The first aim of Technical Mathematics 2 is to enable the student to master a broad range of standard mathematical techniques in statistics, algebra, geometry, co-ordinate geometry and trigonometry to a high level of proficiency. This proficiency is required to support engineering subjects and forms the basis for further mathematical study in year 2. The second aim is to deepen the students understanding of key mathematical ideas regarding data presentation and interpretation, engineering functions, and trigonometry in such a way as to support other engineering modules. The third aim is to extend the students use of software applications in the 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 quadratic functions 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 of engineering functions: solving equations involving logarithmic and exponential functions; growth and decay model problems. Definition of periodic functions. Graphs of trigonometric functions. Alteration of a functional description as a result of transformations in the plane. Plotting the graph of f(x+a) given graph of f(x). Classification of types of signals (even, odd, convex, concave). Construction of simple 2 part piecewise defined 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-normal patterns and their causes. Population and sample. Summary statistics: mean, median, mode, range, standard deviation.
Software skills: Spreadsheets: Formatting text, cells, number, %, currency. Borders and fills. Headers/footers. Sorting data. Zoom. Worksheets. Charts.
