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JulieK
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I am looking for a book/document (mainly free ones) about calculus of variations of practical nature, i.e. very little theory with many examples and solved problems based on physical applications. Any advice is appreciated.
The calculus of variations is a branch of mathematics that deals with finding the optimal values of functions, also known as extremals, through the use of calculus techniques. It involves maximizing or minimizing a certain functional, which is a mathematical expression involving a function and its derivatives.
The calculus of variations is important because it provides a powerful tool for solving optimization problems in various fields such as physics, engineering, and economics. It also has applications in understanding the behavior of systems and predicting their future states.
Some real-world examples of the calculus of variations include finding the shortest path between two points, determining the shape of a hanging chain, and optimizing the flight path of a rocket. It also has applications in economics, such as maximizing profits or minimizing costs.
Some common techniques used in the calculus of variations include the Euler-Lagrange equation, the calculus of variations on multiple variables, and the method of variation of parameters. These techniques allow for the optimization of various types of functionals.
Yes, there are several good books on the calculus of variations, including "Calculus of Variations" by I. M. Gelfand and S. V. Fomin, "Calculus of Variations" by Robert Weinstock, and "An Introduction to the Calculus of Variations" by Charles Fox. It is recommended to choose a book that aligns with your level of mathematical background and provides clear explanations and examples.