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Applied calculus of variations for engineers / Louis Komzsik.

By: Material type: TextTextPublication details: Boca Raton : CRC Press, c2014.Edition: 2nd edDescription: xx, 213 p. : illustrations ; 25 cmISBN:
  • 9781482253597 (acidfree paper)
Subject(s): DDC classification:
  • 620.00151564  23 K81
Contents:
Part I: Mathematical foundation. 1. The foundations of calculus of variations -- 2. Constrained variational problems -- 3. Multivariate function -- 4. Higher order derivatives -- 5. The inverse problem of calculus of variations -- 6. Analytic solutions of variational problems -- 7. Numerical methods of calculus of variations -- Part II: Engineering applications. 8. Differential geometry -- 9. Computational geometry -- 10. Variational equations of motion -- 11. Analytic mechanics -- 12. Computational mechanics-- Closing remarks-- References-- Index.
Summary: 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 engineer's 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 Laplace's equation, and Poisson's equation with various methods.
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Includes bibliographical references and index.

Part I: Mathematical foundation.
1. The foundations of calculus of variations --
2. Constrained variational problems --
3. Multivariate function --
4. Higher order derivatives --
5. The inverse problem of calculus of variations --
6. Analytic solutions of variational problems --
7. Numerical methods of calculus of variations --

Part II: Engineering applications.
8. Differential geometry --
9. Computational geometry --
10. Variational equations of motion --
11. Analytic mechanics --
12. Computational mechanics--
Closing remarks--
References--
Index.

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 engineer's 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 Laplace's equation, and Poisson's equation with various methods.

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