This course is designed to develop the intuitive understanding, theory, and computational skills necessary for the concepts of vector functions, with an emphasis on their applications in sustainable industrialisation. By tying together multivariate calculus with vector concepts, students will explore topics such as include Vector Fields, Stokes theorem, Green's theorem, Gauss' theorem. These mathematical tools are essential for analysing and solving complex problems in sustainable industrial practices, contributing to the advancement of environmentally sound technologies and processes.