The first aim of Technical Mathematics 1 is a thorough revision and consolidation of key numeracy and algebra skills, including the effective use of a calculator. The second aim of Technical Mathematics 1 is to support other engineering modules in year 1 by covering unit conversion, manipulation of engineering formulae, linear laws, the study of right angled triangles and complex numbers. The third aim of the module is to introduce students to the use of software applications in the presentation and manipulation of engineering data.
Arithmetic: Arithmetic of real numbers, indices, fractions, precedence rules. Correct use of the calculator. Error Estimation
Algebraic expressions and formulae: Understanding expressions: counting and listing terms, counting and listing factors, numerator and denominator, indices (powers),multiplication convention, expressions are not equations2.Manipulation of algebraic expressions: algebraic fractions. Factorising and expanding. Rules of indices. Application to unit simplification. Grouping terms. Quadratic factorization.3.Understanding syntax: >, =, etc., “divide”, “cancel”, “quotient” “ratio”, “therefore”, “implies”, “if and only if”4.Operands in algebra and their inverse5.Transposition of formulae where variable of interest occurs once. Parse expression into sequence of operands acting on variable. Transposition as sequence of inverse operands.6.Solve equations involving ratio, proportion. Solving such wordproblems.7.Solving linear equations in one variable. Quadratic equations.8. Solve simultaneously a pair of linear equations.
Linear Laws: Cartesian co-ordinates. Equation of straight line. Plotting simple linear laws, y-intercept and slope. Equation of a linear law from data. Linear laws using a spreadsheet. Intersection of pair of linear laws.
Unit Conversion: Engineering and Scientific notation, indices rules for powers of 10. SI units. Decimal places and significant figures. Word problems. Degrees and Radians.
Trigonometry: Right-angled triangles. Sin, Cos and Tan. Sin, Cos and Tan as lengths in the unit circle. Pythagoras’ theorem. Solution of right-angled triangles. Vector components
Complex numbers: Definition of a complex numbers. Conjugate of a complex number. Argand diagram representation. Addition and subtraction of complex numbers in Cartesian form. Polar form. Cartesian to Polar form conversion on the calculator. Multiplication and division in Polar and Cartesian form.
Software Skills: File management: Managing Files and the Computer Interface: Directory structure. Searching for files. Copy and rename. Spreadsheets: Basic concepts. Entering data to cells. Selecting cells, rows, columns and ranges. Copying/moving cells. Inserting/deleting cells, rows and columns. Entering formulae. Cell referencing. Using the function wizard. Plotting charts & graphs: line/curve fitting.
