How Long to Read Direct Methods in the Calculus of Variations

How Long Does it Take to Read Direct Methods in the Calculus of Variations?

It takes the average reader 5 hours and 17 minutes to read Direct Methods in the Calculus of Variations by Bernard Dacorogna

Assuming a reading speed of 250 words per minute. Learn more

Description

In recent years there has been a considerable renewal of interest in the clas sical problems of the calculus of variations, both from the point of view of mathematics and of applications. Some of the most powerful tools for proving existence of minima for such problems are known as direct methods. They are often the only available ones, particularly for vectorial problems. It is the aim of this book to present them. These methods were introduced by Tonelli, following earlier work of Hilbert and Lebesgue. Although there are excellent books on calculus of variations and on direct methods, there are recent important developments which cannot be found in these books; in particular, those dealing with vector valued functions and relaxation of non convex problems. These two last ones are important in appli cations to nonlinear elasticity, optimal design . . . . In these fields the variational methods are particularly effective. Part of the mathematical developments and of the renewal of interest in these methods finds its motivations in nonlinear elasticity. Moreover, one of the recent important contributions to nonlinear analysis has been the study of the behaviour of nonlinear functionals un der various types of convergence, particularly the weak convergence. Two well studied theories have now been developed, namely f-convergence and compen sated compactness. They both include as a particular case the direct methods of the calculus of variations, but they are also, both, inspired and have as main examples these direct methods.

How long is Direct Methods in the Calculus of Variations?

Direct Methods in the Calculus of Variations by Bernard Dacorogna is 308 pages long, and a total of 79,464 words.

This makes it 104% the length of the average book. It also has 97% more words than the average book.

How Long Does it Take to Read Direct Methods in the Calculus of Variations Aloud?

The average oral reading speed is 183 words per minute. This means it takes 7 hours and 14 minutes to read Direct Methods in the Calculus of Variations aloud.

What Reading Level is Direct Methods in the Calculus of Variations?

Direct Methods in the Calculus of Variations is suitable for students ages 12 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Direct Methods in the Calculus of Variations?

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