The module covers some of the most fundamental prerequisites for studying Numerical Sciences subject at (UK) higher education, hence is highly recommended for those wishing to study these subjects. The aim of this module is to give a solid knowledge of the common techniques and usage of differentiation (Part I) and integration (Part II) of functions. We concentrate on the results, techniques and their applications but a self contained theory using secondary school viewpoints is also developed having the statements validated by proofs. The module covers differentiation, rules, solving optimisation problems (Part I), and integration, Newton-Lebniz theorem basic integration techniques and applications. The module is suitable for students with no or limited knowledge on this topic. However, students who are familiar only with some of the topics or unfamiliar with the proofs are also welcome. Student knowing the material of Part I may enroll only to Part II.