Introduction to the Calculus of Variations and Control with Modern Applications

John A. Burns

August 28, 2013 by Chapman and Hall/CRC
Reference - 562 Pages - 59 B/W Illustrations
ISBN 9781466571396 - CAT# K16538
Series: Chapman & Hall/CRC Applied Mathematics & Nonlinear Science


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  • Introduces a variety of contemporary applications from control theory to numerical analysis
  • Assumes a basic background in differential equations and advanced calculus, making the text suitable for beginning graduate students in mathematics and engineering
  • Presents a complete treatment of the simplest problem in the calculus of variations
  • Describes extensions and generalizations to vector and higher dimensional problems
  • Covers optimal control, the maximum principle, linear optimal control, and feedback design


Introduction to the Calculus of Variations and Control with Modern Applications provides the fundamental background required to develop rigorous necessary conditions that are the starting points for theoretical and numerical approaches to modern variational calculus and control problems. The book also presents some classical sufficient conditions and discusses the importance of distinguishing between the necessary and sufficient conditions.

In the first part of the text, the author develops the calculus of variations and provides complete proofs of the main results. He explains how the ideas behind the proofs are essential to the development of modern optimization and control theory. Focusing on optimal control problems, the second part shows how optimal control is a natural extension of the classical calculus of variations to more complex problems.

By emphasizing the basic ideas and their mathematical development, this book gives you the foundation to use these mathematical tools to then tackle new problems. The text moves from simple to more complex problems, allowing you to see how the fundamental theory can be modified to address more difficult and advanced challenges. This approach helps you understand how to deal with future problems and applications in a realistic work environment.