This book strives to provide a concise and yet comprehensive coverage of all major mathematical methods in engineering. Topics include advanced calculus, ordinary and partial differential equations, complex variables, vector and tensor analysis, calculus of variations, integral transforms, integral equations, numerical methods, and probability and statistics. Application topics consist of linear elasticity, harmonic motions, chaos, and reaction-diffusion systems. This book can serve as a textbook in engineering mathematics, mathematical modelling and scientific computing. This book is organised into 19 chapters. Chapters 1-14 introduce various mathematical methods, Chapters 15-18 concern the numeri-cal methods, and Chapter 19 introduces the probability and statistics.