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Ince E.L. — Integration of ordinary differential equations
Ince E.L. — Integration of ordinary differential equations

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Название: Integration of ordinary differential equations

Автор: Ince E.L.


The object of this book is to provide in a compact form an
account of the methods of integrating explicitly the
commoner types of ordinary differential equation, and in
particular those equations that arise from problems in
geometry and applied mathematics. It takes the existence
of solutions for granted; the reader who desires to look into
the theoretical background of the methods here outlined
will find what he seeks in my larger treatise Ordinary
Differential Equations (Longmans, Green & Co., Ltd., 1927).
With this qualification, it will be found to contain all the
material needed by students of mathematics in our
Universities who do not specialize in differential equations,
as well as by students of mathematical physics and,
As one of the first things a beginner has to learn is to
identify the type to which a given equation belongs, the
examples for solution have not been printed after the
sections to which they refer, but have been collected at the
end of the book. When the contents of the first chapter
have been mastered, the reader may test his skill by
attacking examples selected at random from Nos. 1 to 122,
and similarly for the later chapters. At the same time, the
examples occur roughly in the order of the table of contents,
so that working material is always available as reading
In conclusion, I wish to record my thanks to the General
Editors for the compliment paid me in inviting me to
contribute this book to their series of University
Mathematical Texts, and for their encouragement and help during
its growth and passage through the press.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1939

Количество страниц: 156

Добавлена в каталог: 16.02.2013

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Предметный указатель
Asymptotic point      39
Auxiliary equation      85
Auxiliary equation, complex roots      87
Auxiliary equation, repeated roots      88
Base point      37
Bernoulli equation      22
Bessel equation      127
Bessel function $J_{n}(x)$      128
Bessel function $Y_{n}(x)$      129
Change of variable      24
Clairaut equation      42
col      36
Complementary function      19 81
Condenser, charging of      20
Constant coefficients, linear equation with      82—101
Constant coefficients, linear system with      108—111
Curvature      75
Cusp-locus      53 56
D'Alembert equation      43
Definite integral, solution by      104
Degree      2 40
Degree, equation of second      55
Discriminant locus      52
Envelope      53 57
Euler linear equation      72 101
exact equations      10
Families of plane curves      27
Frobenius, method of      119
General integral      3 40 62
General integral by quadratures      100
Geometrical interpretation      50
Homogeneous types, first order      6 48
Homogeneous types, second order      67—72
Hypergeometric equation      116
Indicial equation      116
Infinity, singularity at      124
Initial conditions      21
Integrability, condition of      11
Integral curves      27—39
Integral, first      73
Integrating factors      13 73
Integrating factors, quotient of      15
Integrating factors, special types      16
Integration      3
Isotropic nodal point      37
Lagrange equation      44
Laplace equation      104
Legendre equation      119
Legendre equation, large |x|      124
Legendre function $P_{n}(x)$      120
Legendre function $Q_{n}(x)$      122
Level lines      34
Limiting point      38
Linear coefficients      8
Linear equation in general      79—107
Linear equation, first order      18—21
Linear fractional equation      36
Linear independence      80
Linear systems      108
Lines of Slope      34
Nodal point      37
normal      28 76
Operator, inverse      90—99
Operator, linear      86
Order      1
Order of a system      109
Order, reduction of      61 81
Ordinary point      113
Orthogonal trajectories      30
p-discriminant      54
Parametric integration      63
Particular integral      3 19 81
Permutable operators      83
Polar co-ordinates      25
Polar co-ordinates, trajectories      32
primitive      3 62
Principal directions      36
Quadratures      5 19 100
Recurrence relation      114
Reduced equation      19 80
Reduced equation, constant coefficients      82—90
Regular singularity      115
Riccati equation      22
Rodrigues formula      122
Second degree, equation of      55
Separation of variables      4
Series solution      112—132
Simultaneous equations      108—111
Singular integrals      3
Singular points      35 115
Subnormal      28
Subtangent      28
Tac-locus      58
Tangent      28
Taylor series      112
Trajectories      29—35
Variable absent      47 62 65
Variation of parameters      106
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