Application
This unit applies to projects or tasks requiring numerical solutions involving numerical solutions and the solution of different types of equations by numerical methods, either manually or through use of an appropriate software package. It is suitable for paraprofessionals and technologists required to solve advanced mathematical problems in an engineering or related field, or those pursuing technologist careers and qualifications and for articulation of qualifications into degree programs.
Prior or concurrent experience in mathematics covering polynomials and differential equations is required.
Prerequisites
Not applicable.
Elements and Performance Criteria
1 | Identify a need for the application of numerical methods | 1.1 | Identify a problem requiring application of numerical methods |
1.2 | Define the problem | ||
1.3 | Determine data currently available for analysis | ||
1.4 | Identify ways of obtaining other required data | ||
1.5 | Determine information required from outcome |
2 | Prepare to solve problem by numerical methods | 2.1 | Determine numerical methods to be applied |
2.2 | Identify and gain access to appropriate computational devices | ||
2.3 | Collect required input data | ||
2.4 | Analyse collected data for suitability and completeness | ||
2.5 | Take appropriate action to address any deficiencies found |
3 | Solve problem using numerical methods | 3.1 | Apply appropriate techniques to collected data |
3.2 | Check answer by appropriate means | ||
3.3 | Interpret answer to determine information required by problem definition |
4 | Communicate outcomes | 4.1 | Communicate outcome to relevant stakeholders by appropriate means |
4.2 | Explain outcome to stakeholders, as appropriate | ||
4.3 | Check outcome has addressed problem |
Required Skills
Required skills |
Required skills include: identifying and defining problems collecting and analysing data reporting and presenting data and quantitative information communicating effectively with stakeholders on problem resolution |
Required knowledge |
Required knowledge includes: numerical solutions: finite difference techniques polynomial interpolation errors: computer arithmetic propagation of errors solution of non-linear equations: fixed point and bisection method Secant and Newton-Raphson iterative methods convergence solution of systems of linear equations: Gaussian elimination pivoting strategies LU factorisation Ill-conditioning errors and residuals iterative methods solution of differential equations: Euler method Taylor and Runge-Kutta methods convergence Interpolation and Approximation: polynomial interpolation Lagrange form Newton’s divide formula error bound finite difference techniques: solution of problems in electrostatics and wave propagation |
Evidence Required
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. | |
Critical aspects for assessment and evidence required to demonstrate competency in this unit | Assessors must be satisfied that the candidate can competently and consistently: identify appropriate numerical methods for engineering or related problems apply the appropriate technique to the problem communicate the outcome of the analysis in an appropriate way. |
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, that is, the candidate is not in productive work, then a simulated working environment must be used where the range of conditions reflects realistic workplace situations. The competency 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 its 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 able not only 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. |
Range Statement
The range statement relates to the unit of competency as a whole. It allows for different work environments and situations that may affect performance. 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. | |
Data available | Data currently available includes: all relevant data which is currently available within the organisation or could be readily obtained |
Information required | Information required is the outcome which needs to be produced in order to solve/assist in resolving the defined problem |
Numerical methods | Numerical methods may include: one or more or any of the techniques listed under ‘required knowledge’ a related technique |
Computational device | Computational devices include: calculators with numerical methods functions computer software packages |
Appropriate action | Appropriate action may include: taking necessary steps to obtain required data obtaining some relevant proxy for the desired data choosing a different numerical method/computational device which will function with available data |
Appropriate technique | Appropriate technique includes: selected numerical method which will yield required outcome technique which is appropriate for the available data and which is relevant to the problem |
Check answer | Checking answer means examining the answer to ensure it is within the range of expected logical results |
Interpret answer | Interpret answer means translating the result of the numerical analysis into a form which is useable by the relevant stakeholders |
Appropriate communication | Appropriate communication may include: report presentation verbal communication web-based electronic or hard copy |
Check outcome | Check outcome includes: ensuring that the result of the analysis does assist in the resolution of the problem |
Sectors
Engineering practice
Employability Skills
This unit contains employability skills.
Licensing Information
Not applicable.