There is a widely understood need for professional engineers and student‘ becoming engineers’ to think mathematically and to use mathematics to describe and analyse different aspects of the real world they seek to engineer. Mathematics has long been known to be problematic for university engineering students and their teachers. Mathematics is the background of every engineering field. Together with physics, mathematics has helped engineering develop. Without it engineering cannot evolved so fast we can see today. Without mathematics, engineering cannot become as fascinating as it is now. Linear algebra, calculus, statistics, differential equations and numerical analysis are taught as they are important to understand many engineering subjects such as fluid mechanics, heat transfer, electric circuits and mechanics of materials to name a few. One thinks of the dynamics of structures and industrial fluid mechanics in the engineering of bridges. Mathematical modeling therefore plays a key role in the formation of engineers, and there has been much research into how engineers should be taught the essential mathematics. Advanced Modern Engineering Mathematics offers a review of standard mathematics coursework while effectively integrating science and engineering throughout the text. In this book, several examples of applications of mathematics in mechanical, chemical, and electrical engineering are covered. Applications in this book are the real ones found in the engineering fields, which may not be the same as discussed in many mathematics textbooks. The contributed chapters are written by renowned authors and specialists in the subject around the globe. This book serves as valuable guide for computer science, mechatronics and electrical engineering students as well as for researchers and practitioners.