The objective of this book is to present a substantial introduction to the ideas, phenomena and methods of the problems that are frequently observed in mathematics, mathematical physics and engineering technology. The book can be appreciated at a considerable number of levels and is designed for everyone from amateurs to research workmen.
Included throughout are applications with appropriate suggestions and discussions, whenever needed, that form a significant and integral part of the text book.
In a word, the text directs at an all-embracing and practical treatment of differential equations with some methods specifically developed for the purpose controlled by computer programs. The effects of this treatment, the computerised solutions for each problem, represented in compact form, sometimes with graphical figures, have been provided for further study.
The operation has been performed by the programming language C++ based on any MS-DOS computer system (version 6.0) applying the classical methods, such as Euler, Simpson, Runge-Kutta, Finite-Difference, etc.
Chapters 4 and 5 provide introductions to first order and second order initial-value problems discussing the possibilities for finding solutions, analytic and computerised. Non-linear types of differential equations have also been considered.
Emphasis has been placed on section 6.3 in Chapter 6 that deals with the problems concerning Fourier series, because the subject matter of numerical evaluation for Fourier series is a predominant topic.
Special attention is focussed on Chapter 7 in view of the fact that the differential equations with boundary conditions are the kernels of the physical and technical problems. The Difference Method for the solution of a two point second-order boundary value problem has been applied. Chapter 8 contains numerically developed methods for the computer solution of elliptic, hyperbolic and parabolic partial differential equations.
A variety of solved examples in each chapter has been given for the students who cannot get any difficulty to understand the conceptual text. Chapter 11 entitled “A Short Review On C++” provides an opportunity to recapitulate the fundamental points on C++.
I prepared the text on personal computer from Compaq (type Presario CDTV528) and on Laptop from Toshiba (type Satellite 110CS) operated on MS-DOS 6.0 and Windows 95. MS-Workgroups (version 3.0) have also been used in the preparation.