Softcover ISBN:  9780821847725 
Product Code:  STML/50 
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Individual Price:  $40.80 
Electronic ISBN:  9781470416355 
Product Code:  STML/50.E 
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Book DetailsStudent Mathematical LibraryVolume: 50; 2009; 252 ppMSC: 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.ReadershipUndergraduate 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 BoisReymond 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. Timeoptimal 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


Additional Material

Reviews

It is useful for libraries supporting applied mathematics programs or advanced course in [certain] disciplines.
CHOICE Magazine


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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.
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 BoisReymond 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. Timeoptimal 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