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The presentation of this book is on the comprehensible application of techniques for the approximation of the mathematical problems that are frequently observed in physical sciences, engineering technology and mathematical physics. The acceptance of the technique for the solution has been justified from mathematical point of view. The Software required for the approximate solution of the problems applying the appropriate Methods, numerically developed is the set of programs written in C++ (Turbo). The text book is primarily intended for advanced Undergraduate and the Graduate levels in all branches of mathematical sciences and engineering technology. A variety of computerised solved problems, physical and technical, has been discussed in each chapter so that the students can understand the conceptual text easily. Chapter 7 on Differential Equations with boundary points is specially focussed because of the fact that a two point second-order boundary value problem is occurred very often in the field. Besides, Ordinary Differential Equations of any art have been presented and the results are analysed elaborately. Some limited examples on Partial differential equations have also been treated. Chapter 9 on Laplace Transforms should be cordially admitted because an appreciable interest has been developing in recent times in the use of Laplace Tranforms for solving particular types of differential equations.

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