The Resource Analytical and Computational Methods of Advanced Engineering Mathematics, by Grant B. Gustafson, Calvin H. Wilcox, (electronic resource)

Analytical and Computational Methods of Advanced Engineering Mathematics, by Grant B. Gustafson, Calvin H. Wilcox, (electronic resource)

Label
Analytical and Computational Methods of Advanced Engineering Mathematics
Title
Analytical and Computational Methods of Advanced Engineering Mathematics
Statement of responsibility
by Grant B. Gustafson, Calvin H. Wilcox
Creator
Contributor
Author
Author
Subject
Language
  • eng
  • eng
Summary
(NOTES)This text focuses on the topics which are an essential part of the engineering mathematics course:ordinary differential equations, vector calculus, linear algebra and partial differential equations. Advantages over competing texts: 1. The text has a large number of examples and problems - a typical section having 25 quality problems directly related to the text. 2. The authors use a practical engineering approach based upon solving equations. All ideas and definitions are introduced from this basic viewpoint, which allows engineers in their second year to understand concepts that would otherwise be impossibly abstract. Partial differential equations are introduced in an engineering and science context based upon modelling of physical problems. A strength of the manuscript is the vast number of applications to real-world problems, each treated completely and in sufficient depth to be self-contained. 3. Numerical analysis is introduced in the manuscript at a completely elementary calculus level. In fact, numerics are advertised as just an extension of the calculus and used generally as enrichment, to help communicate the role of mathematics in engineering applications. 4.The authors have used and updated the book as a course text over a 10 year period. 5. Modern outline, as contrasted to the outdated outline by Kreysig and Wylie. 6. This is now a one year course. The text is shorter and more readable than the current reference type manuals published all at around 1300-1500 pages
Member of
http://library.link/vocab/creatorName
Gustafson, Grant B
Dewey number
519
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • 9STbsCww0LA
  • aPqpI3LHBHU
Image bit depth
0
Language note
English
LC call number
  • TA329-348
  • TA640-643
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Wilcox, Calvin H.
Series statement
Texts in Applied Mathematics,
Series volume
28
http://library.link/vocab/subjectName
  • Engineering mathematics
  • Mathematics
  • Global analysis (Mathematics)
  • Computer science
  • Mathematical and Computational Engineering
  • Applications of Mathematics
  • Analysis
  • Computational Mathematics and Numerical Analysis
Label
Analytical and Computational Methods of Advanced Engineering Mathematics, by Grant B. Gustafson, Calvin H. Wilcox, (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 Numerical Analysis -- 1.1 The Nature of Numerical Analysis -- 1.2 Polynomial Interpolation -- 1.3 Numerical Integration and Differentiation -- 1.4 Solution of Equations -- 1.5 Inverse Functions -- 1.6 Implicit Functions -- 1.7 Numerical Summation of Infinite Series -- 2 Ordinary Differential Equations of First Order -- 2.1 The Nature of Differential Equations -- 2.2 Separable Equations -- 2.3 Linear First-Order Equations -- 2.4 Exact Equations -- 2.5 Applications to Some Second-Order Equations -- 2.6 The Initial Value Problem -- 2.7 Numerical Methods for the Initial Value Problem -- 3 Ordinary Differential Equations of Higher Order -- 3.1 Examples from Engineering and Physics -- 3.2 Linear Second-Order Equations — Structure of Solutions -- 3.3 Linear Second-Order Equations with Constant Coefficients -- 3.4 Linear Second-Order Equations with Analytic Coefficients -- 3.5 Numerical Methods for Second-Order Equations -- 3.6 Linear Equations of Order n > 2 -- 4 The Laplace Transform -- 4.1 The Nature of the Laplace Transform -- 4.2 The Laplace Transforms of Some Elementary Functions -- 4.3 Operational Rules for the Laplace Transform -- 4.4 Applications to Differential Equations -- 4.5 Applications to Systems of Differential Equations -- 5 Linear Algebra -- 5.1 Systems of Linear Equations -- 5.2 The Gauss Elimination Method -- 5.3 Vector Spaces -- 5.4 Matrices and Matrix Algebra -- 5.5 The Fundamental Theorem of Linear Algebra -- 5.6 Determinants and Cramer’s Rule -- 5.7 Eigenvalues and Eigenvectors -- 6 Vector Analysis -- 6.1 Vector Algebra -- 6.2 Vector Calculus of Curves in Space -- 6.3 Vector Calculus of Surfaces in Space -- 6.4 Calculus of Scalar and Vector Fields -- 6.5 Integral Theorems of Vector Calculus -- 6.6 X-Ray Diffraction and Crystal Structure -- 7 Partial Differential Equations of Mathematical Physics -- 7.1 Vibrating Strings: D’Alembert’s Wave Equation -- 7.2 Heat Diffusion in Rods: Fourier’s Heat Equation -- 7.3 Heat Diffusion in Plates -- 7.4 Steady-State Heat Diffusion in Plates: The Laplace Equation -- 7.5 Vibrations of Drums -- 7.6 Heat Diffusion in Solids -- 7.7 Steady-State Heat Diffusion in Solids -- 8 Fourier Analysis and Sturm-Liouville Theory -- 1 Fourier Series -- II Fourier Integrals -- III Sturm-Liouville Theory -- 9 Boundary Value Problems of Mathematical Physics -- 9.1 Heat Diffusion in One Dimension -- 9.2 Vibration of Strings and Traveling Waves -- 9.3 Steady-State Diffusion of Heat in Plates -- 9.4 Transient Diffusion of Heat in Plates -- 9.5 Vibrations of Drums -- 9.6 Steady-State Diffusion of Heat in Solids -- 9.7 The Laplace Transform Method -- Appendix: Answers and Hints to Selected Exercises -- References
Dimensions
unknown
Edition
1st ed. 1998.
Extent
1 online resource (XXIV, 733 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461206330
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-1-4612-0633-0
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000089209
  • (SSID)ssj0001295845
  • (PQKBManifestationID)11986898
  • (PQKBTitleCode)TC0001295845
  • (PQKBWorkID)11348358
  • (PQKB)11518374
  • (DE-He213)978-1-4612-0633-0
  • (MiAaPQ)EBC3074035
  • (EXLCZ)993400000000089209
Label
Analytical and Computational Methods of Advanced Engineering Mathematics, by Grant B. Gustafson, Calvin H. Wilcox, (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 Numerical Analysis -- 1.1 The Nature of Numerical Analysis -- 1.2 Polynomial Interpolation -- 1.3 Numerical Integration and Differentiation -- 1.4 Solution of Equations -- 1.5 Inverse Functions -- 1.6 Implicit Functions -- 1.7 Numerical Summation of Infinite Series -- 2 Ordinary Differential Equations of First Order -- 2.1 The Nature of Differential Equations -- 2.2 Separable Equations -- 2.3 Linear First-Order Equations -- 2.4 Exact Equations -- 2.5 Applications to Some Second-Order Equations -- 2.6 The Initial Value Problem -- 2.7 Numerical Methods for the Initial Value Problem -- 3 Ordinary Differential Equations of Higher Order -- 3.1 Examples from Engineering and Physics -- 3.2 Linear Second-Order Equations — Structure of Solutions -- 3.3 Linear Second-Order Equations with Constant Coefficients -- 3.4 Linear Second-Order Equations with Analytic Coefficients -- 3.5 Numerical Methods for Second-Order Equations -- 3.6 Linear Equations of Order n > 2 -- 4 The Laplace Transform -- 4.1 The Nature of the Laplace Transform -- 4.2 The Laplace Transforms of Some Elementary Functions -- 4.3 Operational Rules for the Laplace Transform -- 4.4 Applications to Differential Equations -- 4.5 Applications to Systems of Differential Equations -- 5 Linear Algebra -- 5.1 Systems of Linear Equations -- 5.2 The Gauss Elimination Method -- 5.3 Vector Spaces -- 5.4 Matrices and Matrix Algebra -- 5.5 The Fundamental Theorem of Linear Algebra -- 5.6 Determinants and Cramer’s Rule -- 5.7 Eigenvalues and Eigenvectors -- 6 Vector Analysis -- 6.1 Vector Algebra -- 6.2 Vector Calculus of Curves in Space -- 6.3 Vector Calculus of Surfaces in Space -- 6.4 Calculus of Scalar and Vector Fields -- 6.5 Integral Theorems of Vector Calculus -- 6.6 X-Ray Diffraction and Crystal Structure -- 7 Partial Differential Equations of Mathematical Physics -- 7.1 Vibrating Strings: D’Alembert’s Wave Equation -- 7.2 Heat Diffusion in Rods: Fourier’s Heat Equation -- 7.3 Heat Diffusion in Plates -- 7.4 Steady-State Heat Diffusion in Plates: The Laplace Equation -- 7.5 Vibrations of Drums -- 7.6 Heat Diffusion in Solids -- 7.7 Steady-State Heat Diffusion in Solids -- 8 Fourier Analysis and Sturm-Liouville Theory -- 1 Fourier Series -- II Fourier Integrals -- III Sturm-Liouville Theory -- 9 Boundary Value Problems of Mathematical Physics -- 9.1 Heat Diffusion in One Dimension -- 9.2 Vibration of Strings and Traveling Waves -- 9.3 Steady-State Diffusion of Heat in Plates -- 9.4 Transient Diffusion of Heat in Plates -- 9.5 Vibrations of Drums -- 9.6 Steady-State Diffusion of Heat in Solids -- 9.7 The Laplace Transform Method -- Appendix: Answers and Hints to Selected Exercises -- References
Dimensions
unknown
Edition
1st ed. 1998.
Extent
1 online resource (XXIV, 733 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461206330
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-1-4612-0633-0
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000089209
  • (SSID)ssj0001295845
  • (PQKBManifestationID)11986898
  • (PQKBTitleCode)TC0001295845
  • (PQKBWorkID)11348358
  • (PQKB)11518374
  • (DE-He213)978-1-4612-0633-0
  • (MiAaPQ)EBC3074035
  • (EXLCZ)993400000000089209

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