The book is designed for use in a graduate program in Numerical Analysis that includes a basic introductory course and subsequent more specialized courses. The latter is envisaged to cover numerical linear algebra, the numerical solution of ordinary and partial differential equations, and perhaps additional topics related to complex analysis, multidimensional analysis, in particular optimization, and functional analysis and related functional equations. Viewed in this context, the first four chapters of our book could serve as a text for the basic introductory course on the Python program, and the remaining chapters could provide a text for an advanced course on the numerical solution of ordinary differential equations. Therefore, the book breaks with tradition in that it no longer attempts to deal with all major topics of numerical mathematics. Those dealing with linear algebra and partial differential equations have developed into major fields of study that have attained a degree of autonomy and identity that justifies their treatment in separate books and separate courses on the graduate level. The term "Numerical Analysis" as used in this book, therefore, is to be taken in the narrow sense of the numerical analog of Mathematical Analysis, comprising such topics as machine arithmetic, the approximation of functions, approximate differentiation and integration, and the approximate solution of nonlinear equations and ordinary differential equations. This book aims to provide a good understanding of Numerical engineering analysis and its applications and optimization. The book begins with studying the concept of Python fundamentals for scientific computing. It then presents their applications in the different configurations shown in lucid detail. For more details, please visit https: //centralwestpublishing.com