How Long to Read Random Walk and the Heat Equation

How Long Does it Take to Read Random Walk and the Heat Equation?

It takes the average reader 2 hours and 50 minutes to read Random Walk and the Heat Equation by Gregory F. Lawler

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

Description

The heat equation can be derived by averaging over a very large number of particles. Traditionally, the resulting PDE is studied as a deterministic equation, an approach that has brought many significant results and a deep understanding of the equation and its solutions. By studying the heat equation and considering the individual random particles, however, one gains further intuition into the problem. While this is now standard for many researchers, this approach is generally not presented at the undergraduate level. In this book, Lawler introduces the heat equations and the closely related notion of harmonic functions from a probabilistic perspective. The theme of the first two chapters of the book is the relationship between random walks and the heat equation. This first chapter discusses the discrete case, random walk and the heat equation on the integer lattice; and the second chapter discusses the continuous case, Brownian motion and the usual heat equation. Relationships are shown between the two. For example, solving the heat equation in the discrete setting becomes a problem of diagonalization of symmetric matrices, which becomes a problem in Fourier series in the continuous case. Random walk and Brownian motion are introduced and developed from first principles. The latter two chapters discuss different topics: martingales and fractal dimension, with the chapters tied together by one example, a random Cantor set. The idea of this book is to merge probabilistic and deterministic approaches to heat flow. It is also intended as a bridge from undergraduate analysis to graduate and research perspectives. The book is suitable for advanced undergraduates, particularly those considering graduate work in mathematics or related areas.

How long is Random Walk and the Heat Equation?

Random Walk and the Heat Equation by Gregory F. Lawler is 170 pages long, and a total of 42,500 words.

This makes it 57% the length of the average book. It also has 52% more words than the average book.

How Long Does it Take to Read Random Walk and the Heat Equation Aloud?

The average oral reading speed is 183 words per minute. This means it takes 3 hours and 52 minutes to read Random Walk and the Heat Equation aloud.

What Reading Level is Random Walk and the Heat Equation?

Random Walk and the Heat Equation is suitable for students ages 10 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 Random Walk and the Heat Equation?

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