The module will initially complete the learners knowledge of the fundamentals of mathematics by covering the topic of vectors. The module then covers the foundational elements of differential and integral calculus needed for any engineering programme. This will enable the learner to use vector algebra fluently during their career as an engineer.
Vectors: The definition of a vector as a quantity with direction and magnitude. Physical quantities such as velocity, acceleration and force defined as vectors and their derivatives. The addition of vectors; resolution of two or more vectors.
The Concept of the Derivative: The concept of the Derivative as a rate-of-change, as the slope of a curve. Defining and calculating the derivative of a function by first principles. Establishing the derivatives of simple functions, such as linear, quadratic and cubic functions using first principles. The derivatives of common functions encountered in the physical sciences and engineering, including polynomials, the logarithm and exponential functions and the basic trigonometric functions.
Differential Calculus: The product and quotient rules and their application to finding derivatives. Composite functions and the Chain rule. The derivatives of common functions found in engineering formed from the basic functions. Finding the maxima and minima and the turning points of a range of functions and interpreting the results. The concept of a McLaurin series and the method of calculating the series directly by repeated differentiation.
Integration: Integration as the inverse operation to the derivative. Identifying the integrals of common functions from this concept. The definite integral and its interpretation as the area below a curve. The mean square and root mean square of functions and the use of these ideas in electrical science. The average power of an electrical circuit.
