Welcome to the Mathematics Laboratory Manual for Engineering Students, designed specifically for the first year of your engineering journey. This manual aims to provide you with a comprehensive understanding of mathematical concepts and their practical applications using MATLAB, a powerful computational tool widely used in engineering disciplines. Mathematics forms the foundation of engineering, providing a language through which complex problems can be analyzed, modeled, and solved. Understanding and applying mathematical principles are essential skills for any aspiring engineer. This manual is designed to bridge the gap between theoretical concepts and their real-world implementations, empowering you to develop a solid mathematical foundation. Throughout this manual, you will encounter a series of carefully designed experiments and exercises that cover a wide range of mathematical topics relevant to engineering disciplines. Starting from fundamental concepts such as vectors, matrices, and basic operations, you will progress towards more advanced topics including calculus, differential equations, and numerical analysis. It is important to note that this manual assumes no prior knowledge of MATLAB. The introductory chapters will guide you through the basics of MATLAB programming, ensuring that you have a solid foundation before delving into the more complex mathematical topics. Each experiment is designed to build upon the knowledge acquired from previous ones, enabling a seamless learning progression. Each lab contains an explanation that the teacher can demonstrate, as well as tasks that students can complete within a two-hour lab session. On each page, there is a designated box that provides instructions on what the student needs to write in their record book. For example, each task, the student has to write it in the record book. The teacher can instruct the student to write code on the ruled page, while the input, output, and graph can be written on the unruled page of the record book. We sincerely hope that this Mathematics Laboratory Manual enhances your learning experience and serves as a valuable resource throughout your first year of engineering. The combination of theoretical knowledge and practical application will empower you to excel in your academic pursuits and equip you with the essential skills needed to solve real-world engineering challenges.