How Long to Read Painleve Transcendents

How Long Does it Take to Read Painleve Transcendents?

It takes the average reader 9 hours and 30 minutes to read Painleve Transcendents by A. S. Fokas

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

Description

At the turn of the twentieth century, the French mathematician Paul Painleve and his students classified second order nonlinear ordinary differential equations with the property that the location of possible branch points and essential singularities of their solutions does not depend on initial conditions. It turned out that there are only six such equations (up to natural equivalence), which later became known as Painleve I-VI. Although these equations were initially obtainedanswering a strictly mathematical question, they appeared later in an astonishing (and growing) range of applications, including, e.g., statistical physics, fluid mechanics, random matrices, and orthogonal polynomials. Actually, it is now becoming clear that the Painleve transcendents (i.e., the solutionsof the Painleve equations) play the same role in nonlinear mathematical physics that the classical special functions, such as Airy and Bessel functions, play in linear physics. The explicit formulas relating the asymptotic behaviour of the classical special functions at different critical points, play a crucial role in the applications of these functions. It is shown in this book, that even though the six Painleve equations are nonlinear, it is still possible, using a new technique called theRiemann-Hilbert formalism, to obtain analogous explicit formulas for the Painleve transcendents. This striking fact, apparently unknown to Painleve and his contemporaries, is the key ingredient for the remarkable applicability of these ``nonlinear special functions''. The book describes in detail theRiemann-Hilbert method and emphasizes its close connection to classical monodromy theory of linear equations as well as to modern theory of integrable systems. In addition, the book contains an ample collection of material concerning the asymptotics of the Painleve functions and their various applications, which makes it a good reference source for everyone working in the theory and applications of Painleve equations and related areas.

How long is Painleve Transcendents?

Painleve Transcendents by A. S. Fokas is 570 pages long, and a total of 142,500 words.

This makes it 192% the length of the average book. It also has 174% more words than the average book.

How Long Does it Take to Read Painleve Transcendents Aloud?

The average oral reading speed is 183 words per minute. This means it takes 12 hours and 58 minutes to read Painleve Transcendents aloud.

What Reading Level is Painleve Transcendents?

Painleve Transcendents 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 Painleve Transcendents?

Painleve Transcendents by A. S. Fokas is sold by several retailers and bookshops. However, Read Time works with Amazon to provide an easier way to purchase books.

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