TAFE Diploma in Engineering
Advance Engineering Mathematics A
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 Advanced Engineering Mathematics A and Advance Engineering
Mathematics B as 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.
References:
Set of Unit Notes developed by Swinburne College of TAFE Industrial Science Department.
The following texts have been recommended for further reference:
Berkey D.D. Calculus - Saunders
Bird J.O and May A.J.C Checkbook Series (Books 1, 2, 3 and 4): Butterworths
Bird J.O and May A.J.C: Statistics for Technicians: Longman
Fitzpatrick J.B. Galbraith P & Henry B: Change and Approximation
Heinemann Senior Mathematics
Fitzpatrick J.B Galbraith P & Henry B: Space and Number
Heinemann Senior Mathematics
Grossman S: Calculus: Academic Press
Hunt R.A: Calculus with Analytic Geometry: Harper & Row
Kuhfittig Peter: Basic Technical Mathematics with Calculus: Brooks / Cole
Munem M & Foulis D: Calculus with Analytic Geometry - Worth
Porter S & Ernst J:Basic Technical Mathematics with Calculus: Addison Wesley
Smith Karl: Finite Mathematics -Glenview
Stewart James: Calculus-Brooks / Cole & Nelson
Stroud: Engineering Mathematics -MacMillan
Thomas G & Finny R: Calculus with Analytic Geometry - Addison Wesley
Learning Outcomes:
On satisfactory completion of this subject, the student will be able to:
- Simplify expressions and solve simple problems involving hyperbolic and inverse
- Hyperbolic functions, sing identities, graphical techniques and /or a calculator.
- Use a Taylor polyonomial to express a given function in terms of a linear or quadratic
approximation at a given point, and determine the accuracy of the approximation.
- Use a Maclaurin series for a function to approximate the value of an integral.
- Express position vectors in i. J. k. representation and determine such applications as
magnitudes or vectors, differentiation and integration of vectors and applications,
resolution of vectors, differentiation and integration of vectors and applications.
- Use the techniques above in applications in dynamics, including Newton’s Laws,
works and energy.
- Apply vector techniques to describe geometric representations of lines and planes in 3
dimensions.
- Represent data in graphical form, using appropriate graph paper, and use graphs to
determine constants and variables. Graphs to include exponential growth and decay:
- Logarithmic scales, method of least squares and poplar graphs.
- Identify and sketch the graphs of a function of two variables.
- Identify and determine the equation of some standard quadric surfaces.
- Use differentiation techniques, including partial, implicit and logarithmic
differentiation to solve problems in curve sketching, optimisation, rates of change and
small increments.
- Use directional derivatives to solve problems in optimization.
Contents:
Unit (a) Exponential, Trigonometric and Hyperbolic Functions
- Series
- Vectors
- Analytical Geometry
- Graphing Techniques
- Differential Calculus
Performance Criteria:
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
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 subject 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 (A)
Assessment: An assignment consisting of 10 questions
Performance: The student must obtain a minimum of 80% on this assignment.
Learning Outcome (B)
Assessment: A test consisting of 3 questions
Performance: The student must obtain as minimum of 60% on the test.
Learning Outcome (C)
Assessment: A test consisting of approximately 10 questions.
Performance: The student must obtain a minimum of 60% on the test
Learning Outcome (D)
Assessment: A test consisting of 5 questions.
Performance: The student must obtain a minimum of 50% on the test.
Learning Outcome (E)
Assessment: A test consisting of 6 questions.
Performance: The student must obtain a minimum of 50% on the test.
Learning Outcome (F)
Assessment: A test consisting of 7 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.
Units:
- Exponential, Trigonometric and Hyperbolic, Functions
Revision – Functionally, Inverse Functions, Exponential and Logarithmic Functions,
Inverse Trigonometric Functions.
- Series
Revision – Progress
Limits
Linear and Quadratic Approximations. Taylors Polynomials
Partial Sums
Geometric Series
Power Series
Maclaurin Series
- Vectors
Vectors in 3 Dimensions
i j k Notation
Scalar Product
Vector Product
Resolution of Vectors
Differentiation and Integration of Vectors
Dynamics - Newton’s Law
Engery
The Work – Energy Theorem
Potential Energy
- Analytical Geometry
Equation of a Plane
The Angle between two Planes
The Distance from a Point to a Plane
Lines in 3 –Dimensional Space
- Graphing Techniques
Co-Ordinate Geometry
Graphs of Exponential Growth and Decay
Graphs with Logarithmic Scales
Method of Least Squares
Polar Co-ordinates and Polar Graphs
Graphs of Functions of Two Variables
Quadric Surfaces
- Differential Calculus
Introduction – Review of Standard Derivatives and Rules
Higher Order Derivatives
Graph Sketching
Maxima and Minima
Rates of Change
Small Increments
Implicit Differentiation
Logarithmic Differentiation
Directional Derivatives
