UNIT CODE

DCSMTH610

UNIT TITLE

Use mathematics in engineering

APPLICATION

This unit covers concepts of mathematics appropriate to engineering situations.

The unit of competency is applied by technicians and drafting personnel working in a civil and structural engineering environment to solve problems.

No licensing, legislative, regulatory or certification requirements apply to this unit at the time of publication.

ELEMENT

Elements describe the essential outcomes.

PERFORMANCE CRITERIA

Performance criteria describe the performance needed to demonstrate achievement of the element.

1.    Use exponential functions and their graphs.

1.1.      Simplify algebraic expressions containing indices using the index laws.

1.2.      Transpose formulae involving indices.

1.3.      Solve simple exponential equations using the index laws and without using logarithms.

1.4.      Draw and interpret graphs of exponential functions.

2.    Use logarithmic equations and their graphs in problem solving.

2.1.      Interpret the meaning of a logarithm as an exponent.

2.2.      Evaluate logarithms using a calculator.

2.3.      Simplify expressions using the laws of logarithms.

2.4.      Solve exponential equations using logarithms.

2.5.      Transpose formulae involving the exponential or logarithmic function.

2.6.      Draw the graph of the logarithmic function.

2.7.      Transpose exponential and power equations into logarithmic form so they can be plotted as linear graphs.

2.8.       Use a calculator to determine the least squares regression line equations for data related by either an exponential or power law.

2.9.       Solve problems involving exponential growth and decay, graphically and analytically.

3.    Solve problems involving trigonometry.

3.1.      Define sin θ, cos θ and tan θ in terms of the unit circle.

3.2.      Define the reciprocal trigonometric ratios cosecant, secant and cotangent in terms of sine, cosine and tangent respectively.

3.3.      Express angles as fractions and multiples of θ.

3.4.      Convert radians to degrees and degrees to radians using a calculator.

3.5.      Determine the values of the six trigonometric functions for any angle given in degrees or radians.

3.6.      Determine from the trigonometric ratio the measure of any angle in either degrees or radians.

3.7.      Calculate angular displacement and angular velocity.

3.8.      Calculate the area of a sector using A = ¹/₂ r²θ (θ given in degrees or radians).

3.9.      Simplify trigonometric expressions and prove identities using the ratios sin, cos, tan, cosec, sec and cot.

3.10.    Simplify trigonometric expressions and prove identities using the Pythagorean identities:

                                   Sin²θ + Cos²θ =1

                                   Sec²θ = 1 + tan²θ 

                                   Cosec²θ = 1 + Cot²θ 

3.11.     Sketch the graphs of functions of the form:

              y = asin(bx+c) + d and y = acos(bx+c) + d

              where a,b,c,d are constants,

              by determining the amplitude, period, phase shift and vertical displacement.

3.12.     Solve graphically equations of the form:

              asinbx = c and acos(bx+c) = d

              where a, b, c, d are constants

3.13.      Solve algebraically, over a given domain, equations of the form:

              asinbx = c and acosbx = c

              where a, b, c, are constants.

3.14.      Solve oblique triangles using the sine rule and/or cosine rule.

3.15.      Solve applied problems requiring the use of the sine rule and/or cosine rule.

4.1.        Define a matrix and the give examples of its use.

4.2.        Explain the meaning of terms such as order of a matrix, square matrix, identity matrix, transpose of a matrix, etc.

4.3.        Add, subtract and multiply matrices, including multiplying a matrix by a scalar.

4.4.        Define and calculate the determinant of a 2 x 2 and 3 x 3 matrix.

4.5.        Obtain the inverse of a 2 x 2 and 3 x 3 matrix using the determinant.

4.6.        Solve a system of 3 linear equations in 3 unknowns using both the inverse matrix method, and determinants (Cramer’s Rule).

4.7.        Solve applied problems using matrices.

              functions using the limit definition of the derivative

5.2.        Differentiate elementary algebraic functions.

5.3.        Use the derivative to determine the slope and equation of the tangent line to a curve at a point on the curve.

5.4.        Differentiate algebraic functions using the product, quotient and chain rules.

5.5.        Integrate elementary algebraic functions.

5.6.        Evaluate definite integrals using the Fundamental Theorem of Calculus              

5.7.        Evaluate area under the curve for simple functions.

5.8.        Apply Simpson’s rule to approximate the area under a curve.

FOUNDATION SKILLS

Foundation skills essential to performance are explicit in the performance criteria of this unit of competency.

UNIT MAPPING INFORMATION

41979 Use mathematics in engineering is equivalent

TITLE

Assessment requirements for DCSMTH610 Use mathematics in engineering

PERFORMANCE EVIDENCE

To achieve competency in this unit a person must satisfy the requirements of the elements and performance criteria, foundation skills and range of conditions included in the unit.

The person must also:

• correctly solve written problems in mathematics
• collect and analyse data
• report and present data in an appropriate format

Note: If a specific volume or frequency is not stated, then evidence must be provided at least once for each criterion.

KNOWLEDGE EVIDENCE

To achieve competency in this unit, a person must demonstrate knowledge of:

• Key concepts in mathematics, including
  • 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 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 procedures for using trigonometric identities to simplify trigonometric expressions
  • the selection of the correct rule to solve oblique triangles
  • terminology relating to matrices
  • the procedures in carrying out matrix algebra
  • various ways of solving a system of simultaneous equations
  • simple differentiation and integration rules
  • function notation
  • the meaning of “gradient” and “area finding” function
  • the procedures relating to Simpson’s Rule

ASSESSMENT CONDITIONS

Assessment conditions:

All assessment must be completed in accordance with work health and safety standards.

When assessments are conducted remotely, invigilation software must be used to ensure authenticity of work completed.

Model answers or marking guides must be provided for all assessments to ensure reliability of assessment judgements when marking is undertaken by different assessors.

The candidate must have access to all tools, equipment, materials and documentation required.

Assessor Requirements:

Assessors must satisfy the assessor requirements in the standards for registered training organisation (RTOs) current at the time of assessment.

Assessors must also hold a tertiary qualification in engineering or related field.

Assessors must have worked for at least 3 years in industry where they have applied the skills and knowledge covered in this unit of competency.

The RTO must also ensure that trainers and assessors keep their industry knowledge up to date through ongoing professional development.

The RTO must take appropriate steps, as an ongoing procedure, to verify information about trainer and assessor’s qualifications, vocational competencies and current industry skills