Mathematics plays a central role in modern culture, and a basic understanding of the nature of mathematics is required for scientific literacy. This new textbook will prepare readers to continue to develop analytical and numerical skills through the study of a variety of mathematical techniques. The statistical element of this textbook enhances readers’ ability to organise and interpret data. Most of the topics covered in this textbook are widely used in various areas of engineering, including industrial engineering, to analyse complex systems, optimise processes and make informed decisions to improve efficiency, productivity and reliability in various industrial settings. From the complexities of double integration and ordinary differential equations to the complexities of linear systems of differential equations, Fourier series and Laplace transform, Foundation Engineering Mathematics unfolds with careful attention to detail, offering readers a structured approach to mastering these fundamental topics. Each chapter of this book is carefully presented to provide a balance between theoretical foundations and practical applications, ensuring that readers not only grasp the underlying principles but also appreciate their relevance in real-world engineering scenarios. Each chapter is accompanied by practical examples, illustrative diagrams and engineering applications to reinforce understanding and demonstrate the relevance of mathematical concepts in engineering practice. Whether you’re a student embarking on your journey into the world of mathematics or an experienced engineer seeking to deepen your understanding of mathematical concepts, this book serves as an invaluable resource, guiding you through the complexities of mathematical theory and its engineering applications. A solutions manual and a set of PowerPoint slides are available for qualified textbook adoptions.