For introductory courses in Differential Equations. This best-selling text by these well-known authors blends the traditional algebra problem solving skills with the conceptual development and geometric visualization of a modern differential equations course that is essential to science and engineering students. It reflects the new qualitative approach that is altering the learning of elementary differential equations, including the wide availability of scientific computing environments like Maple, Mathematica, and MATLAB. Its focus balances the traditional manual methods with the new computer-based methods that illuminate qualitative phenomena and make accessible a wider range of more realistic applications. Seldom-used topics have been trimmed and new topics added: it starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout the text.
This textbook stays within traditional coverage of basic topics in differential equations. ... Since a complex number (let us denote it by z) is a vector on the plane, it is a custom to denote it by z = x + y j rather than z = xi + y j, ...
The text can be used in courses when partial differential equations replaces Laplace transforms. There is sufficient linear algebra in the text so that it can be used for a course that combines differential equations and linear algebra.
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, ...
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...
Millikan repeated this experiment many times, and from the data that he gathered he was able to deduce the charge on an electron. R B w FIGURE 2.3.5 A body falling in a dense fluid (see Problem 21). 22.
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.
As boundary value problems arise in several branches of math given the fact that any physical differential equation will have them, this book will provide a timely presentation on the topic.
The last chapter is devoted to nodal solutions for BVPs with separated boundary conditions as well as for non-local problems.While this Volume II complements , it can be used as a stand-alone work.
This book strikes a balance between the traditional and the modern—combining the traditional material with a modern systems emphasis. Chapter topics cover an introduction to differential equations, first-order equations, modeling...
AND B. SWARTZ, “Collocation at Gaussian points," SIAM J. Numer. Anal. 10 (1973), 582-606. DE BOOR, C., AND B. SWARTZ, “Comments on the comparison of global methods for linear two-point boundary value problems," Math. Comp.