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Applied calculus of variations for engineers

Author: Louis Komzsik
Publisher: Boca Raton, FL : CRC Press/Taylor and Francis, [2020]
Edition/Format:   eBook : Document : English : Third editionView all editions and formats
Summary:
"This third edition extends the focus of the book to academia to also support variational calculus and mathematical modeling classes. The newly added sections, extended explanations, numerous examples and exercises aid the students in learning, the professors in teaching, and the engineers in applying variational concepts"--
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Komzsik, Louis.
Applied calculus of variations for engineers
Boca Raton, FL : CRC Press/Taylor and Francis, [2020]
(DLC) 2019046081
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Louis Komzsik
ISBN: 9781003009740 1003009743 9781000764758 1000764753 9781000764376 1000764370
OCLC Number: 1125303404
Description: 1 online resource
Contents: Preface Acknowledgments Author Introduction I Mathematical foundation 1 The foundations of calculus of variations 1.1 The fundamental problem and lemma of calculus of variations 1.2 The Legendre test 1.3 The Euler-Lagrange differential equation 1.4 Minimal path problems 1.5 Open boundary variational problems 1.6 Exercises 2 Constrained variational problems 2.1 Algebraic boundary conditions 2.2 Lagrange's solution 2.3 Isoperimetric problems 2.4 Closed-loop integrals 2.5 Exercises 3 Multivariate functionals 3.1 Functionals with several functions 3.2 Variational problems in parametric form 3.3 Functionals with two independent variables 3.4 Minimal surfaces 3.5 Functionals with three independent variables3.6 Exercises 4 Higher order derivatives 4.1 The Euler-Poisson equation 4.2 The Euler-Poisson system of equations 4.3 Algebraic constraints on the derivative 4.4 Linearization of second order problems 4.5 Exercises 5 The inverse problem 5.1 Linear differential operators 5.2 The variational form of Poisson's equation 5.3 The variational form of eigenvalue problems 5.4 Sturm-Liouville problems 5.5 Exercises 6 Analytic solutions 6.1 Laplace transform solution 6.2 d'Alembert's solution 6.3 Complete integral solutions 6.4 Poisson's integral formula 6.5 Method of gradients 6.6 Exercises 7 Approximate methods 7.1 Euler's method 7.2 Ritz method 7.3 Galerkin's method 7.4 Approximate solutions of Poisson's equation 7.5 Kantorovich's method 7.6 Boundary integral method 7.7 Finite element method 7.8 Exercises II Modeling applications8 Differential geometry 8.1 The geodesic problem 8.2 A system of differential equations for geodesic curves 8.3 Geodesic curvature 8.4 Generalization of the geodesic concept 9 Computational geometry9.1 Natural splines 9.2 B-spline approximation 9.3 B-splines with point constraints 9.4 B-splines with tangent constraints9.5 Generalization to higher dimensions 9.6 Weighting and nonuniform parametrization 9.7 Industrial applications 10 Variational equations of motion 10.1 Legendre's dual transformation 10.2 Hamilton's principle 10.3 Hamilton's canonical equations 10.4 Lagrange's equations of motion 10.5 Orbital motion 10.6 Variational foundation of fluid motion 11 Analytic mechanics 11.1 Elastic string vibrations 11.2 The elastic membrane 11.3 Bending of a beam under its own weight 11.4 Buckling of a beam under axial load 11.4.1 Axial vibration of a beam 11.5 Simultaneous axial and transversal loading of beam 11.6 Heat diffusion in a beam 12 Computational mechanics12.1 The finite element technique 12.2 Three-dimensional elasticity 12.3 Mechanical system analysis 12.4 Heat conduction 12.5 Fluid mechanicsSolutions Notations List of Tables List of Figures References Index
Responsibility: by Louis Komzsik.

Abstract:

"This third edition extends the focus of the book to academia to also support variational calculus and mathematical modeling classes. The newly added sections, extended explanations, numerous  Read more...

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