Applied Calculus of Variations for Engineers, 2nd Edition

Book description

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

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.

Table of contents

  1. Front Cover (1/2)
  2. Front Cover (2/2)
  3. Contents
  4. Preface to the second edition
  5. Preface to the first edition
  6. Acknowledgments
  7. About the author
  8. List of notations
  9. Part I: Mathematical foundation
  10. Chapter 1: The foundations of calculus of variations (1/5)
  11. Chapter 1: The foundations of calculus of variations (2/5)
  12. Chapter 1: The foundations of calculus of variations (3/5)
  13. Chapter 1: The foundations of calculus of variations (4/5)
  14. Chapter 1: The foundations of calculus of variations (5/5)
  15. Chapter 2: Constrained variational problems (1/3)
  16. Chapter 2: Constrained variational problems (2/3)
  17. Chapter 2: Constrained variational problems (3/3)
  18. Chapter 3: Multivariate function (1/3)
  19. Chapter 3: Multivariate function (2/3)
  20. Chapter 3: Multivariate function (3/3)
  21. Chapter 4: Higher order derivatives (1/2)
  22. Chapter 4: Higher order derivatives (2/2)
  23. Chapter 5: The inverse problem of calculus of variations (1/3)
  24. Chapter 5: The inverse problem of calculus of variations (2/3)
  25. Chapter 5: The inverse problem of calculus of variations (3/3)
  26. Chapter 6: Analytic solutions of variational problems (1/4)
  27. Chapter 6: Analytic solutions of variational problems (2/4)
  28. Chapter 6: Analytic solutions of variational problems (3/4)
  29. Chapter 6: Analytic solutions of variational problems (4/4)
  30. Chapter 7: Numerical methods of calculus of variations (1/4)
  31. Chapter 7: Numerical methods of calculus of variations (2/4)
  32. Chapter 7: Numerical methods of calculus of variations (3/4)
  33. Chapter 7: Numerical methods of calculus of variations (4/4)
  34. Part II: Engineering applications
  35. Chapter 8: Differential geometry (1/3)
  36. Chapter 8: Differential geometry (2/3)
  37. Chapter 8: Differential geometry (3/3)
  38. Chapter 9: Computational geometry (1/4)
  39. Chapter 9: Computational geometry (2/4)
  40. Chapter 9: Computational geometry (3/4)
  41. Chapter 9: Computational geometry (4/4)
  42. Chapter 10: Variational equations of motion (1/3)
  43. Chapter 10: Variational equations of motion (2/3)
  44. Chapter 10: Variational equations of motion (3/3)
  45. Chapter 11: Analytic mechanics (1/4)
  46. Chapter 11: Analytic mechanics (2/4)
  47. Chapter 11: Analytic mechanics (3/4)
  48. Chapter 11: Analytic mechanics (4/4)
  49. Chapter 12: Computational mechanics (1/6)
  50. Chapter 12: Computational mechanics (2/6)
  51. Chapter 12: Computational mechanics (3/6)
  52. Chapter 12: Computational mechanics (4/6)
  53. Chapter 12: Computational mechanics (5/6)
  54. Chapter 12: Computational mechanics (6/6)
  55. Closing remarks
  56. References
  57. List of Figures
  58. List of Tables
  59. Back Cover

Product information

  • Title: Applied Calculus of Variations for Engineers, 2nd Edition
  • Author(s): Louis Komzsik
  • Release date: June 2014
  • Publisher(s): CRC Press
  • ISBN: 9781482253603