problems encountered in the modelization of physical phenomena is proposed in the present chapter. | To help with the reading of the next chapters, this chapter provides a quick classification of various mathematical problems encountered in the modeling of physical phenomena. |
| More precisely, the problems considered in this chapter are those that can be reduced to the finding of the solution of a partial differential equation (PDE). | More precisely, the problems considered in this chapter are those that can be reduced to finding the solution of a partial deifferential equation(PDE). |
| Indeed, for many physicists, to provide a model of a phenomenon means to provide a PDE describing this phenomenon. | In fact, for many physicists, providing a model of a phenomenon means providing an EDP that describes that phenomenom. |
| They can be boundary problems, spectral problems, evolution problems. | They can be boundary, spectral problems, evolution problems. |
| General ideas about the methods of exact and approximate solving of those PDE is also proposed[1]. | General ideas about exact and approximate resolution methods for these PDs[1] are also proposed. |
| This chapter contains numerous references to the "physical" part of this book which justify the interest given to those mathematical problems. | This chapter contains numerous references to the "physics" part of this book which justify the interest given to these mathematical problems. |
| In classical books about PDE, equations are usually classified into three categories: hyperbolic, parabolic and elliptic equation. | In classic EDP textbooks, equations are generally classified into three categories: hiperbolic, parabolic and elliptic equations. |
| This classification is connected to the proof of existence and unicity of the solutions rather than to the actual way of obtaining the solution. | This classification is more linked to the proof of the existence and uniqueness of the solutions than to the actual way of obtaining the solution. |
| We present here another classification connected to the way one obtains the solutions: we distinguish mainly boundary problems and evolution problems. | Here we present another classification linked to the way in wich solutions are obtained: we distinguish mainly between boundary problems and evolution problems. |
| In order to help the reading of the next chapters, a quick classification of various mathematical problems encountered in the modelization of physical phenomena is proposed in the present chapter. | To help with the reading of the next chapters, this chapter provides a quick classification of various mathematical problems encountered in the modeling of physical phenomena. |
| More precisely, the problems considered in this chapter are those that can be reduced to the finding of the solution of a partial differential equation (PDE). | More precisely, the problems considered in this chapter are those that can be reduced to finding the solution of a partial deifferential equation(PDE). |
| Indeed, for many physicists, to provide a model of a phenomenon means to provide a PDE describing this phenomenon. | In fact, for many physicists, providing a model of a phenomenon means providing an EDP that describes that phenomenom. |
| They can be boundary problems, spectral problems, evolution problems. | They can be boundary, spectral problems, evolution problems. |
| General ideas about the methods of exact and approximate solving of those PDE is also proposed[1]. | General ideas about exact and approximate resolution methods for these PDs[1] are also proposed. |
| This chapter contains numerous references to the "physical" part of this book which justify the interest given to those mathematical problems. | This chapter contains numerous references to the "physics" part of this book which justify the interest given to these mathematical problems. |
| In classical books about PDE, equations are usually classified into three categories: hyperbolic, parabolic and elliptic equation. | In classic EDP textbooks, equations are generally classified into three categories: hiperbolic, parabolic and elliptic equations. |
| This classification is connected to the proof of existence and unicity of the solutions rather than to the actual way of obtaining the solution. | This classification is more linked to the proof of the existence and uniqueness of the solutions than to the actual way of obtaining the solution. |
| We present here another classification connected to the way one obtains the solutions: we distinguish mainly boundary problems and evolution problems. | Here we present another classification linked to the way in wich solutions are obtained: we distinguish mainly between boundary problems and evolution problems. |
| In order to help the reading of the next chapters, a quick classification of various mathematical problems encountered in the modelization of physical phenomena is proposed in the present chapter. | To help with the reading of the next chapters, this chapter provides a quick classification of various mathematical problems encountered in the modeling of physical phenomena. |
| More precisely, the problems considered in this chapter are those that can be reduced to the finding of the solution of a partial differential equation (PDE). | More precisely, the problems considered in this chapter are those that can be reduced to finding the solution of a partial deifferential equation(PDE). |
| Indeed, for many physicists, to provide a model of a phenomenon means to provide a PDE describing this phenomenon. | In fact, for many physicists, providing a model of a phenomenon means providing an EDP that describes that phenomenom. |
| They can be boundary problems, spectral problems, evolution problems. | They can be boundary, spectral problems, evolution problems. |
| General ideas about the methods of exact and approximate solving of those PDE is also proposed[1]. | General ideas about exact and approximate resolution methods for these PDs[1] are also proposed. |
| This chapter contains numerous references to the "physical" part of this book which justify the interest given to those mathematical problems. | This chapter contains numerous references to the "physics" part of this book which justify the interest given to these mathematical problems. |
| In classical books about PDE, equations are usually classified into three categories: hyperbolic, parabolic and elliptic equation. | In classic EDP textbooks, equations are generally classified into three categories: hiperbolic, parabolic and elliptic equations. |
| This classification is connected to the proof of existence and unicity of the solutions rather than to the actual way of obtaining the solution. | This classification is more linked to the proof of the existence and uniqueness of the solutions than to the actual way of obtaining the solution. |
| We present here another classification connected to the way one obtains the solutions: we distinguish mainly boundary problems and evolution problems. | Here we present another classification linked to the way in wich solutions are obtained: we distinguish mainly between boundary problems and evolution problems. |
| In order to help the reading of the next chapters, a quick classification of various mathematical problems encountered in the modelization of physical phenomena is proposed in the present chapter. | To help with the reading of the next chapters, this chapter provides a quick classification of various mathematical problems encountered in the modeling of physical phenomena. |
| More precisely, the problems considered in this chapter are those that can be reduced to the finding of the solution of a partial differential equation (PDE). | More precisely, the problems considered in this chapter are those that can be reduced to finding the solution of a partial deifferential equation(PDE). |
| Indeed, for many physicists, to provide a model of a phenomenon means to provide a PDE describing this phenomenon. | In fact, for many physicists, providing a model of a phenomenon means providing an EDP that describes that phenomenom. |
| They can be boundary problems, spectral problems, evolution problems. | They can be boundary, spectral problems, evolution problems. |
| General ideas about the methods of exact and approximate solving of those PDE is also proposed[1]. | General ideas about exact and approximate resolution methods for these PDs[1] are also proposed. |
| This chapter contains numerous references to the "physical" part of this book which justify the interest given to those mathematical problems. | This chapter contains numerous references to the "physics" part of this book which justify the interest given to these mathematical problems. |
| In classical books about PDE, equations are usually classified into three categories: hyperbolic, parabolic and elliptic equation. | In classic EDP textbooks, equations are generally classified into three categories: hiperbolic, parabolic and elliptic equations. |
| This classification is connected to the proof of existence and unicity of the solutions rather than to the actual way of obtaining the solution. | This classification is more linked to the proof of the existence and uniqueness of the solutions than to the actual way of obtaining the solution. |
| We present here another classification connected to the way one obtains the solutions: we distinguish mainly boundary problems and evolution problems. | Here we present another classification linked to the way in wich solutions are obtained: we distinguish mainly between boundary problems and evolution problems. |
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Ostatnia aktywność
Przetłumaczył(a) 216 jednostek/ki tłumaczeniowych/e
z dziedzin: physics and mathematics
Feb 21, 2024
