The first aim of the module is a thorough revision and consolidation of key numeracy and algebra skills, including the effective use of a calculator. The second aim of the module 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 show the range of applicability of mathematics in diverse branches of engineering.
1. Arithmetic
a. Arithmetic of real numbers, fractions. Indices, floating point, scientific and engineering notation. Significant figures, rounding to nearest, estimation in engineering.
b. Precedence rules. Effective use of the calculator.
2. Algebraic expressions and formulae
a. Understanding expressions: counting and listing terms, counting and listing factors, numerator and denominator, indices (powers), expressions are not equations
b. Manipulation of algebraic expressions: algebraic fractions. Factorising and expanding. Rules of indices with application to unit simplification. Grouping terms. Quadratic factorization.
c. Understanding syntax: >, =, etc., “divide”, “cancel”, “quotient”, “ratio”, “therefore”, “implies”, “if and only if”
d. Operands in algebra and their inverse (+-, ´/, () etc)
e. Transposition of formulae where variable of interest occurs once. Parse an expression into a sequence of operands acting on variable. Transposition as sequence of inverse operands.
f. Solve equations involving ratio, proportion. Solving such word problems.
g. Solving linear and quadratic equations in one variable.
h. Resolve a more general equation in one variable into a linear or quadratic equation.
i. Solve a pair of linear equations.
j. Complete the square
3. Linear Laws
Cartesian co-ordinates. Equation of straight line. Average point of data and plotting the ‘best’ straight line through the average point by eye. y-intercept and slope. Equation of a linear law from its plot. Linear laws in an engineering context.
4. Unit Conversion
Recap of engineering and scientific notation, indices rules for powers of 10. SI units. Unit conversion within SI units as an algebraic exercise.
5. Basic 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 and trigonometry in an engineering context. Sine and Cosine rules.
6. Complex numbers
Definition of a complex number. Addition and subtraction of complex numbers in Cartesian form. Conjugate of a complex number. Argand diagram representation, modulus and argument. Polar form and Cartesian Û Polar form conversion. Multiplication and division in Polar and Cartesian form. Complex solutions of quadratics. Complex numbers in an engineering context.
