This subject aims to make the student highly proficient in a range of mathematicaltechniques in linear algebra, analysis and calculus required to support ElectronicEngineering subjects. It forms the basis for year 2.
Functions and their graphs
Basic concepts. Domain and range. Graphs of functions.Graphs of continuousand smooth functions. 1-1 and onto functions. Function inverse. Algebra offunctions.Engineering functions: Polynomials. Rational functions. Periodic functions.Natural log and exponential functions. Engineering functions on the calculator.Solving equations involving natural log and exponential functions. Fittingexponential data using a log-linear plot.
Differentiation
Average and instantaneous rate of change. Geometric interpretation ofthe derivative. Differentiation of engineering functions. Linearity rules.Product, quotient and chain rules. Second derivative.Applications of differentiation: Max/min problems for polynomial examples.Rates of change. Velocity and acceleration. Current and voltage. Error analysisin 1D.
Integration
Introduction to integration. Integration of engineering functions.Linearity.Integration of a derivative. Substitution of simple linear variables andcorresponding change of limits. Area under a curve.
Vectors and matrices
Examples of vectors. Addition and subtraction of column vectors. Modulus of avector. Unit vectors. Scalar product. Resolution.2D transformations (shear, rotation, dilation). Composition of transformations.Introduction to 2D matrices as transformations. Matrix algebra.Transformation/Matrix inverse.Introduction to Matrix algebra. Algebra of matrices (addition andmultiplication) up to and including matrices of order 3, including matrices withcomplex entries. Determinants, cofactors, inverses. Solution of equations usingmatrix inversion. Applications to Electronic Engineering.
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Other Assessment(s) | 30 |
| Formal Examination | 70 |