Module: EA003
Engineering Mathematics B
Module Purpose:
This module aims to provide students with all the core skills in the mathematical
functions and matricies common to all engineering disciplines.
Relationship to competency standards:
This module will be modified in line with the requirements of the National Metals and
Engineering Standards when they become available.
This module contains the knowledge and skills identified and agreed by all
states/territories. It has been developed on the assumption that these will be reflected
in the Standards.
Prerequisites and/or corequisites:
(EA 002) Engineering Mathematics A
Summary of content:
Matrices:
The operations: addition (subtraction), scalar multiplication, matrix multiplication up
to 3x3 matrices. Identity matrix, inverse matrix Elementary algebraic manipulation of
matricies
Solve up to three equations (linear) in three unknowns using inverse matrices and
determinants.
Quadratic Functions:
Graphs of quadratic functions represented by parabolas and significance of the leading
coefficient Zeros represented graphically
Solve quadratic equations by factoring and quadratic formula.
Solve simultaneously linear and quadratic equations algebraically and geometrically.
Exponential and Logarithmic Functions:
Laws if indices
Graph of f(x) = ka/bx , emphasising a = 1- , e
Definition of the logarithm to any base
Graph of f(x) = K log/a bx, emphasising a = 10, e
Solve exponential and simple log equations using indices, logs, calculator,
graphically.
Change of log base, emphasising 10 and e
Growth and decay.
Trigonometric Functions:
The ratios: sin, cos, tan, cosec, sec, cot
Degrees, radians
Graphs of k f(ax + b) where f(x) = sin x, cos x, tan x,
and significance of k,a,b, for example V = V/m sin (wt + f).
Trigonometric identities
Solve trigonometric equations.
DELIVERY:
The sequential nature of mathematics requires regular and consistent assessment to
demonstrate the mastery of mathematical skills and techniques. Regular marked assignments
(homework) will form 20% of the total assessment.
The three 1 hour tests assessing competence in the skills and techniques for each topic
will form 30% of the total assessment.
A final 2 hour examination will assess students’ ability to solve more complex
problems requiring the understanding and application of various skills and techniques
drawn from across the module. It will test knowledge of the range of relationships within
and between topics and will require interpretation and analysis of verbally formulated
problems. It will form 50% of the total assessment.
Learning Outcomes:
On completion of this module the learner will be able to:
Learning outcome 1:
Use matrix algebra and determinants to solve up to three linear equations in three
unknown.
Assessment Criteria:
Perform the basic operations on matrices up to 3 x 3
Manipulate matrix equations and expressions.
Recognise inverse and identity matrices up to 3 x 3 and use to solve systems of linear
equations
Find determinants up to 3 x 3 and use to solve systems of linear equations.
Conditions:
Assessment Method:
Assignments and 1 hour test.
Learning Outcome 2:
Graph quadratic functions and solve quadratic equations
Assessment Criteria:
Sketch and interpret and graphs of quadratics functions showing the significance of the
leading coefficient and the zeros.
Solve quadratic equations by factoring and using quadratic formula
Solve simultaneously linear and quadratic and linear equations and solve.
Conditions:
Assessment method:
Assignments and 1 hour test.
Learning Outcome 3
Graph exponential and logarithmic functions and solve exponential and logarithmic
equations.
Assessment Criteria:
Manipulate and simplify arithmetic and algebraic expressions using the laws of indices
and logarithms.
Sketch the graphs of simple exponential and logarithmic functions showing behaviour for
large and small values.
Solve exponential and simple logarithm equations using indices, logarithms, calculator,
graphical techniques.
Convert logarithms between bases, especially base 10 and base e.
Transform non-linear functions (including exponential) to linear forms and plot data.
Draw curves of best fit, interpolate data and estimate constants in suggested
relationships.
Interpret verbally formulated problems involving growth and decay, and solve.
Conditions:
Assessment method:
Assignments and 1 hour test.
Learning Outcome 4:
Graph trigonometric functions and solve trigonometric equations.
Assessment Criteria:
Sketch the graphs of simple trigonometric functions showing the significance of
amplitude, period and phase angle.
Solve trigonometric equations
Conditions:
Assessment method:
Assignments and 1 hour test.
