MEM23001A: Apply advanced mathematical techniques in a manufacturing engineering or related environment
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Updated TL: July 2009.  Nominal Hours: 36 | 9154 Dip / 9163 Adv Dip: (Group 3) | Competency


Pre-requisites

MEM16008A

Interact with computing technology

MEM30012A

Apply mathematical techniques in a manufacturing engineering or related environment


This unit covers advanced concepts of mathematics appropriate to engineering situations within the individuals area of engineering expertise.

Comment: 
This maths subject is allocated 36 hours but is a lot shorter then the 36 hour pre-requisite MEM30012A.



ASSESSMENT
Assessment is a combination of multiple choice tests and hand-in reports. Assessment Task Schedules: Note: Content follows the textbook rather than the CIDO delivery plan.
A  Mathematical Techniques
Task Description and Link Quiz ID Due Week  Workload
%
Must
Pass 
1 Logs and Exponentials MathsOnline* - 25 Y
2 Trig Equations MathsOnline* - 25 Y
3 Curves and Graphs MathsOnline* - 25 Y
4 Numerical Analysis - - 25Y
- TOTAL - - 100 -

*MathsOnline: You can practice the test using a "parent" account, then when you are ready to sit the test, log in to my Teacher account to record a mark. See topic webpages (linked in above table) for details on which tests need to be completed.


MEM23001A UNIT INFORMATION (CIDO)

Elements of Competency and Performance Criteria

Competency   Competency Elements

1. Graph exponential and logarithmic functions and solve exponential and logarithmic equations

1.1

Simplify arithmetic and algebraic expressions using the laws of indices and logarithms.

 

1.2

Sketch the graphs of exponential and logarithmic functions.

 

1.3

Convert logarithms between bases.

 

1.4

Draw curves of best fit, interpolate data and estimate constants.

 

1.5

Solve problems involving growth and decay.

2. Graph trigonometric functions and solve trigonometric equations

2.1

Sketch graphs of simple trigonometric functions.

 

2.2

Simplify trigonometric expressions.

 

2.3

Solve trigonometric equations.

3. Apply basic computer numerical methods to engineering situations

3.1

Apply appropriate number systems to a range of engineering applications requiring manipulations of decimal, binary and hexadecimal information.

 

3.2

Apply computer techniques to the solution of engineering problems involving products, sums, divisions and subtraction of variables.

 

3.3

Apply computer techniques to the solution of engineering problems involving linear, quadratic, logarithmic, trigonometric equations.

 

3.4

Apply computer techniques to the solution of engineering problems and vector analysis.

4. Sketch and describe complex figures mathematically

4.1

Sketch complex figures including intersections to implement pattern developments.

 

4.2

Describe complex figures mathematically.  Relate mathematical models to computer graphics models.

Glossary (Range Statement) 

Complex figures

May include cones, pyramids, spheres, frustums and intersections of figures singularly or in combination 

Knowledge and Skills

Skills
  • simplifying arithmetic and algebraic expressions using the laws of indices and logarithms  
  • correctly sketching exponential and logarithmic functions  
  • accurately converting logarithms from one base to another  
  • drawing curves of best fit for given sets of data  
  • accurately interpolating data from plotted data and/or drawn curves  
  • solving problems involving growth and decay  
  • accurately sketching trigonometric functions  
  • simplifying trigonometric expressions using trigonometric identities  
  • correctly solving trigonometric equations  
  • selecting an appropriate number system  
  • developing an appropriate program for the engineering situation
  • running a program to achieve an appropriate solution
Knowledge
  • the laws of indices and logarithms  
  • the procedures for simplifying arithmetic and algebraic expressions  
  • the procedures for sketching exponential and logarithmic functions  
  • the effects on the curve due to variation in size of constants  
  • the procedures for converting logarithms between bases  
  • the procedures for drawing curves of best fit and interpolating results  
  • the procedures for estimating constants in suggested relationships  
  • the concept of growth and decay  
  • the procedures for solving problems involving growth and decay  
  • the significance of amplitude, period and phase angle  
  • the procedures for sketching trigonometric functions  
  • the trigonometric identities  
  • the procedures for using trigonometric identities to simplify trigonometric expressions  
  • matching of engineering situations to appropriate number systems  
  • use of number systems for particular applications  
  • identification and description of engineering situations appropriate for analysis using simple programming techniques
  • procedure for using programs to analyse engineering situation and the identification of program limitations

Delivery Plan 


1.Exponential/logarithmic functions/equations

 

  • simplification
      • laws of indices/logarithms
  • graphs of functions
  • logarithmic base conversion
  • curves of best fit
      • interpolate data
      • estimate constants
  • growth and decay

2. Trigonometric functions/equations

  • sketching graphs
  • simplification of expressions
  • solution of equations

3. Basic computer numerical methods

  • appropriate number systems
      • decimal
      • binary
      • hexadecimal
  • techniques
      • products
      • sums
      • divisions
      • subtraction
  • equations
      • linear
      • quadratic
      • logarithmic
      • trigonometric
  • vector analysis

4. Complex figures

  • sketch
      • intersections
      • pattern developments
  • mathematical
      • models v. computer graphics