Calculus of variations / Forsyth, Andrew Russell (1960)

Public ISBD Titre : Calculus of variations Type de document : texte imprimé Auteurs : Forsyth, Andrew Russell, Auteur Editeur : New York : Dover publications Année de publication : 1960 Importance : XXII-656 p. Présentation : ill. Format : 21 cm Note générale : Notes bibliogr. Index Langues : Anglais (eng) Mots-clés : Calculus of variations Integrals Index. décimale : 517.3 Calcul intégral. Intégration Note de contenu : In summary : 1. Integrals of the first order : maxima and minima for special weak variation : euler test, legendre test, jacobi test 2. Integrals of the first order : general weak variation : the method of weierstrass 3. Integrals involving derivatives of the second order : special weak variations, by the method of jacobi; general weak variations; by the method of weierstrass 4. Integrals involving two dependent variables and their first derivatives : special weak variations 5. Integrals involving two dependent variables and their first derivatives : general weak variations 6. Integrals with two dependent variables and derivatives of the second ordder : mainly special weak variations 7. Ordinary integrals under strong variations, and the weierstrauss test : solid of least resistance : action 8. Relative maxima and minima of single integrals : isoperimetrical problems 9. Double integrals with derivatives of the first order : weak variation : minimal surfaces .... Calculus of variations [texte imprimé] / Forsyth, Andrew Russell, Auteur . - New York : Dover publications, 1960 . - XXII-656 p. : ill. ; 21 cm. Notes bibliogr. Index Langues : Anglais (eng) Mots-clés : Calculus of variations Integrals Index. décimale : 517.3 Calcul intégral. Intégration Note de contenu : In summary : 1. Integrals of the first order : maxima and minima for special weak variation : euler test, legendre test, jacobi test 2. Integrals of the first order : general weak variation : the method of weierstrass 3. Integrals involving derivatives of the second order : special weak variations, by the method of jacobi; general weak variations; by the method of weierstrass 4. Integrals involving two dependent variables and their first derivatives : special weak variations 5. Integrals involving two dependent variables and their first derivatives : general weak variations 6. Integrals with two dependent variables and derivatives of the second ordder : mainly special weak variations 7. Ordinary integrals under strong variations, and the weierstrauss test : solid of least resistance : action 8. Relative maxima and minima of single integrals : isoperimetrical problems 9. Double integrals with derivatives of the first order : weak variation : minimal surfaces ....

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Theory of differential equations. Part 1. Exact aquations and Pfaff's problem ; Part 2, vol. 2. Ordinary equations, not linear / Forsyth, Andrew Russell (1959)

Public ISBD Titre de série : Theory of differential equations Titre : Part 1. Exact aquations and Pfaff's problem ; Part 2, vol. 2. Ordinary equations, not linear Type de document : texte imprimé Auteurs : Forsyth, Andrew Russell, Auteur Editeur : New York : Dover publications Année de publication : 1959 Importance : 1 vol. (XIII, 340, XI, 344) p. Format : 21 cm Note générale : Six volumes bound as three; this volume contains two parts Index Langues : Anglais (eng) Mots-clés : Équations différentielles Pfaff, Équations de Index. décimale : 517.9 Équations différentielles. Équations intégrales. Autres équations fonctionnelles. Équations aux dérivées finies. Calcul des variations. Analyse fonctionnelle Note de contenu : In summary : Part. 1 1. Single exact equation 2. System of exact equations 3. Historical summary of methods of treating Pfaff's problem 4. Pfaff's reduction, completed as by Gauss and Jacobi 5. Grassmann's method 6. Natani's method 7. Application to partial differential equations of the first order 8. Clebsch's method 9. Tangential transformations 10. Lie's method 11. Frobenius method 12. Abstract of darboux's method 13. Systems of Pfaffians Part. 2 1. Cauchy's theorem on the existence of regular integrals of a system of equations 2. Classes of non-ordinary points connected with the form of the equation of the first order and first degree in the derivative 3. Influence, upon the integral, of an oxidental singularity of the first kind possessed by the equation 4. Reduction of the differential equation to final typical forms, valid in the vicinity of an occidental singularity of the second kind 5. The character of the integrals possessed by the respective reduced forms of the original equation in the vicinity of the accidental singularity of the second kind 6. Effect, upon integrals, of essential singularities of the equation 7. Branch-points of an equation of the first order and any degree, as determined by the equation : singular and particular solutions 8. Differential equations of the first order having their integrals free from parametric branch-ponits 9. Equations of first order with uniform integrals, and with algebrical integrals Theory of differential equations. Part 1. Exact aquations and Pfaff's problem ; Part 2, vol. 2. Ordinary equations, not linear [texte imprimé] / Forsyth, Andrew Russell, Auteur . - New York : Dover publications, 1959 . - 1 vol. (XIII, 340, XI, 344) p. ; 21 cm. Six volumes bound as three; this volume contains two parts Index Langues : Anglais (eng) Mots-clés : Équations différentielles Pfaff, Équations de Index. décimale : 517.9 Équations différentielles. Équations intégrales. Autres équations fonctionnelles. Équations aux dérivées finies. Calcul des variations. Analyse fonctionnelle Note de contenu : In summary : Part. 1 1. Single exact equation 2. System of exact equations 3. Historical summary of methods of treating Pfaff's problem 4. Pfaff's reduction, completed as by Gauss and Jacobi 5. Grassmann's method 6. Natani's method 7. Application to partial differential equations of the first order 8. Clebsch's method 9. Tangential transformations 10. Lie's method 11. Frobenius method 12. Abstract of darboux's method 13. Systems of Pfaffians Part. 2 1. Cauchy's theorem on the existence of regular integrals of a system of equations 2. Classes of non-ordinary points connected with the form of the equation of the first order and first degree in the derivative 3. Influence, upon the integral, of an oxidental singularity of the first kind possessed by the equation 4. Reduction of the differential equation to final typical forms, valid in the vicinity of an occidental singularity of the second kind 5. The character of the integrals possessed by the respective reduced forms of the original equation in the vicinity of the accidental singularity of the second kind 6. Effect, upon integrals, of essential singularities of the equation 7. Branch-points of an equation of the first order and any degree, as determined by the equation : singular and particular solutions 8. Differential equations of the first order having their integrals free from parametric branch-ponits 9. Equations of first order with uniform integrals, and with algebrical integrals

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Theory of differential equations. Part 2, vol. 3. Ordinary equations, not linear ; part. 3, vol. 4. Ordinary linear equations / Forsyth, Andrew Russell (1959)

Public ISBD Titre de série : Theory of differential equations Titre : Part 2, vol. 3. Ordinary equations, not linear ; part. 3, vol. 4. Ordinary linear equations Type de document : texte imprimé Auteurs : Forsyth, Andrew Russell, Auteur Editeur : New York : Dover publications Année de publication : 1959 Importance : 01 vol. (X, 391, XVI, 534) p. Format : 21 cm Note générale : Six volumes bound as three; this volume contains two parts. - Index Langues : Anglais (eng) Mots-clés : Équations différentielles Index. décimale : 517.9 Équations différentielles. Équations intégrales. Autres équations fonctionnelles. Équations aux dérivées finies. Calcul des variations. Analyse fonctionnelle Note de contenu : In summary : Part. 2 1. Reduced forms of systems of equations of the first order in the vicinity of singulariries of the derivatives 2. The integrals of the reduced forms of a system of equations, chiffly of two dependent variables 3. Systems of equations with multiform values of the derivatives; singular solutions 4. Equations of the second order and the first degree 5. Equations of the second order and any degree 6. Equation of the second order with sub-uniform integrals : with some general considerations 7. General theorems on algebraic integrals : Brun's theorem Part 3 1. Linear equations : existence of synectic integrals : fundamental systems 2. General forms and properties of integrals near a singularity 3. Regular integrals : equation having all its integrals regular near a singularity 4. Equations having their integrals regular in the vicinity of every singularity (including infinity) 5. Linear equation of the second and the third orders possessing algebraic integrals 6. Equations having only some of their integrals regular near a singularity 7. Normal integrals : subnormal integrals 8. Infinite determinants, and their application to the solution of linear equations 9. Equations with uniform periodic coefficients 10. Equations having algebraic coefficients Theory of differential equations. Part 2, vol. 3. Ordinary equations, not linear ; part. 3, vol. 4. Ordinary linear equations [texte imprimé] / Forsyth, Andrew Russell, Auteur . - New York : Dover publications, 1959 . - 01 vol. (X, 391, XVI, 534) p. ; 21 cm. Six volumes bound as three; this volume contains two parts. - Index Langues : Anglais (eng) Mots-clés : Équations différentielles Index. décimale : 517.9 Équations différentielles. Équations intégrales. Autres équations fonctionnelles. Équations aux dérivées finies. Calcul des variations. Analyse fonctionnelle Note de contenu : In summary : Part. 2 1. Reduced forms of systems of equations of the first order in the vicinity of singulariries of the derivatives 2. The integrals of the reduced forms of a system of equations, chiffly of two dependent variables 3. Systems of equations with multiform values of the derivatives; singular solutions 4. Equations of the second order and the first degree 5. Equations of the second order and any degree 6. Equation of the second order with sub-uniform integrals : with some general considerations 7. General theorems on algebraic integrals : Brun's theorem Part 3 1. Linear equations : existence of synectic integrals : fundamental systems 2. General forms and properties of integrals near a singularity 3. Regular integrals : equation having all its integrals regular near a singularity 4. Equations having their integrals regular in the vicinity of every singularity (including infinity) 5. Linear equation of the second and the third orders possessing algebraic integrals 6. Equations having only some of their integrals regular near a singularity 7. Normal integrals : subnormal integrals 8. Infinite determinants, and their application to the solution of linear equations 9. Equations with uniform periodic coefficients 10. Equations having algebraic coefficients

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Theory of differential equations. Part 4, vol. 5 ; vol. 6. Partial differential equations / Forsyth, Andrew Russell (1959)

Public ISBD Titre de série : Theory of differential equations Titre : Part 4, vol. 5 ; vol. 6. Partial differential equations Type de document : texte imprimé Auteurs : Forsyth, Andrew Russell, Auteur Editeur : New York : Dover publications Année de publication : 1959 Importance : 01 vol. (XX, 478, XIII, 596) p. Format : 21 cm Note générale : Six volumes bound as three; this volume contains two parts. - Index Langues : Anglais (eng) Mots-clés : Équations différentielles Index. décimale : 517.9 Équations différentielles. Équations intégrales. Autres équations fonctionnelles. Équations aux dérivées finies. Calcul des variations. Analyse fonctionnelle Note de contenu : In summary: 1. Introduction : two existence-theorems 2. Cauchy's theorem 3. Linear equations and complete linear systems 4. Non-linear equations : Jacobi's second method, with Mayer's development 5. Classes of integrals possessed by equations of the first order 6. The method of characteristics for equations in two independent variables 7. Singular integrals and their geometrical properties 8. The method of characteristics in any number of independent variables 9. Lie's methods applied to equations of the first order 10. The equations of theoretical dynamics 11. Simultaneous equations of the first order 12. General integrals of equations of orders higher than the first 13. Linear equations of the second order in two independent variables 14. Adjoint equations 15. Forms of equations of the second order in two independent variables having their general integrals in explicit finite form 16. Equation of the second order in two independent variables having an intermediate integral 17. Ampère's method applied to equations of the second order in two independent variables 18. Darboux's method and other methods for equations of the second order in two independent variables 19. Generalisation of integrals 20. Characteristics of equations of second order 21. General transformation of equations of the second order 22. Equations of the third and higher orders, in two independent variables 23. Equations of the second order in more than two independent variables, having an intermediate integral 24. Equations of the second order in three independent variables, not necessarily having an intermediate integral Theory of differential equations. Part 4, vol. 5 ; vol. 6. Partial differential equations [texte imprimé] / Forsyth, Andrew Russell, Auteur . - New York : Dover publications, 1959 . - 01 vol. (XX, 478, XIII, 596) p. ; 21 cm. Six volumes bound as three; this volume contains two parts. - Index Langues : Anglais (eng) Mots-clés : Équations différentielles Index. décimale : 517.9 Équations différentielles. Équations intégrales. Autres équations fonctionnelles. Équations aux dérivées finies. Calcul des variations. Analyse fonctionnelle Note de contenu : In summary: 1. Introduction : two existence-theorems 2. Cauchy's theorem 3. Linear equations and complete linear systems 4. Non-linear equations : Jacobi's second method, with Mayer's development 5. Classes of integrals possessed by equations of the first order 6. The method of characteristics for equations in two independent variables 7. Singular integrals and their geometrical properties 8. The method of characteristics in any number of independent variables 9. Lie's methods applied to equations of the first order 10. The equations of theoretical dynamics 11. Simultaneous equations of the first order 12. General integrals of equations of orders higher than the first 13. Linear equations of the second order in two independent variables 14. Adjoint equations 15. Forms of equations of the second order in two independent variables having their general integrals in explicit finite form 16. Equation of the second order in two independent variables having an intermediate integral 17. Ampère's method applied to equations of the second order in two independent variables 18. Darboux's method and other methods for equations of the second order in two independent variables 19. Generalisation of integrals 20. Characteristics of equations of second order 21. General transformation of equations of the second order 22. Equations of the third and higher orders, in two independent variables 23. Equations of the second order in more than two independent variables, having an intermediate integral 24. Equations of the second order in three independent variables, not necessarily having an intermediate integral

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Theory of differential equations. Partial differential equations. Part 4, vol. 5 ; vol. 6 / Forsyth, Andrew Russell (1959)

Public ISBD Titre de série : Theory of differential equations Titre : Partial differential equations. Part 4, vol. 5 ; vol. 6 Type de document : texte imprimé Auteurs : Forsyth, Andrew Russell, Auteur Editeur : New York : Dover publications Année de publication : 1959 Importance : 1 vol. (XX, 478, XIII, 596) p. Format : 21 cm Note générale : Six volumes bound as three; this volume contains two parts. - Index . Langues : Français (fre) Note de contenu : In summary : 1. Introduction : two existence-theorem 2. Cauchy's theorem 3. Linear equations and complete linear systems 4. Non linear equations : Jacobi's second method, with Mayer's development 5. Classes of integrals possessed by equations of the first order : generalization of integrals 6. The method of characteristics for equations in two independent variables : geometrical relations of the various integrals 7. Singular integrals and their geometrical properties : singularities of the characteristics 8. The method of characteristics in any number of independent variables 9. Lies's methods applied to the equations of the first order 10. The equations of theoritical dynamics 11. Simultaneous equations of the first order 12. General integrals of equations of orders higher than the first Theory of differential equations. Partial differential equations. Part 4, vol. 5 ; vol. 6 [texte imprimé] / Forsyth, Andrew Russell, Auteur . - New York : Dover publications, 1959 . - 1 vol. (XX, 478, XIII, 596) p. ; 21 cm. Six volumes bound as three; this volume contains two parts. - Index . Langues : Français (fre) Note de contenu : In summary : 1. Introduction : two existence-theorem 2. Cauchy's theorem 3. Linear equations and complete linear systems 4. Non linear equations : Jacobi's second method, with Mayer's development 5. Classes of integrals possessed by equations of the first order : generalization of integrals 6. The method of characteristics for equations in two independent variables : geometrical relations of the various integrals 7. Singular integrals and their geometrical properties : singularities of the characteristics 8. The method of characteristics in any number of independent variables 9. Lies's methods applied to the equations of the first order 10. The equations of theoritical dynamics 11. Simultaneous equations of the first order 12. General integrals of equations of orders higher than the first

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