Modelling with differential equations is an effective tool to provide methodical and quantitative solutions to real-world phenomena including investigating measurable features, consolidation and processing of data, and to design and develop complex engineering systems. This book describes differential equations correlation with qualitative and quantitative analysis, and mathematical modelling in the engineering and applied sciences. Given equations are explained from multidimensional characterizations with MATLAB codes. Features: Addresses differential equation-based approaches to solve varied engineering problems. Discusses derivation and solution of major equations of engineering and applied science. Reviews qualitative and quantitative (numerical) analysis and mathematical modelling. Includes mathematical models of the discussed problems. Discusses MATLAB code and online materials related to the differential equations. This book is aimed at researchers, graduate students in electrical and electronics engineering, control systems, electron devices society, applied physics, engineering design.

The membrane separation process has emerged as a powerful separation technique and has become an integral part of modern process industries. This has found wide applications in the field of biotechnology, beverage, dairy industry, clarification of fruit juice, waste water treatment etc. The advantages of these processes are their unique separation capabilities, low energy consumption, high throughput, and ease of scaling etc., compared to conventional separation processes. However, the application of membrane separation process has been limited by the presence of concentration polarisation and membrane fouling. These lead to decline in permeate flux and change in retention behaviour. Therefore, the ways to reduce concentration polarisation and thereby enhancing the filtration rate are currently active areas of research in view of the increasing demand of membranes application to various industrial separation processes. To minimise the membrane fouling and concentration polarisation, several techniques have been investigated. In this regard, application of external d.c. (direct current) electric field across the membrane is a promising method to reduce concentration polarisation and fouling. This book deals with the relevant principles, technology and the theoretical details involved in this process. It is to be emphasised that no such book dealing with electric field assisted membrane filtration exists currently. Therefore, this book obviously has significant advancement compared to existing books on membrane technology. This book can be used as one of the Texts for the course like "Novel Separation Processes" taught in Postgraduate level. Of course, this book can be an extremely useful reference book for the students and professionals in Chemical and Environmental Engineering. We believe this book will have two fold impacts. Firstly, its academic value is quite high; Secondly, it will have remarkable impact of scaling up such system in actual industrial scale from pilot plant data in an emerging area. Moreover, a book on such a topic does not exist today; the importance of it from an academic point of view is undoubtedly remarkable. This book presents detailed description of the effect of electric field to a number of typical applications, e.g. fruit juice clarification, separation and fractionation of protein solution, micellar enhanced ultra-filtration for dye removal. The results are analysed in full detail.