Building on the foundations laid in the companion text Modern Engineering Mathematics 3e, this book gives an extensive treatment of some of the advanced areas of mathematics that have applications in various fields of engineering, particularly as tools for computer-based system modelling, analysis and design. Despite the advanced level of this text, the philosophy of learning by doing is retained, with continuing emphasis on the development of students` ability to use mathematics with understanding to solve engineering problems. Key features of this new edition: New design in a larger format highlighting new student features. Additional graded examples and exercises. Increased emphasis on software packages, particularly symbolic algebra packages. Particular emphasis on use of MATLAB and MAPLE, with basic commands introduced and illustrated. More emphasis on numerical methods such as the treatment of finite elements. Updated Solutions Manual, a downloadable resource for lecturers. Professor Glyn James is currently Emeritus Professor within the School of Mathematical and Information Sciences at Coventry University, having previously been Dean of the School.. As in previous editions he has drawn on the relevant knowledge and experience of his fellow co-authors to provide an excellent new edition..