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標(biāo)題: Titlebook: Introduction to the Theory and Application of the Laplace Transformation; Gustav Doetsch Book 1974 Springer-Verlag Berlin Heidelberg 1974 [打印本頁]

作者: 大口水罐    時間: 2025-3-21 16:05
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作者: 冷淡周邊    時間: 2025-3-21 21:27
The Solutions of the Differential Equation for Specific Excitations,combination of functions of the type .; it is easy to survey. Therefore we disregard this part of the problem here, and we presume that .; that is, the system is assumed to be initially at rest. Thus we find the corresponding solution in the image space: . and, consequently, in the original space:
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Book 1974technics, mechanics etc. Chiefly, they treat problems which, in mathematical language, are governed by ordi- nary and partial differential equations, in various physically dressed forms. The theoretical foundations of the Laplace transformation are presented usually only in a simplified manner, pres
作者: Radiculopathy    時間: 2025-3-22 13:29
as electrotechnics, mechanics etc. Chiefly, they treat problems which, in mathematical language, are governed by ordi- nary and partial differential equations, in various physically dressed forms. The theoretical foundations of the Laplace transformation are presented usually only in a simplified ma
作者: 挖掘    時間: 2025-3-22 19:41
The Ordinary Differential Equation, specifying Initial Values for Derivatives of Arbitrary Order, a, .′ (0), and .″ (0) were given. Then we would form the higher derivatives, . . (.) and . (.). For . = 0, we would obtain two linear equations in the unknowns .′ (0) and .″ (0). Having solved these equations, we can write the complete solution .(.).
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Gustav Doetschn authoritative and comprehensive reference covering all major aspects of the science and engineering of tribology that are relevant to researchers across all engineering industries and related scientific disciplines. This is the first major reference that brings together the science, engineering an
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Gustav Doetschn authoritative and comprehensive reference covering all major aspects of the science and engineering of tribology that are relevant to researchers across all engineering industries and related scientific disciplines. This is the first major reference that brings together the science, engineering an
作者: MURAL    時間: 2025-3-24 13:21
Gustav Doetscha single work.Developed by authoritative experts in the fiel.TRIBOLOGY – the study of friction, wear and lubrication – impacts almost every aspect of our daily lives. The Springer Encyclopedia of Tribology is an authoritative and comprehensive reference covering all major aspects of the science and
作者: 謊言    時間: 2025-3-24 16:13
Gustav Doetschn authoritative and comprehensive reference covering all major aspects of the science and engineering of tribology that are relevant to researchers across all engineering industries and related scientific disciplines. This is the first major reference that brings together the science, engineering an
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作者: 遺忘    時間: 2025-3-25 03:02
Gustav Doetscha single work.Developed by authoritative experts in the fiel.TRIBOLOGY – the study of friction, wear and lubrication – impacts almost every aspect of our daily lives. The Springer Encyclopedia of Tribology is an authoritative and comprehensive reference covering all major aspects of the science and
作者: 刻苦讀書    時間: 2025-3-25 05:29
Gustav Doetschn authoritative and comprehensive reference covering all major aspects of the science and engineering of tribology that are relevant to researchers across all engineering industries and related scientific disciplines. This is the first major reference that brings together the science, engineering an
作者: 欺騙世家    時間: 2025-3-25 09:59
Gustav Doetscha single work.Developed by authoritative experts in the fiel.TRIBOLOGY – the study of friction, wear and lubrication – impacts almost every aspect of our daily lives. The Springer Encyclopedia of Tribology is an authoritative and comprehensive reference covering all major aspects of the science and
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作者: 粉筆    時間: 2025-3-25 23:01
Gustav Doetscha single work.Developed by authoritative experts in the fiel.TRIBOLOGY – the study of friction, wear and lubrication – impacts almost every aspect of our daily lives. The Springer Encyclopedia of Tribology is an authoritative and comprehensive reference covering all major aspects of the science and
作者: 遠(yuǎn)足    時間: 2025-3-26 02:23

作者: frugal    時間: 2025-3-26 06:11
Gustav Doetschn authoritative and comprehensive reference covering all major aspects of the science and engineering of tribology that are relevant to researchers across all engineering industries and related scientific disciplines. This is the first major reference that brings together the science, engineering an
作者: Intact    時間: 2025-3-26 11:54
The Unique Inverse of the Laplace Transformation,responding image function, obviously in a unique manner. This relation may be looked at in the inverse orientation; that is, one may begin with some specific image function and seek the corresponding original functions. This inverse transformation will be designated as .-transformation. Clearly, thi
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The Initial Value Problem of Ordinary Differential Equations with Constant Coefficients,ntegrating ordinary linear differential equations with constant coefficients in the interval . ≧ 0, for specified values of the solution and some of its derivatives at . = 0, the initial values (Initial Value Problem). This is a problem which may be solved by a familiar classical technique: First on
作者: 無意    時間: 2025-3-27 10:18
The Ordinary Differential Equation, specifying Initial Values for Derivatives of Arbitrary Order, a 0. However, one could encounter some initial value problem with . specified values at . = 0 for derivatives of arbitrary order. For instance, for same third order differential equation one might specify the initial values . .(0), . .(0), . . (0). In this case, we would solve the problem as if . (0)
作者: 售穴    時間: 2025-3-27 16:56

作者: 財產(chǎn)    時間: 2025-3-27 18:02
The Ordinary Linear Differential Equation in the Space of Distributions,ibution-derivative equations.” In the latter, the given and the sought quantities are distributions. To emphasize the analogy to the case of functions, we shall employ here for the designation of distributions lower case letters like ., ., . . . (which are usually reserved for functions) instead of
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作者: armistice    時間: 2025-3-28 18:49
The Mapping of the Convolution,vestigate operations which involve more than one function, like sum or product of functions. The formula for the sum of functions . is immediately obvious. However, the image of the product of two original functions, . · . say, is quite complicated, thus necessitating that its study be deferred to Chapter 31.
作者: preservative    時間: 2025-3-29 01:41
Introduction of the Laplace Integral from Physical and Mathematical Points of View,The integral . is known as the Laplace integral; ., the dummy variable of integration, scans the real numbers between 0 and ∞, and the parameter . may be real-valued or complex-valued. Should this integral converge for some values of ., then it defines a function .(.):..
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作者: muster    時間: 2025-3-29 10:56
The Half-Plane of Convergence,Reviewing the examples of Chapter 2, we observe that for each of these functions the Laplace integral converges in a right half-plane. We shall show in_this Chapter that this is generally true for Laplace integrals. Prior to that, we shall determine the domain of absolute convergence of a Laplace integral.
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作者: 冰雹    時間: 2025-3-29 16:21
The Laplace Transform as an Analytic Function,On p. 5 we developed the Laplace integral as a continuous analogue of the power series. In this Chapter, we shall demonstrate that a Laplace integral, like a power series, always represents an analytic function.
作者: needle    時間: 2025-3-29 23:43
The Mapping of Differentiation,Using Theorem 8.1, we shall derive, in this Chapter, Theorem 9.1, which provides the image of differentiation. The latter will prove extremely useful in practical applications of the .-transformation. A few introductory remarks will aid the subsequent development.
作者: prolate    時間: 2025-3-30 03:02
Applications of the Convolution Theorem: Integral Relations,The .-transformation permits the transformation of the convolution, a complicated integral representation, into a simple algebraic product. This facility can be utilized to produce simple proofs of integral relations which are otherwise difficult to verify.
作者: 鎮(zhèn)壓    時間: 2025-3-30 06:53

作者: precede    時間: 2025-3-30 08:25
Rules of Mapping for the ,-Transformation of Distributions,Throughout this Chapter 14, we shall presume that ., where .(.) represents a function which complies with the conditions (12.4,5), and we shall use: ..
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作者: 大火    時間: 2025-3-31 04:43
Gustav Doetschuded. As a six-volume set, the Springer Encyclopedia of Tribology comprises 1630 entries written by authoritative experts in each subject area, under the guidance of an international panel of key researchers from academia, national laboratories and industry. With alphabetically-arranged entries, con
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作者: 不可磨滅    時間: 2025-3-31 12:15
Gustav Doetschuded. As a six-volume set, the Springer Encyclopedia of Tribology comprises 1630 entries written by authoritative experts in each subject area, under the guidance of an international panel of key researchers from academia, national laboratories and industry. With alphabetically-arranged entries, con
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Gustav Doetschuded. As a six-volume set, the Springer Encyclopedia of Tribology comprises 1630 entries written by authoritative experts in each subject area, under the guidance of an international panel of key researchers from academia, national laboratories and industry. With alphabetically-arranged entries, con




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