TAFE Diploma in Engineering
Advance Engineering Mathematics B
Purpose:
This subject together with Advance Engineering Mathematics B, will familiarise the
student with the essential techniques and develop competency in their application to
enable them to proceed with the second year of study in degree programs in Engineering.
Nominal Duration:
This subject would consist of approximately 40 hours of instruction depending on the
Mathematics background of the student. Some students may complete the necessary units in
less time.
Pre-requisites and Co-requisites:
Students must have successfully completed either Engineering Computations 2A and 2B or
Mathematics 1E or their equivalent. Students who have further studies in Mathematics
should be able to accelerate through the subject.
Students should be studying Advance Engineering Mathematics A and Advance Engineering
Mathematics B at the same time.
Resources:
Students should have access to an IBM compatible computer with at least 512K memory and
a CGA, EGA or Hercules card or equivalent.
Learning Outcomes:
On satisfactory completion of this subject with student will be able to:
(G) Use integration techniques to solve problems involving areas, volumes arc length,
surface area, mean and RMS values centre of mass and first moments of inertia and kinetic
energy, fluid pressure.
(H) Express complex numbers in cartesian, polar exponential and logarithmic form and
use the theory of complex numbers in application to mesh current network analysis.
(I) Apply the theory of first and second order linear differential equations to solve
problems involving resisted gravitational motion, simple harmonic motion and vibratory
motion.
(J) Describe data in terms of measure of central tendency and measure of dispersion and
represent the data graphically
(K) Represent problems in terms of systems of equations, and solve them, using matrices
and determinants and making use of appropriate computer software. The variety of methods
including Cramer’s Rule, the Adjoint/determinant method, Gaussian Elimination, Jordan
Elimination and Iterative methods.
Contents:
Units:
- Integral Calculus
- Complex Numbers
- Differential Equations
- Statistics
- Linear Algebra
PerformanceCriteria:
It should be kept in mind that this subject together with Advance Engineering
Mathematics B is designed to enable students to successfully proceed to the second year of
a degree program. The subjects are not intended to completely replace the first year in
Engineering. Students should be assessed as being proficient with the given technique.
Each unit within the subjects could be assessed separately using tests and assignments,
however, some units could be assessed together.
There will be no final examination in this subject, but the students must have achieved
the required performance in each of the learning outcomes.
Learning Outcome (G)
Assessment: A test consisting of 14 questions
Performance: The student must obtain a minimum of 50% on the test
Learning Outcome (H)
Assessment: A test consisting of 7 questions
Performance: The student must obtain a minimum of 60% on the test
Learning Outcome (I)
Assessment: A test consisting of 8 questions
Performance: The student must obtain a minimum of 50% on the test
Learning Outcome (J)
Assessment: An assignment consisting of 4 questions
Performance: The student must obtain a minimum of 80% on the assignment.
Learning Outcome (K)
Assessment: A test consisting of 3 questions
Performance: The student must obtain a minimum of 60% on the test.
Samples tests are provided for each unit in the set of unit notes developed by
Swinburne College of TAFE Industrial Science Department.
Appendix:
Units developed for bridging TAFE Associate Diploma (Engineering) students to second
year degree programs.
Unit:
- Integral Calculus
Revision – Integration Techniques, Areas, Volumes.
Partial Fractions
Integration by Parts
Trig and Hyperbolic substitution
Improper Integral
Integration of Partial Derivatives
Arc Length
Surface Area
Mean and RMS Values
Approximate Integration – The Trapezoidal Rule, Simpson’s Rule
Centre of Mass
Centroid of a Plane Region
Moments of Inertia and Kinetic Energy
Fluid Pressure
- Complex Numbers
Introduction to Complex Numbers: Cartesian Forms
the Argand Plane
Trigonometric and Polar Form
Subsets of the Theorem
De Moivre’s Theorem
Exponential Form of Complex Numbers
Application to Mesh Current Network Analysis
- Differential Equations
Definitions of a Differential Equation
First Order D E’s – Separation of Variable, Applications
Second Order D E’s of the form d2y/dx2 = f ( x )
Motions:
Kinematics
Resisted Gravitational Motion
Simple Harmonic Motion
First Order D E’s of the form dy/dx + Py = Q
Second Order D E’s of the form: a d2y/dx2 + b dy/dx + c y = 0
Second Order D E’s of the form: a d2y/dx2 + b dy/dx + c y + f ( x )
Vibratory Motion
- Statistics
Discrete and Continuous Data
Presentation of Data: Frequency Distribution Tables
Histograms
Ogives
Measures of Central Tendency: Arithmetic Mean
Median
Mode
Measures of Dispersion Standard Deviation
Range
Interquartile Range
- Linear Algebra
Matrix Algebra Basic Operations
Applications
Transformations
Determinant
