Mathematics for IT 2

This Mathematics for IT module will enable the learner to build on the knowledge and skills acquired at stage one through the mathematics modules. This module ensures the learner sees mathematics as an integral part of their studies and is necessary as part of successful progression both horizontally and vertically within the programme.

Functions & Graphing:

• The graph of a function, vertical line test, horizontal line tests
• Linear functions, polynomial (including quadratic & cubic) functions
• Exponential, logarithmic and reciprocal functions
• Trigonometric functions
• Inverse functions (and domain restriction) of the above-named functions
• Transformations of the above-named functions
• Asymptotes and limits of a function

Calculus:

• Differentiation from first principles
• Derivative of polynomials and polynomial-like functions (negative/rational powers)
• Derivative of exponentials, logs, trigonometric functions
• Standard derivatives formulas: the product rule, quotient rule and chain rule
• Second derivative
• Applications of derivatives: rates of change, critical points, maxima and minima
• Definite and indefinite integrals
• Applications of integrals

Vectors:

• Vectors as n-tuples, column vector notation, and as arrows in Cartesian space
• The i, j and k unit vectors, and putting vectors into components using these
• Adding and subtracting vectors, and scalar multiplication
• Magnitude (length/norm) and direction of vectors
• Dot product, and angle between two vectors
• Cross product

Linear Algebra:

• Definition of a linear map
• Solving sets of linear equations using Gauss-Jordan elimination (and knowing the number of solutions)
• Representing points or vectors as columns in a matrix (e.g. a polygon)
• Vector and matrix (e.g. polygon) transformations: translations, scaling, reflections, rotations, projections
• Eigenvalues and eigenvectors
• Diagonalization of matrices