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Methods for Constructing Exact Solutions of Partial Differential Equations: Mathematical and Analytical Techniques with Applications to Engineering

S. V. Meleshko

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Institución detectada Año de publicación Navegá Descargá Solicitá
No detectada 2005 SpringerLink

Información

Tipo de recurso:

libros

ISBN impreso

978-0-387-25060-1

ISBN electrónico

978-0-387-25265-0

Editor responsable

Springer Nature

País de edición

Reino Unido

Fecha de publicación

Información sobre derechos de publicación

© Springer Science+Business Media, Inc. 2005

Tabla de contenidos

Equations with One Dependent Function

S. V. Meleshko

In the previous chapters I described observational research projects that can be done using equipment that is commonly available in the amateur astronomer’s toolkit, or which can be added at modest expense. I avoided projects that require the use of math beyond standard high-school algebra. There are, of course, valuable projects that go outside these arbitrary boundaries. The purpose of this chapter is to identify additional projects that may be of interest to the amateur researcher. If you are willing to invest in some specialized equipment, or do some more complex math, then these projects can be brought within the boundaries of your universe. The equipment needed for some of them is likely to cost you a couple of thousand dollars, and may also require that you do some custom design, construction, and de-bugging. Depending on your budget and your enthusiasm for a particular area of research, these can be extremely rewarding investments in your hobby.

Pp. 1-44

Systems of Equations

S. V. Meleshko

In the previous chapters I described observational research projects that can be done using equipment that is commonly available in the amateur astronomer’s toolkit, or which can be added at modest expense. I avoided projects that require the use of math beyond standard high-school algebra. There are, of course, valuable projects that go outside these arbitrary boundaries. The purpose of this chapter is to identify additional projects that may be of interest to the amateur researcher. If you are willing to invest in some specialized equipment, or do some more complex math, then these projects can be brought within the boundaries of your universe. The equipment needed for some of them is likely to cost you a couple of thousand dollars, and may also require that you do some custom design, construction, and de-bugging. Depending on your budget and your enthusiasm for a particular area of research, these can be extremely rewarding investments in your hobby.

Pp. 45-66

Method of the Degenerate Hodograph

S. V. Meleshko

In the previous chapters I described observational research projects that can be done using equipment that is commonly available in the amateur astronomer’s toolkit, or which can be added at modest expense. I avoided projects that require the use of math beyond standard high-school algebra. There are, of course, valuable projects that go outside these arbitrary boundaries. The purpose of this chapter is to identify additional projects that may be of interest to the amateur researcher. If you are willing to invest in some specialized equipment, or do some more complex math, then these projects can be brought within the boundaries of your universe. The equipment needed for some of them is likely to cost you a couple of thousand dollars, and may also require that you do some custom design, construction, and de-bugging. Depending on your budget and your enthusiasm for a particular area of research, these can be extremely rewarding investments in your hobby.

Pp. 67-130

Method of Differential Constraints

S. V. Meleshko

In the previous chapters I described observational research projects that can be done using equipment that is commonly available in the amateur astronomer’s toolkit, or which can be added at modest expense. I avoided projects that require the use of math beyond standard high-school algebra. There are, of course, valuable projects that go outside these arbitrary boundaries. The purpose of this chapter is to identify additional projects that may be of interest to the amateur researcher. If you are willing to invest in some specialized equipment, or do some more complex math, then these projects can be brought within the boundaries of your universe. The equipment needed for some of them is likely to cost you a couple of thousand dollars, and may also require that you do some custom design, construction, and de-bugging. Depending on your budget and your enthusiasm for a particular area of research, these can be extremely rewarding investments in your hobby.

Pp. 131-168

Invariant and Partially Invariant Solutions

S. V. Meleshko

In the previous chapters I described observational research projects that can be done using equipment that is commonly available in the amateur astronomer’s toolkit, or which can be added at modest expense. I avoided projects that require the use of math beyond standard high-school algebra. There are, of course, valuable projects that go outside these arbitrary boundaries. The purpose of this chapter is to identify additional projects that may be of interest to the amateur researcher. If you are willing to invest in some specialized equipment, or do some more complex math, then these projects can be brought within the boundaries of your universe. The equipment needed for some of them is likely to cost you a couple of thousand dollars, and may also require that you do some custom design, construction, and de-bugging. Depending on your budget and your enthusiasm for a particular area of research, these can be extremely rewarding investments in your hobby.

Pp. 169-248

Symmetries of Equations with Nonlocal Operators

S. V. Meleshko

In the previous chapters I described observational research projects that can be done using equipment that is commonly available in the amateur astronomer’s toolkit, or which can be added at modest expense. I avoided projects that require the use of math beyond standard high-school algebra. There are, of course, valuable projects that go outside these arbitrary boundaries. The purpose of this chapter is to identify additional projects that may be of interest to the amateur researcher. If you are willing to invest in some specialized equipment, or do some more complex math, then these projects can be brought within the boundaries of your universe. The equipment needed for some of them is likely to cost you a couple of thousand dollars, and may also require that you do some custom design, construction, and de-bugging. Depending on your budget and your enthusiasm for a particular area of research, these can be extremely rewarding investments in your hobby.

Pp. 249-285

Symbolic Computer Calculations

S. V. Meleshko

In the previous chapters I described observational research projects that can be done using equipment that is commonly available in the amateur astronomer’s toolkit, or which can be added at modest expense. I avoided projects that require the use of math beyond standard high-school algebra. There are, of course, valuable projects that go outside these arbitrary boundaries. The purpose of this chapter is to identify additional projects that may be of interest to the amateur researcher. If you are willing to invest in some specialized equipment, or do some more complex math, then these projects can be brought within the boundaries of your universe. The equipment needed for some of them is likely to cost you a couple of thousand dollars, and may also require that you do some custom design, construction, and de-bugging. Depending on your budget and your enthusiasm for a particular area of research, these can be extremely rewarding investments in your hobby.

Pp. 287-330

Appendix

S. V. Meleshko

In the previous chapters I described observational research projects that can be done using equipment that is commonly available in the amateur astronomer’s toolkit, or which can be added at modest expense. I avoided projects that require the use of math beyond standard high-school algebra. There are, of course, valuable projects that go outside these arbitrary boundaries. The purpose of this chapter is to identify additional projects that may be of interest to the amateur researcher. If you are willing to invest in some specialized equipment, or do some more complex math, then these projects can be brought within the boundaries of your universe. The equipment needed for some of them is likely to cost you a couple of thousand dollars, and may also require that you do some custom design, construction, and de-bugging. Depending on your budget and your enthusiasm for a particular area of research, these can be extremely rewarding investments in your hobby.

Pp. 331-338