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Bredensteiner E.J. — Differential Equations

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Название: Differential Equations

Автор: Bredensteiner E.J.

Аннотация:

What could be better than the bestselling Schaum's Outline series? For students looking for a quick nuts-and-bolts overview, it would have to be Schaum's Easy Outline series. Every book in this series is a pared-down, simplified, and tightly focused version of its bigger predecessor. With an emphasis on clarity and brevity, each new title features a streamlined and updated format and the absolute essence of the subject, presented in a concise and readily understandable form. Graphic elements such as sidebars, reader-alert icons, and boxed highlights feature selected points from the text, illuminate keys to learning, and give students quick pointers to the essentials.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 136

Добавлена в каталог: 21.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Adams — Bashforth — Moulton method      109 111—112
Amplitude      53
Analytic functions      86—87
Archimedes' principle      51
Bernoulli equations      6 14
Bessel functions      99—100
Boundary-value problems      5 115—120
Buoyancy problems      51—52
Characteristic equations      34—35 73
Circular frequency      53
Classifying solutions      52—53
Coefficients      see “Constant coefficients” “Undetermined “Variable
Completing the square      58
Constant coefficients      30
Constant coefficients, Laplace transforms solutions      66—67
Constant coefficients, linear equations      79—83
Constant matrix      70
Convolutions      59—60
Critically damped motion      53
Damped motion      53
Decay problems      20—21
Defining properties      10—11
Denominators      58—59
derivatives      65—66 72
Differential equations      see also “Linear differential equations”
Differential equations, applications      20—26
Differential equations, classifying      5—7
Differential equations, definitions      2—5
Differential equations, first-order      8—14 20—26 105—112
Differential equations, general solutions      4—5
Differential equations, notation      3
Differential equations, order      3
Differential equations, particular solutions      4
Differential equations, solutions      3—5 8—14
Differential forms      5—6
Dilution problems      23—25
Direction fields      105
Dummy index      101
Eigenfunctions      117 119—120
eigenvalue problems      117
Eigenvalues      117
Electrical circuit problems      49—51
electrical circuits      25—26
Equations      see also “Differential” “Linear
Equations, Bernoulli      6 14
Equations, characteristic      34—35 73
Equations, exact      7 10—12
Equations, homogeneous      6—7 9—10 30 87—88
Equations, indicial      91
Equations, n-th order      34—35
Equations, nonhomogeneous      32 39—44 88—89
Equations, ordinary differential      2
Equations, partial differential      2—3
Equations, second-order      34 35—36
Equations, separable      7
Equilibrium position      47
Euler's method      106 108 111
exact equations      7 10—12
Falling body problems      21—22
First-order differential equations      8—14
First-order differential equations, applications      20—26
First-order differential equations, numerical methods      105—112
First-order systems      79—83 110
Forced motion      53
Fourier series      120—121
Free motion      52—53
Froebenius, method of      90—91
Functions, Bessel      99—100
Functions, gamma      98—99
Gamma functions      98—99
general solutions      4—5 32
Growth problems      20—21
Homogeneous equations      6—7 9—10 30 87—88;
Hooke's law      48—49
Identity matrix      72
Independent variables      57
Indicial equation      91
Initial-value problems      5 9 44 82 89
integral      72
Integrating factors      11—12
Inverse Laplace transforms      57—58
Isoclines      105
Kirchhoff's law      50
Laplace transforms      56—62 124—132
Laplace transforms, inverse      57—58
Laplace transforms, solutions by      65—67
Laws, Hooke's      48—49
Laws, Kirchhoff's      50—51
Laws, Newton's of cooling      21
Laws, Newton's second of motion      22
Line elements      105
Linear differential equations      6 12—14
Linear differential equations, first-order      105—112
Linear differential equations, homogeneous      30 34—37 39—44
Linear differential equations, nonhomogeneous      39—44
Linear differential equations, reduction to first-order system      79—83

Linear differential equations, second-order      47—53 86 115—117
Linear differential equations, solutions      34—37 79—83
Linear differential equations, theory of solutions      29—32
Linear systems      67
Linearly dependent solutions      31
Linearly independent solutions      31
Matrices      70—75
Matrix addition      71
Matrix exponential      73—75
Matrix multiplication      71
Matrix solution methods      79—83
Method of Frobenius      90—91
Method of undetermined coefficients      40—42
Methods, Adams — Bashforth — Moulton      109 111—112
Methods, Euler's      106 108 111
Methods, Frobenius      90—91
Methods, modified Euler's      108
Methods, numerical for first-order equations      105—112
Methods, predictor-corrector      108
Methods, Runge — Kutta      108—109 111
Methods, undetermined coefficients      40—42
Modified Euler's method      108
Motion      52—53
Natural frequency      53
Natural length      49
Newton's law of cooling      21
Newton's Second Law of Motion      22
Nonhomogeneous equations      32 39—44 88—89
Notation      3
nth-order equations      34—36
Numerators      59
Numerical instability      107
Numerical methods      105—112
Ordinary differential equations      2
Ordinary points      87
Orthogonal trajectories      26
Oscillatory damped motion      53
Overdamped motion      53
Partial differential equation      2—3
Partial fractions      58—59
Particular solutions      4
Period      53
Phase angle      53
Power scries      86—92
Power scries method      87—88
Predictor-corrector method      108
Problems, boundary-value      5 115—120
Problems, buoyancy      51—52
Problems, decay      20—21
Problems, dilution      23—25
Problems, eigenvalue      117
Problems, electrical circuit      49—51
Problems, falling body      21—22
Problems, growth      20—21
Problems, initial-value      44 82
Problems, spring      47—49
Problems, Sturm — Liouville      117—118
Problems, temperature      21
Recurrence formula      88
Regular singular points      89—90
Runge — Kutta method      108—109 111
Scalar multiplication      71
Second-order equations      34 35—36
Second-order linear differential equations      47—53 86 115—117
separable equations      7
simple harmonic motion      53
Solutions      3—5
Solutions, classifying      52—53
Solutions, first-order differential equations      8—14
Solutions, initial-value problems      82
Solutions, Laplace transforms      65—67
Solutions, linear differential      34—37 79—83
Solutions, linear systems      67
Solutions, linearly dependent      31
Solutions, linearly independent      31
Solutions, matrix methods      79—83
Solutions, no initial conditions      82—83
Solutions, particular      4
Solutions, power scries      86—92
Solutions, theory of      29—32
Spring problems      47—49
Square matrix      70
Standard forms      5—6
Steady-state motion      53
Step sizes      107
Sturm — Liouville problems      117—118
Temperature problems      21
Transient motion      53
Translations      61—62
Undamped motion      53
Underdamped motion      53
Undetermined coefficients      40—42
Unit step function      60—61
Variable coefficients      30 86
Variation of parameters      42—44
Vectors      70
Wronskian, the      31—32

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