Mathematics

Mathematics is a powerful tool used for solving practical problems and is a highly creative field of study, combining logic and precision with intuition and imagination. The ability to employ mathematical reasoning is a fundamental skill for any well-educated individual in the pure and applied sciences. 

This preliminary course is designed to provide a solid foundation for students interested in further studies in mathematics and also to give students in the Sciences the mathematical tools necessary for their work. It is a prerequisite for students who intend to take advanced level courses in mathematics or statistics.

This course serves to sharpen the analytical and critical reasoning skills of the student and to improve his/her ability to express mathematical ideas with coherence and clarity.

In a broad sense, calculus is the mathematical study of change consisting of differential calculus (concerning rates of change and slopes of curves) and integral calculus (concerning accumulation of quantities and the area under/between curves).

The course covers the fundamental concepts of the differential and integral calculus of a single variable. The used approach is intuitive and informal but nevertheless prepares students to understand the rigorous proofs at a subsequent level. A sound knowledge of the required prerequisite material (CAPE Pure Mathematics Units 1 & 2 or Preliminary Mathematics 1 & 2) is assumed. While there is a considerable overlap with the ideas encountered in the prerequisite courses, a greater emphasis is put on the fundamental ideas involved in differentiation and integration. The main results are derived and illustrated although often heuristic proofs are used.

This course will treat the limits, continuity and differentiability of a function of a single variable and applications thereof, e.g., finding maxima and minima of functions. Integrals are introduced via Riemann sums and methods for their evaluation using antiderivatives are considered.

Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables: the differentiation and integration of functions involving multiple variables, rather than just one. Techniques of multivariable calculus are used to study many objects of interest in the material world like curves, surfaces and vector fields.