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Applied Calculus of Variations for Engineers 2nd edition [Kõva köide]

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(Siemens, Cypress, California, USA)
  • Formaat: Hardback, 234 pages, kõrgus x laius: 234x156 mm, kaal: 524 g
  • Ilmumisaeg: 06-Jun-2014
  • Kirjastus: Apple Academic Press Inc.
  • ISBN-10: 1482253593
  • ISBN-13: 9781482253597
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Applied Calculus of Variations for Engineers 2nd editionSuurem pilt
  • Formaat: Hardback, 234 pages, kõrgus x laius: 234x156 mm, kaal: 524 g
  • Ilmumisaeg: 06-Jun-2014
  • Kirjastus: Apple Academic Press Inc.
  • ISBN-10: 1482253593
  • ISBN-13: 9781482253597
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781482253597.html
The purpose of the calculus of variations is to find optimal solutions to engineering problems whose optimum may be a certain quantity, shape, or function. Applied Calculus of Variations for Engineers addresses this important mathematical area applicable to many engineering disciplines. Its unique, application-oriented approach sets it apart from the theoretical treatises of most texts, as it is aimed at enhancing the engineers understanding of the topic.





This Second Edition text:















Contains new chapters discussing analytic solutions of variational problems and Lagrange-Hamilton equations of motion in depth





Provides new sections detailing the boundary integral and finite element methods and their calculation techniques





Includes enlightening new examples, such as the compression of a beam, the optimal cross section of beam under bending force, the solution of Laplaces equation, and Poissons equation with various methods





Applied Calculus of Variations for Engineers, Second Edition extends the collection of techniques aiding the engineer in the application of the concepts of the calculus of variations.

Arvustused

"There is definitely a need for engineers and scientists alike to master a plethora of tools and techniques in their careers. The calculus of variations has long been viewed as esoteric and theoretical, hence explaining its absence from most universities' engineering curricula. But mentalities need to be changed as products developed today are becoming more and more sophisticated. Hence there is a need for more books in this field that are targeted to the engineering profession, and I expect that this second edition of Dr. Komzsik's book will gain widespread popularity. ... All scientific and non-scientific fields (such as financial engineering) can benefit from the concept of calculus of variations. This book, with its rather high level of math, will appeal most to those in engineering and the natural sciences." -Dr. Yogeshwarsing Calleecharan, Department of Engineering Sciences and Mathematics, Lulea University of Technology, Sweden "The author has explained a very difficult subject in a manner which can be understood, even by those with limited backgrounds. ... The book's subject is one of the basic building blocks for deeper understanding of the finite element method. ... This topic has been written about by many mathematicians. However, a complete discussion of this topic, clearly explained by a practical engineer, is definitely a plus for both the engineering and mathematical communities." -Prof. Duc T. Nguyen Old Dominion University, Norfolk, Virginia, USA

Preface to the second edition xi
Preface to the first edition xiii
Acknowledgments xv
About the author xvii
List of notations
xix
I Mathematical foundation
1(108)
1 The foundations of calculus of variations
3(22)
1.1 The fundamental problem and lemma of calculus of variations
3(4)
1.2 The Legendre test
7(2)
1.3 The Euler-Lagrange differential equation
9(2)
1.4 Application: minimal path problems
11(10)
1.4.1 Shortest curve between two points
12(2)
1.4.2 The brachistochrone problem
14(4)
1.4.3 Fermat's principle
18(2)
1.4.4 Particle moving in the gravitational field
20(1)
1.5 Open boundary variational problems
21(4)
2 Constrained variational problems
25(12)
2.1 Algebraic boundary conditions
25(2)
2.2 Lagrange's solution
27(2)
2.3 Application: iso-perimetric problems
29(6)
2.3.1 Maximal area under curve with given length
29(2)
2.3.2 Optimal shape of curve of given length under gravity
31(4)
2.4 Closed-loop integrals
35(2)
3 Multivariate functionals
37(12)
3.1 Functionals with several functions
37(1)
3.2 Variational problems in parametric form
38(1)
3.3 Functionals with two independent variables
39(1)
3.4 Application: minimal surfaces
40(4)
3.4.1 Minimal surfaces of revolution
43(1)
3.5 Functionals with three independent variables
44(5)
4 Higher order derivatives
49(8)
4.1 The Euler-Poisson equation
49(2)
4.2 The Euler-Poisson system of equations
51(1)
4.3 Algebraic constraints on the derivative
52(2)
4.4 Linearization of second order problems
54(3)
5 The inverse problem of calculus of variations
57(12)
5.1 The variational form of Poisson's equation
58(1)
5.2 The variational form of eigenvalue problems
59(3)
5.2.1 Orthogonal eigensolutions
61(1)
5.3 Sturm-Liouville problems
62(7)
5.3.1 Legendre's equation and polynomials
64(5)
6 Analytic solutions of variational problems
69(20)
6.1 Laplace transform solution
69(2)
6.2 Separation of variables
71(5)
6.3 Complete integral solutions
76(4)
6.4 Poisson's integral formula
80(5)
6.5 Method of gradients
85(4)
7 Numerical methods of calculus of variations
89(20)
7.1 Euler's method
89(2)
7.2 Ritz method
91(5)
7.2.1 Application: solution of Poisson's equation
95(1)
7.3 Galerkin's method
96(2)
7.4 Kantorovich's method
98(5)
7.5 Boundary integral method
103(6)
II Engineering applications
109(96)
8 Differential geometry
111(14)
8.1 The geodesic problem
111(3)
8.1.1 Geodesics of a sphere
113(1)
8.2 A system of differential equations for geodesic curves
114(5)
8.2.1 Geodesics of surfaces of revolution
116(3)
8.3 Geodesic curvature
119(3)
8.3.1 Geodesic curvature of helix
121(1)
8.4 Generalization of the geodesic concept
122(3)
9 Computational geometry
125(18)
9.1 Natural splines
125(3)
9.2 B-spline approximation
128(5)
9.3 B-splines with point constraints
133(3)
9.4 B-splines with tangent constraints
136(3)
9.5 Generalization to higher dimensions
139(4)
10 Variational equations of motion
143(14)
10.1 Legendre's dual transformation
143(1)
10.2 Hamilton's principle for mechanical systems
144(2)
10.2.1 Newton's law of motion
145(1)
10.3 Lagrange's equations of motion
146(1)
10.4 Hamilton's canonical equations
147(3)
10.4.1 Conservation of energy
149(1)
10.5 Orbital motion
150(3)
10.6 Variational foundation of fluid motion
153(4)
11 Analytic mechanics
157(20)
11.1 Elastic string vibrations
157(5)
11.2 The elastic membrane
162(7)
11.2.1 Circular membrane vibrations
165(2)
11.2.2 Non-zero boundary conditions
167(2)
11.3 Bending of a beam under its own weight
169(8)
12 Computational mechanics
177(28)
12.1 Three-dimensional elasticity
177(3)
12.2 Lagrangian formulation
180(4)
12.3 Heat conduction
184(2)
12.4 Fluid mechanics
186(3)
12.5 The finite element method
189(16)
12.5.1 Finite element meshing
189(2)
12.5.2 Shape functions
191(4)
12.5.3 Element matrix generation
195(4)
12.5.4 Element matrix assembly and solution
199(6)
Closing remarks 205(2)
References 207(2)
Index 209(2)
List of Figures 211(2)
List of Tables 213
Dr. Louis Komzsik is a graduate of the Technical University of Budapest, Hungary and the Eötvös Loránd University, Budapest, Hungary. He has been working in the industry for more than 40 years, and is currently the chief numerical analyst in the Office of Architecture and Technology at Siemens PLM Software, Cypress, California, USA. Dr. Komzsik is the author of the NASTRAN Numerical Methods Handbook, first published by MSC in 1987. His book, The Lanczos Method, published by SIAM, has also been translated into Japanese, Korean, and Hungarian. His book, Computational Techniques of Finite Element Analysis, published by CRC Press, is in its second print, and his Approximation Techniques for Engineers was published by Taylor and Francis in 2006. He is also the coauthor of the book Computational Techniques of Rotor Dynamics with the Finite Element Method, published by Taylor and Francis in 2012.