The evidence guide provides advice on assessment and must be read in conjunction with the performance criteria, required skills and knowledge, range statement and the Assessment Guidelines for the Training Package.

Overview of assessment

A person who demonstrates competency in this unit must be able to apply advanced mathematics and numerical methods techniques to engineering-related problems within the context of specified engineering applications and solution validation and technical oversight procedures. The candidate may demonstrate competence through either working individually or as part of a team.

Critical aspects for assessment and evidence required to demonstrate competency in this unit

Assessors must be satisfied that the candidate can competently and consistently:

solve engineering problems using advanced mathematics and numerical methods techniques

validate results of simple examples using advanced mathematics and numerical methods either analytically and/or graphically using appropriate software or scientific calculators

assist decision making processes in industry by analysis of data using advanced mathematics and numerical methods concepts and tools.

Context of and specific resources for assessment

This unit may be assessed on the job, off the job or a combination of both on and off the job. Where assessment occurs off the job then a simulated working environment must be used where the range of conditions reflects realistic workplace situations. The competencies covered by this unit would be demonstrated by an individual working alone or as part of a team.

Where applicable, reasonable adjustment must be made to work environments and training situations to accommodate ethnicity, age, gender, demographics and disability.

Access must be provided to appropriate learning and/or assessment support when required. Where applicable, physical resources should include equipment modified for people with disabilities.

Method of assessment

Assessment must satisfy the endorsed Assessment Guidelines of the MEM05 Metal and Engineering Training Package.

Assessment methods must confirm consistency and accuracy of performance (over time and in a range of workplace relevant contexts) together with application of underpinning knowledge.

Assessment methods must be by direct observation of tasks and include questioning on underpinning knowledge to ensure correct interpretation and application.

Assessment may be applied under project-related conditions (real or simulated) and require evidence of process.

Assessment must confirm a reasonable inference that competency is not only able to be satisfied under the particular circumstance, but is able to be transferred to other circumstances.

Assessment may be in conjunction with assessment of other units of competency where required.

Guidance information for assessment

Assessment processes and techniques must be culturally appropriate and appropriate to the language and literacy capacity of the candidate and the work being performed.

Required skills

Required skills include:

analysing engineering applications to determine relevant algebra and numerical methods

applying relevant advanced mathematics and numerical methods concepts and tools to engineering situations

using appropriate software and/or scientific calculators to generate solutions to algebra and numerical methods problems

establishing appropriate procedures for checking and validating solutions

logical layout and presentation of data developed using algebra and numerical methods

reporting and effectively communicating the results of advanced mathematics and numerical methods-based analysis

Required knowledge

Required knowledge includes:

vectors:

vectors in 3-D

i, j and k notation

magnitude of a vector

unit vectors and direction angles

scalar or ‘dot’ product of two vectors

vector or ‘cross’ product of two vectors

resolution of vectors

differentiation and integration of vectors

dynamics:

Newton’s Laws of Motion

energy, work and power

work-energy theorem

moment of a force

analytical geometry:

equation of a plane

angle between two planes

distance from a point to a plane

lines in 3-D space

graphing techniques:

coordinate geometry

graphs of exponential growth and decay

graphs with logarithmic scales

method of least squares

polar coordinates and polar graphs

graphs of functions of two variables

quadric surfaces

complex numbers:

introduction to complex numbers

cartesian form

the Argand plane

trigonometric and polar form

linear algebra:

matrix algebra

transformations

determinants

numerical solutions:

finite difference techniques

errors:

computer arithmetic

propagation of errors

interpolation and approximation:

polynomial interpolation

Lagrange form

Newton’s divide formula

error bound

The range statement relates to the unit of competency as a whole. It allows for different work environments and situations that may affect performance. Bold italicised wording, if used in the performance criteria, is detailed below. Essential operating conditions that may be present with training and assessment (depending on the work situation, needs of the candidate, accessibility of the item, and local industry and regional contexts) may also be included.

Engineering applications related to advanced mathematics and numerical methods techniques in this unit

Most engineering disciplines will have applications supported by the advanced mathematics and numerical methods skills described in this unit, including mechanical, manufacturing, maintenance and mechatronics engineering. Examples of engineering applications requiring advanced mathematics and numerical methods skills described in this unit may include:

assisting decision making in industry by analysis of data using advanced mathematics and numerical methods concepts and tools

assisting presentation of data in industry by use of advanced graphical techniques

solution of problems involving rectilinear and rotation motion

solution of problems involving work, energy and power

solution of problems in electrostatics and wave propagation

Scope of advanced mathematics and numerical methods techniques

The scope of advanced mathematics and numerical methods techniques required for an engineering or manufacturing application will vary and may include:

vectors in 3-D, including i, j, k notation, scalar and vector products

dynamics, including Newton’s Laws of Motion, energy, work and power and work-energy theorem

analytical geometry

graphing techniques, including coordinate geometry, polar coordinates and polar graphs

complex numbers, including Cartesian, trigonometric and polar form

linear algebra, including matrix algebra

numerical solutions, including finite difference techniques

errors and propagation of errors

interpolation and approximation