Random Walk and the Heat Equation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Random Walk and the Heat Equation write by Gregory F. Lawler. This book was released on 2010-11-22. Random Walk and the Heat Equation available in PDF, EPUB and Kindle. 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.
The Heat Equation
The Heat Equation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Heat Equation write by D. V. Widder. This book was released on 1976-01-22. The Heat Equation available in PDF, EPUB and Kindle. The Heat Equation
The One-Dimensional Heat Equation
The One-Dimensional Heat Equation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The One-Dimensional Heat Equation write by John Rozier Cannon. This book was released on 1984-12-28. The One-Dimensional Heat Equation available in PDF, EPUB and Kindle. This is a version of Gevrey's classical treatise on the heat equations. Included in this volume are discussions of initial and/or boundary value problems, numerical methods, free boundary problems and parameter determination problems. The material is presented as a monograph and/or information source book. After the first six chapters of standard classical material, each chapter is written as a self-contained unit except for an occasional reference to elementary definitions, theorems and lemmas in previous chapters.
Elementary Differential Equations with Boundary Value Problems
Elementary Differential Equations with Boundary Value Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elementary Differential Equations with Boundary Value Problems write by William F. Trench. This book was released on 2001. Elementary Differential Equations with Boundary Value Problems available in PDF, EPUB and Kindle. Written in a clear and accurate language that students can understand, Trench's new book minimizes the number of explicitly stated theorems and definitions. Instead, he deals with concepts in a conversational style that engages students. He includes more than 250 illustrated, worked examples for easy reading and comprehension. One of the book's many strengths is its problems, which are of consistently high quality. Trench includes a thorough treatment of boundary-value problems and partial differential equations and has organized the book to allow instructors to select the level of technology desired. This has been simplified by using symbols, C and L, to designate the level of technology. C problems call for computations and/or graphics, while L problems are laboratory exercises that require extensive use of technology. Informal advice on the use of technology is included in several sections and instructors who prefer not to emphasize technology can ignore these exercises without interrupting the flow of material.
Differential Equations and Linear Algebra
Differential Equations and Linear Algebra - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Differential Equations and Linear Algebra write by Gilbert Strang. This book was released on 2015-02-12. Differential Equations and Linear Algebra available in PDF, EPUB and Kindle. Differential equations and linear algebra are two central topics in the undergraduate mathematics curriculum. This innovative textbook allows the two subjects to be developed either separately or together, illuminating the connections between two fundamental topics, and giving increased flexibility to instructors. It can be used either as a semester-long course in differential equations, or as a one-year course in differential equations, linear algebra, and applications. Beginning with the basics of differential equations, it covers first and second order equations, graphical and numerical methods, and matrix equations. The book goes on to present the fundamentals of vector spaces, followed by eigenvalues and eigenvectors, positive definiteness, integral transform methods and applications to PDEs. The exposition illuminates the natural correspondence between solution methods for systems of equations in discrete and continuous settings. The topics draw on the physical sciences, engineering and economics, reflecting the author's distinguished career as an applied mathematician and expositor.
