The applicability of calculus and linear algebra is so broad that fluency in it is essential for a successful career in a variety of areas including science and engineering. This unit is devoted to the conceptual and logical development of these two main areas of mathematics, gradually building the tools for solving innumerable problems of great practicle importance. In calculus part of the unit, a brief look at the Real Number System and their properties will lead us to the study of Functions in general and the study of special functions such as trogonometric, exponential and logarithmic functions. The notion of limits will be utilised to define continuity and differentiability of functions, emphasising the importance of understanding the material conceptually and graphically. This area will also help establish the technical skills necessary to solve problems arising in practical situations. One highlight of the unit will be the discussion of the Fundamental Theorem of Calculus, which unifies differential and integral calculus. The concept of Complex Numbers will also be introduced together with their fundamental operations, basic knowledge of which is essential for the units involved in Real and Complex Analysis and Differential equations. An introduction to two and three dimensional vector spaces will be an essential part of the unit as the knowledge in that area is vital, particularly for studies in engineering and physics. If time permits, systems of linear equations and introduction to matrices is a potential chapter under Linear Algebra.