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Lecture Notes on Differential Equations (Shapiro B.E)



EBook NameLecture Notes on Differential Equations (Shapiro B.E)
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Partial Differential Equations: A unified Hilbert Space Approach

This book presents a systematic approach to a solution theory for linear partial differential equations developed in a Hilbert space setting based on a Sobolev Lattice structure, a simple extension of the well established notion of a chain (or scale) of Hilbert spaces. The focus on a Hilbert space setting is a highly adaptable and suitable approach providing a more transparent framework for presenting the main issues in the development of a solution theory for partial differential equations. This global point of view is taken by focussing on the issues involved in determining the appropriate functional analytic setting in which a solution theory can naturally be developed. Applications to many areas of mathematical physics are presented. The book aims to be a largely self-contained. Full proofs to all but the most straightforward results are provided. It is therefore highly suitable as a resource for graduate courses and for researchers, who will find new results for particular evolutionary system from mathematical physics.

The Differential Equations Tutor

Solving higher order differential equations is challenging for most students simply because the solution methods usually run several pages in length even for the easier problems. The student must identify the type of equation to solve and apply the appropriate solution method, which can lead to valuable lost time on an exam if the wrong solution method is chosen at the outset.

Partial Differential Equations with Fourier Series and Boundary Value Problems

This example-rich reference fosters a smooth transition from elementary ordinary differential equations to more advanced concepts. Asmar's relaxed style and emphasis on applications make the material accessible even to readers with limited exposure to topics beyond calculus. Encourages computer for illustrating results and applications, but is also suitable for use without computer access. Contains more engineering and physics applications, and more mathematical proofs and theory of partial differential equations, than the first edition.

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