To introduce students to the fundamental concepts of calculus and linear algebra. To develop and integrate the basic mathematical skills relevant to technology. The module will also provide students with the mathematics to support the study of Euclidean Geometry and Transformation Geometry.

Functions: graphs and functions, linear, quadratic and polynomial functions, exponential and logarithm, inverse function, limits and continuity; Trigonometry:basic ideas, definitions, formulae and identities, sine and cosine rules, applications, circular functions; the Derivative and its applications: basic concept, rate of change, differentiation of sum product, quotient, chain rule, derivative of standard functions, simple applications, tangent and normal; Experimental Laws:curve-fitting, graphical techniques, expressions reducible to linear form, least-square approximation (formula only); Linear equations:solution of systems of linear equations by Gaussian elimination, examples with a unique solution, an infinite number or no solutions;Vectors:definition, addition, components, resultant, position vector, scalar product, dot product and angle between vectors. Complex Numbers:necessity, examples, definition, properties, equality, conjugate, modulus, geometric representations, Argand diagram, polar form: argument, exponential form, de Moivres theorem, powers and roots. Euclidean geometry: definition, points, lines, dimensions, Pythagorean theorem, plane geometry, solid figures, conic sections; Transformation Geometry: definition, translation, reflection, rotation, resizing, graphical techniques.

On successful completion of this module, students will be able to: Define elementary functions including polynomials, exponential logarithms and graph simple examples. Define trigonometric functions and use formulas and identities including sine and cosine rules. Differentiate elementary functions using the laws of differentiation and apply to curve-sketching. Fit line to data points using the method of least squares. Solve systems of linear equations using the method of Gauss elimination. Construct vectors in two and three dimensions, calculate dot products and the angle between two vectors. Define and use complex numbers in standard and polar/exponential forms and their algebraic properties, including roots and powers. Analyse plane and solid figures underpinned by principles from Euclidean geometry and Transformation geometry. Demonstrate numerical problem-solving aiding and supporting the study of mathematics.

On successful completion of this module, students will be able to: Develop awareness of the value of graphical communication in aiding and supporting the study of mathematics.

On successful completion of this module, students will be able to: Identify and demonstrate the principles of solid figures from Euclidean geometry and Transformation geometry.

Normal lecture and tutorial delivery. A mid-term exam is to be encouraged. Examples should be kept simple and with applications where appropriate.