The first aim of Technical Mathematics 3 is to develop the students’ competence in a range of mathematical techniques in discrete mathematics, probability as applied to reliability, array handling and basic calculus in such a way as to support other engineering modules. The second aim is to deepen the students understanding of key mathematical ideas regarding number systems, logic, probability, rates of change and matrices as a basis for further mathematical study in semester 4. The third aim is to extend the students use of software applications in the manipulation and processing of engineering data.
Computing: Number bases: binary decimal hexadecimal. Translation between them.
Discrete Mathematics: Simple and compound propositions. Truth tables. Simple logic circuits: AND, OR, NAND, NOR, EXCLUSIVE Tabular simplification technique.
Probability (Reliability): Definition of probability. Calculating probabilities. The laws of probability. Reliability engineering: components in series and in parallel ( use of AND/OR).
Probability distributions: Recognize Poisson and exponential distributions and use them in problems on reliability and rate of defects.
Differentiation: Use of a table of derived functions. Use of the multiple, sum, product, quotient and chain rules. Average and instantaneous rate of change. Definition of derivative of a function at a point. Geometric interpretation of the derivative.
Function investigation using differentiation: Increasing and decreasing functions. Stationary points. Classifying stationary points and the second derivative test. Applied Maximum /minimum and approximate error problems.
Geometry and Matrices: Matrix definition. Matrix algebra. Matrix determinant, special matrices and the matrix of a geometric transformation. Inverse matrix formula for 2´2. Systems of linear equations in matrix form. Row reduction for finding the inverse of a matrix. Solution of system of linear equations using row reduction (Gaussian elimination).
Software skills: Spreadsheets and spreadsheet formulas for reliability. Matrices, vectors, matrix inverse, solving systems of linear equations in Matlab. Calculus in Geogbea.
