How Long to Read Harmonic Mappings in the Plane

How Long Does it Take to Read Harmonic Mappings in the Plane?

It takes the average reader 4 hours and 1 minute to read Harmonic Mappings in the Plane by Peter Duren

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

Description

Harmonic mappings in the plane are univalent complex-valued harmonic functions of a complex variable. Conformal mappings are a special case where the real and imaginary parts are conjugate harmonic functions, satisfying the Cauchy-Riemann equations. Harmonic mappings were studied classically by differential geometers because they provide isothermal (or conformal) parameters for minimal surfaces. More recently they have been actively investigated by complex analysts as generalizations of univalent analytic functions, or conformal mappings. Many classical results of geometric function theory extend to harmonic mappings, but basic questions remain unresolved. This book is the first comprehensive account of the theory of planar harmonic mappings, treating both the generalizations of univalent analytic functions and the connections with minimal surfaces. Essentially self-contained, the book contains background material in complex analysis and a full development of the classical theory of minimal surfaces, including the Weierstrass-Enneper representation. It is designed to introduce non-specialists to a beautiful area of complex analysis and geometry.

How long is Harmonic Mappings in the Plane?

Harmonic Mappings in the Plane by Peter Duren is 236 pages long, and a total of 60,416 words.

This makes it 80% the length of the average book. It also has 74% more words than the average book.

How Long Does it Take to Read Harmonic Mappings in the Plane Aloud?

The average oral reading speed is 183 words per minute. This means it takes 5 hours and 30 minutes to read Harmonic Mappings in the Plane aloud.

What Reading Level is Harmonic Mappings in the Plane?

Harmonic Mappings in the Plane 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 Harmonic Mappings in the Plane?

Harmonic Mappings in the Plane by Peter Duren 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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