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A Primer on the Calculus of Variations and Optimal Control Theory
 
Mike Mesterton-Gibbons Florida State University, Tallahassee, FL
A Primer on the Calculus of Variations and Optimal Control Theory
Softcover ISBN:  978-0-8218-4772-5
Product Code:  STML/50
List Price: $59.00
Individual Price: $47.20
Sale Price: $35.40
eBook ISBN:  978-1-4704-1635-5
Product Code:  STML/50.E
List Price: $49.00
Individual Price: $39.20
Sale Price: $29.40
Softcover ISBN:  978-0-8218-4772-5
eBook: ISBN:  978-1-4704-1635-5
Product Code:  STML/50.B
List Price: $108.00 $83.50
Sale Price: $64.80 $50.10
A Primer on the Calculus of Variations and Optimal Control Theory
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A Primer on the Calculus of Variations and Optimal Control Theory
Mike Mesterton-Gibbons Florida State University, Tallahassee, FL
Softcover ISBN:  978-0-8218-4772-5
Product Code:  STML/50
List Price: $59.00
Individual Price: $47.20
Sale Price: $35.40
eBook ISBN:  978-1-4704-1635-5
Product Code:  STML/50.E
List Price: $49.00
Individual Price: $39.20
Sale Price: $29.40
Softcover ISBN:  978-0-8218-4772-5
eBook ISBN:  978-1-4704-1635-5
Product Code:  STML/50.B
List Price: $108.00 $83.50
Sale Price: $64.80 $50.10
  • Book Details
     
     
    Student Mathematical Library
    Volume: 502009; 252 pp
    MSC: Primary 49; Secondary 92

    The calculus of variations is used to find functions that optimize quantities expressed in terms of integrals. Optimal control theory seeks to find functions that minimize cost integrals for systems described by differential equations.

    This book is an introduction to both the classical theory of the calculus of variations and the more modern developments of optimal control theory from the perspective of an applied mathematician. It focuses on understanding concepts and how to apply them. The range of potential applications is broad: the calculus of variations and optimal control theory have been widely used in numerous ways in biology, criminology, economics, engineering, finance, management science, and physics. Applications described in this book include cancer chemotherapy, navigational control, and renewable resource harvesting.

    The prerequisites for the book are modest: the standard calculus sequence, a first course on ordinary differential equations, and some facility with the use of mathematical software. It is suitable for an undergraduate or beginning graduate course, or for self study. It provides excellent preparation for more advanced books and courses on the calculus of variations and optimal control theory.

    Readership

    Undergraduate and graduate students interested in the calculus of variations and optimal control.

  • Table of Contents
     
     
    • Chapters
    • Lecture 1. The Brachistochrone
    • Lecture 2. The fundamental problem. Extremals
    • Lecture 3. The insufficiency of extremality
    • Lecture 4. Important first integrals
    • Lecture 5. The du Bois-Reymond equation
    • Lecture 6. The corner conditions
    • Lecture 7. Legendre’s necessary condition
    • Lecture 8. Jacobi’s necessary condition
    • Lecture 9. Weak versus strong variations
    • Lecture 10. Weierstrass’s necessary condition
    • Lecture 11. The transversality conditions
    • Lecture 12. Hilbert’s invariant integral
    • Lecture 13. The fundamental sufficient condition
    • Lecture 14. Jacobi’s condition revisited
    • Lecture 15. Isoperimetrical problems
    • Lecture 16. Optimal control problems
    • Lecture 17. Necessary conditions for optimality
    • Lecture 18. Time-optimal control
    • Lecture 19. A singular control problem
    • Lecture 20. A biological control problem
    • Lecture 21. Optimal control to a general target
    • Lecture 22. Navigational control problems
    • Lecture 23. State variable restrictions
    • Lecture 24. Optimal harvesting
    • Afterword
    • Solutions or hints for selected exercises
  • Reviews
     
     
    • It is useful for libraries supporting applied mathematics programs or advanced course in [certain] disciplines.

      CHOICE Magazine
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 502009; 252 pp
MSC: Primary 49; Secondary 92

The calculus of variations is used to find functions that optimize quantities expressed in terms of integrals. Optimal control theory seeks to find functions that minimize cost integrals for systems described by differential equations.

This book is an introduction to both the classical theory of the calculus of variations and the more modern developments of optimal control theory from the perspective of an applied mathematician. It focuses on understanding concepts and how to apply them. The range of potential applications is broad: the calculus of variations and optimal control theory have been widely used in numerous ways in biology, criminology, economics, engineering, finance, management science, and physics. Applications described in this book include cancer chemotherapy, navigational control, and renewable resource harvesting.

The prerequisites for the book are modest: the standard calculus sequence, a first course on ordinary differential equations, and some facility with the use of mathematical software. It is suitable for an undergraduate or beginning graduate course, or for self study. It provides excellent preparation for more advanced books and courses on the calculus of variations and optimal control theory.

Readership

Undergraduate and graduate students interested in the calculus of variations and optimal control.

  • Chapters
  • Lecture 1. The Brachistochrone
  • Lecture 2. The fundamental problem. Extremals
  • Lecture 3. The insufficiency of extremality
  • Lecture 4. Important first integrals
  • Lecture 5. The du Bois-Reymond equation
  • Lecture 6. The corner conditions
  • Lecture 7. Legendre’s necessary condition
  • Lecture 8. Jacobi’s necessary condition
  • Lecture 9. Weak versus strong variations
  • Lecture 10. Weierstrass’s necessary condition
  • Lecture 11. The transversality conditions
  • Lecture 12. Hilbert’s invariant integral
  • Lecture 13. The fundamental sufficient condition
  • Lecture 14. Jacobi’s condition revisited
  • Lecture 15. Isoperimetrical problems
  • Lecture 16. Optimal control problems
  • Lecture 17. Necessary conditions for optimality
  • Lecture 18. Time-optimal control
  • Lecture 19. A singular control problem
  • Lecture 20. A biological control problem
  • Lecture 21. Optimal control to a general target
  • Lecture 22. Navigational control problems
  • Lecture 23. State variable restrictions
  • Lecture 24. Optimal harvesting
  • Afterword
  • Solutions or hints for selected exercises
  • It is useful for libraries supporting applied mathematics programs or advanced course in [certain] disciplines.

    CHOICE Magazine
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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