The first aim of Technical Mathematics 3 is to develop the students’ competence in a range ofmathematical techniques in discrete mathematics, probability as applied to reliability, arrayhandling and basic calculus in such a way as to support other engineering modules. The secondaim is to deepen the students understanding of key mathematical ideas regarding numbersystems, logic, probability, rates of change and matrices as a basis for further mathematicalstudy in semester 4. The third aim is to extend the students use of software applications in themanipulation and processing of engineering data.????PROGRAMMING content edit???
Computing :
Number bases: binary decimal hexadecimal. Translation betweenthem.
Discrete Mathematics:
Simple and compound propositions. Truth tables. Simple logiccircuits: AND, OR, NAND, NOR, EXCLUSIVETabular simplification technique.
Probability (Reliability)
Definition of probability. Calculatingprobabilities. 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 ofa function at a point. Geometric interpretation of the derivative.
Function investigation using differentiation:
Increasing and decreasing functions. Stationary points. Classifyingstationary points and the second derivative test. Applied Maximum /minimum and approximate error problems.
Geometry and Matrices:
Matrix definition. Matrix algebra. Matrix determinant, specialmatrices and the matrix of a geometric transformation. Inversematrix formula for 2´2. Systems of linear equations in matrix form.Row reduction for finding the inverse of a matrix. Solution of systemof 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.
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Other Assessment(s) | 45 |
| Formal Examination | 55 |