Elementary Differential Equations with Boundary Value Problems integrates the underlying theory, the solution procedures, and the numerical/computational aspects of differential equations in a seamless way. For example, whenever a new type of problem is introduced (such as first-order equations, higher-order equations, systems of differential equations, etc.) the text begins with the basic existence-uniqueness theory. This provides the student the necessary framework to understand and solve differential equations. Theory is presented as simply as possible with an emphasis on how to use it. The Table of Contents is comprehensive and allows flexibility for instructors.
This text offers a clear and concise writing style that is student oriented, combining thorough explanations, an accurate mathematical presentation, and well defined terms.
The general aim of the present monograph is to study boundary-value problems for second-order elliptic operators in Lipschitz sub domains of Riemannian manifolds.
The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, ...
(3-2) V “U: lijui—l,j+bijui,j—l+rijui+l,j+tijui,j+l dijuij+€ijr di'j = li'j = ' ' ', 6 ... (Approximating normal derivatives is harder, by all methods!) For example, one can let this H This is the approximation used by Shortley-Weller ...
Suppose there does exist a finite set of vectors {ps : s = 1,2,..., m} in Lee, each of which depends non-trivially on (at most) k of the summands {S, re N}, and such there is a linear combination *n. X_3.p. with 3s € C for s = 1, ...
Coverage includes Fourier series, orthogonal functions, boundary value problems, Green's functions, and transform methods. This text is ideal for readers interested in science, engineering, and applied mathematics.
Normal 0 false false false This book emphasizes the physical interpretation of mathematical solutions and introduces applied mathematics while presenting differential equations.
KEY BENEFIT Emphasizing physical interpretations of mathematical solutions, this book introduces applied mathematics and presents partial differential equations.
Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, ...
This book was written with the student's understanding firmly in mind. Using a straightforward, readable, and helpful style, this book provides a thorough treatment of boundary-value problems and partial differential equations.