The module continues the learners introduction to the fundamental mathematical concepts and methods needed in engineering. It builds upon previous work on the fundamentals of algebra and introduces differential and integral calculus. The module also begins the learners engagement with statistical methods by setting out the basics of descriptive statistics.
Calculus: Derivatives of elementary functions. The properties of the derivative, including the product rule, the quotient rule, composite functions and the chain rule. Maxima and minima problems and points of inflexion. Applications to mechanics; velocity, acceleration and the equations of motion. Optimisation of engineering problems using calculus.
Partial Differentiation. Introduction to the concept of multivariate calculus and first order partial derivatives.
Integration. Indefinite and definite integrals of the basic mathematic functions used in engineering; the trigonometric, log and exponential functions. Substitution techniques. Area under curve and volume of rotation. The concept of Numerical integration and Simpson’s rule.
Statistics: Analysis and presentation of data, including basic graphs. Measures of central tendency and dispersion. Simple probability; definitions and basic calculations.
