The Resource Applied Laplace Transforms and z-Transforms for Scientists and Engineers : A Computational Approach using a Mathematica Package, by Urs Graf, (electronic resource)

Applied Laplace Transforms and z-Transforms for Scientists and Engineers : A Computational Approach using a Mathematica Package, by Urs Graf, (electronic resource)

Label
Applied Laplace Transforms and z-Transforms for Scientists and Engineers : A Computational Approach using a Mathematica Package
Title
Applied Laplace Transforms and z-Transforms for Scientists and Engineers
Title remainder
A Computational Approach using a Mathematica Package
Statement of responsibility
by Urs Graf
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
The theory of Laplace transformation is an important part of the mathematical background required for engineers, physicists and mathematicians. Laplace transformation methods provide easy and effective techniques for solving many problems arising in various fields of science and engineering, especially for solving differential equations. What the Laplace transformation does in the field of differential equations, the z-transformation achieves for difference equations. The two theories are parallel and have many analogies. Laplace and z­ transformations are also referred to as operational calculus, but this notion is also used in a more restricted sense to denote the operational calculus of Mikusinski. This book does not use the operational calculus of Mikusinski, whose approach is based on abstract algebra and is not readily accessible to engineers and scientists. The symbolic computation capability of Mathematica can now be used in favor of the Laplace and z-transformations. The first version of the Mathematica Package LaplaceAndzTransforrns developed by the author appeared ten years ago. The Package computes not only Laplace and z-transforms but also includes many routines from various domains of applications. Upon loading the Package, about one hundred and fifty new commands are added to the built-in commands of Mathematica. The code is placed in front of the already built-in code of Laplace and z-transformations of Mathematica so that built-in functions not covered by the Package remain available. The Package substantially enhances the Laplace and z-transformation facilities of Mathematica. The book is mainly designed for readers working in the field of applications
http://library.link/vocab/creatorName
Graf, Urs
Dewey number
515.7
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
jxgyR2_R910
Image bit depth
0
Language note
English
LC call number
QA319-329.9
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/subjectName
  • Functional analysis
  • Algebra
  • Integral Transforms
  • Computer science
  • Functional Analysis
  • Symbolic and Algebraic Manipulation
  • Integral Transforms, Operational Calculus
  • Computational Mathematics and Numerical Analysis
Label
Applied Laplace Transforms and z-Transforms for Scientists and Engineers : A Computational Approach using a Mathematica Package, by Urs Graf, (electronic resource)
Instantiates
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Color
not applicable
Content category
text
Content type code
txt
Contents
1 Laplace Transformation -- 1.1 The One-Sided Laplace Transform -- 1.2 The Two-Sided Laplace Transform -- 1.3 Ordinary Linear Differential Equations -- 2 z-Transformation -- 2.1 z-Transforms and Inverse z-Transforms -- 2.2 Difference Equations -- 3 Laplace Transforms with the Package -- 3.1 Basics -- 3.2 The Use of Transformation Rules -- 3.3 The Finite Laplace Transform -- 3.4 Special Functions -- 3.5 Inverse Laplace Transformation -- 3.6 Differential Equations -- 4 z-Transformation with the Package -- 4.1 Basics -- 4.2 Use of Transformation Rules -- 4.3 Difference Equations -- 5 Applications To Automatic Control -- 5.1 Controller Configurations -- 5.2 State-Variable Analysis -- 5.3 Second Order Differential Systems -- 5.4 Stability -- 5.5 Frequency Analysis -- 5.6 Sampled-Data Control Systems -- 6 Laplace Transformation: Further Topics -- 6.1 The Complex Inversion Formula -- 6.2 Laplace Transforms and Asymptotics -- 6.3 Differential Equations -- 7 z-Transformation: Further Topics -- 7.1 The Advanced z-Transformation -- 7.2 Applications -- 7.3 Use of the Package -- 8 Examples from Electricity -- 8.1 Transmission Lines -- 8.2 Electrical Networks -- 9 Examples from Control Engineering -- 9.1 Control of an Inverted Pendulum -- 9.2 Controling a Seesaw-Pendulum -- 9.3 Control of a DC Motor -- 9.4 A Magnetic-Ball-Suspension-System -- 9.5 A Sampled-Data State-Variable Control System -- 10 Heat Conduction and Vibration Problems -- 10.1 Flow of Heat -- 10.2 Waves and Vibrations in Elastic Solids -- 11 Further Techniques -- 11.1 Duhamel’s Formulas -- 11.2 Green’s Functions -- 11.3 Fundamental Solutions -- 11.4 Finite Fourier Transforms -- 12 Numerical Inversion of Laplace Transforms -- 12.1 Inversion by the Use of Laguerre Functions -- 12.2 Inversion by Use of Fourier Analysis -- 12.3 The Use of Gaussian Quadrature Formulas -- 12.4 The Method of Gaver and Stehfest -- 12.5 Example -- Appendix: Package Commands
Dimensions
unknown
Edition
1st ed. 2004.
Extent
1 online resource (X, 500 p.)
File format
multiple file formats
Form of item
online
Isbn
9783034878463
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-3-0348-7846-3
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000101341
  • (SSID)ssj0000933585
  • (PQKBManifestationID)11582208
  • (PQKBTitleCode)TC0000933585
  • (PQKBWorkID)10890327
  • (PQKB)11502936
  • (DE-He213)978-3-0348-7846-3
  • (MiAaPQ)EBC3086079
  • (EXLCZ)993400000000101341
Label
Applied Laplace Transforms and z-Transforms for Scientists and Engineers : A Computational Approach using a Mathematica Package, by Urs Graf, (electronic resource)
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Color
not applicable
Content category
text
Content type code
txt
Contents
1 Laplace Transformation -- 1.1 The One-Sided Laplace Transform -- 1.2 The Two-Sided Laplace Transform -- 1.3 Ordinary Linear Differential Equations -- 2 z-Transformation -- 2.1 z-Transforms and Inverse z-Transforms -- 2.2 Difference Equations -- 3 Laplace Transforms with the Package -- 3.1 Basics -- 3.2 The Use of Transformation Rules -- 3.3 The Finite Laplace Transform -- 3.4 Special Functions -- 3.5 Inverse Laplace Transformation -- 3.6 Differential Equations -- 4 z-Transformation with the Package -- 4.1 Basics -- 4.2 Use of Transformation Rules -- 4.3 Difference Equations -- 5 Applications To Automatic Control -- 5.1 Controller Configurations -- 5.2 State-Variable Analysis -- 5.3 Second Order Differential Systems -- 5.4 Stability -- 5.5 Frequency Analysis -- 5.6 Sampled-Data Control Systems -- 6 Laplace Transformation: Further Topics -- 6.1 The Complex Inversion Formula -- 6.2 Laplace Transforms and Asymptotics -- 6.3 Differential Equations -- 7 z-Transformation: Further Topics -- 7.1 The Advanced z-Transformation -- 7.2 Applications -- 7.3 Use of the Package -- 8 Examples from Electricity -- 8.1 Transmission Lines -- 8.2 Electrical Networks -- 9 Examples from Control Engineering -- 9.1 Control of an Inverted Pendulum -- 9.2 Controling a Seesaw-Pendulum -- 9.3 Control of a DC Motor -- 9.4 A Magnetic-Ball-Suspension-System -- 9.5 A Sampled-Data State-Variable Control System -- 10 Heat Conduction and Vibration Problems -- 10.1 Flow of Heat -- 10.2 Waves and Vibrations in Elastic Solids -- 11 Further Techniques -- 11.1 Duhamel’s Formulas -- 11.2 Green’s Functions -- 11.3 Fundamental Solutions -- 11.4 Finite Fourier Transforms -- 12 Numerical Inversion of Laplace Transforms -- 12.1 Inversion by the Use of Laguerre Functions -- 12.2 Inversion by Use of Fourier Analysis -- 12.3 The Use of Gaussian Quadrature Formulas -- 12.4 The Method of Gaver and Stehfest -- 12.5 Example -- Appendix: Package Commands
Dimensions
unknown
Edition
1st ed. 2004.
Extent
1 online resource (X, 500 p.)
File format
multiple file formats
Form of item
online
Isbn
9783034878463
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-3-0348-7846-3
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000101341
  • (SSID)ssj0000933585
  • (PQKBManifestationID)11582208
  • (PQKBTitleCode)TC0000933585
  • (PQKBWorkID)10890327
  • (PQKB)11502936
  • (DE-He213)978-3-0348-7846-3
  • (MiAaPQ)EBC3086079
  • (EXLCZ)993400000000101341

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