The first aim of Technical Mathematics 2 is to enable the student to master a broad range ofstandard mathematical techniques in statistics, algebra, geometry, co-ordinate geometry andtrigonometry to a high level of proficiency. This proficiency is required to support engineeringsubjects and forms the basis for further mathematical study in year 2. The second aim is todeepen the students understanding of key mathematical ideas regarding data presentation andinterpretation, engineering functions, and trigonometry in such a way as to support otherengineering modules. The third aim is to extend the students use of software applications inthe visualisation and processing of engineering data.
Vectors:
Scalars and vectors. Addition and subtraction of vectors. Modulus of a vector. Unit vectors. Resolution into component form. Scalar product. Angle between two vectors in 2-D. Transformation of vectors in 2-D by f: (x,y) to ( ax + by, cx + dy)
Functions:
Basic concepts. Graphs of functions. Completing the square.Drawing graphs of quadraticfunctions using the completed square. Function inverses
Engineering Functions:
Engineering functions on a calculator. Polynomials, rational, power,exponential and logarithmic (natural, base 2, base 10) functions.Plotting functions using appropriate tools. Application ofengineering functions: solving equations involving logarithmic andexponential functions; growth and decay model problems. Definition of periodic functions. Graphs of trigonometric functions. Alterationof a functional description as a result of transformations in theplane. Plotting the graph of f(x+a) given graph of f(x). Classificationof types of signals (even, odd, convex, concave). Construction of simple 2 part piecewisedefined functions using if then else ( e.g. sawtooth wave).
Trigonometry:
Sine and cosine rules. Solving trigonometric equations of form Acos(Bx+C) = D and Asin(Bx+C) = D .
Programming Skills
Programming Basics: documentation (use of comments and indentation), use of built-in I/O and mathematical functions, debugging and testing. Datatypes: Numbers, characters, arrays. Control Structures: selection structures ( if etc. using conditional expressions), repetition structures (for).
Working with data:
Collecting data: tallies. Organising data: frequency tables. Graphs:histograms, pie charts, frequency curves - typical non-normalpatterns and their causes. Population and sample. Summarystatistics: mean, median, mode, range, standard deviation.
Software skills:
Spreadsheets: Formatting text, cells, number, %, currency. Bordersand fills. Headers/footers. Sorting data. Zoom. Worksheets. Charts.
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Other Assessment(s) | 30 |
| Formal Examination | 70 |