Course Title: Use mathematics for higher level engineering

Part B: Course Detail

Teaching Period: Term1 2014

Course Code: CIVE5699

Course Title: Use mathematics for higher level engineering

School: 130T Vocational Engineering

Campus: City Campus

Program: C6093 - Advanced Diploma of Engineering Design

Course Contact: Program Manager

Course Contact Phone: +61 3 9925 4468

Course Contact Email: engineering-tafe@rmit.edu.au


Name and Contact Details of All Other Relevant Staff

Dr Elmas Aliu
+61 3 9925 4360
elmas.aliu@rmit.edu.au
 

Nominal Hours: 60

Regardless of the mode of delivery, represent a guide to the relative teaching time and student effort required to successfully achieve a particular competency/module. This may include not only scheduled classes or workplace visits but also the amount of effort required to undertake, evaluate and complete all assessment requirements, including any non-classroom activities.

Pre-requisites and Co-requisites

EDX130B Use technical mathematics (basic)
EDX140B Use technical mathematics (advanced)
EAX110B Use calculus

Course Description

This unit covers the competency to differentiate and integrate nth degree polynomials, exponential and logarithmic functions, trigonometric and inverse trigonometric functions and hyperbolic and inverse hyperbolic functions.
This unit also covers the skills and knowledge required in solving engineering mathematics problems by using differentiation, integration and systems of linear equations in conjunction with the deployment of a suitable software application package. This unit also covers the competencies achieved in first semester Engineering athematics at university.


National Codes, Titles, Elements and Performance Criteria

National Element Code & Title:

EAX095B Use mathematics for higher level engineering

Element:

01. Graph simple functions

Performance Criteria:

1.1 Numbers are identified as ∈R
1.2 Absolute value is defined.
1.3 Domain and range of functions are determined.
1.4 Graphs of absolute value, quadratic and composite functions are
drawn
 

Element:

02. Use systems of linear equations to solve Engineering mathematics problems.

Performance Criteria:

2.1 Linear equations are represented as a matrix.
2.2 Elementary row operations are applied to a matrix.
2.3 Gaussian elimination is used to solve an augmented matrix.
2.4 The solutions of a matrix are interpreted.2.5
2.5 The transpose, inverse and determinant of a matrix up to 3×3 is
determined and interpreted.
2.6 Matrices are solved using parameters.
2.7 A software application package is used to solve and interpret
linear systems.
 

Element:

03. Define and evaluate rate of change.

Performance Criteria:

3.1 Functions are examined for various limits.
3.2 The derivative is defined from first principles.
3.3 Non differentiable functions are examined.
 

Element:

04. Use the derivative of a function to calculate rates of change.

Performance Criteria:

4.1 Units are substituted into functions to calculate the rate of
change.
4.2 The product, quotient and chain rule are used to find the
derivative of a function
 

Element:

05. Examine the derivatives of the six trigonometric functions.

Performance Criteria:

5.1 Sinusoidal functions are graphed and interpreted.
5.2 First derivatives of sin, cos and tan are proved from first
principles
5.3 Implicit functions are derived.
5.4 Trigonometric functions are subject to second order
differentiation.
5.5 A computer application package is used to graph Trigonometric
functions.
 

Element:

06. Graph functions using the first and second derivative.

Performance Criteria:

6.1 Critical values are used to define stationary and inflection points.
6.2 The angle of intersection between two curves is found using
differentiation
6.3 A computer application package is used to graph functions.
 

Element:

07. Determine the maximum or minimum of functions in engineering situations.

Performance Criteria:

7.1 Relationships between functions are examined through related
rates of change.
7.2 Maxima and minima problems are solved using related rates of
change.
7.3 The mean value theorem is applied to differentiation
 

Element:

08. Relate density, mass and moment using antiderivatives or indefinite integrals.

Performance Criteria:

8.1 The mass of a beam is determined using integration
8.2 The moment of a blade is determined though integration.
8.3 Bounded area is calculated using upper and lower Riemann
Sum.
 

Element:

09. Integrate functions using the properties of The Fundamental Theorem of Calculus.

Performance Criteria:

9.1 Definite integrals are derived and calculated.
9.2 Functions are integrated using the Second Fundamental
Theorem of Calculus.
9.3 Functions are integrated using substitution.
9.4 A Computer application package is used to calculate definite
integrals.
 

Element:

10. Apply the definite integral to engineering calculations.

Performance Criteria:

10.1 The area between two curves is calculated.
10.2 The volume of an ellipsoid is calculated.
10.4 The length of an arc is calculated.
10.5 Work done is calculated.
10.6 Centre of mass and the first moment is calculated.
10.7 Centroid of a plane region is calculated.
 

Element:

11. Integrate exponential and Logarithmic functions.

Performance Criteria:

11.1 An inverse function is defined.
11.2 The properties of exponential and logarithmic functions are
examined.
11.3 The function ex is derived and integrated.
11.4 The function lnx is derived and integrated.
11.5 Exponential and logarithmic functions are graphed using a
computer application package.
11.6 Growth and decay rates are calculated.
 

Element:

12. Integrate inverse Trigonometric Functions.

Performance Criteria:

12.1 Inverse trigonometric functions are defined.
12.2 The derivative of inverse trigonometric functions is determined.
12.3 The definite integral of inverse trigonometric functions is
determined.
12.4 Inverse trigonometric functions are graphed using a computer
software application package.
 

Element:

13. Differentiate and integrate Hyperbolic and Inverse Hyperbolic Functions.

Performance Criteria:

13.1 Coshx, sinhx, tanhx are defined.
13.2 The derivative of sinhx, coshx and tanhx are defined.
13.3 Engineering mathematics problems are solved using the
derivative of Hyperbolic functions.
13.4 Inverse hyperbolic functions are differentiated and integrated.
 


Learning Outcomes


. Refer to elements


Details of Learning Activities

You will involve in the following learning activities to meet requirements for this course


Teaching Schedule

Week Topic Delivered                                                                                                                                        Elements / Performance Criteria
1Download/Explain course including assessments and policies/Revision of Pre Requisite course
Real Numbers are defined and identified Basic concepts
The Absolute value
Assignment (part A) handed out (worth 5% of total mark) due date end of week 4.
 
1.1,1.2
2Domain and range of functions are determined.
Graphs of absolute value, quadratic and composite functions are drawn
1.3, 1.4
3Linear Algebra:
Linear equations are represented as a matrix.
Matrix Algebra
Definition and Matrix Algebra
Elementary row operations
2.1,2.2,2.3
4Matrix Algebra
The Transpose, the Inverse of a matrix
2.4,2.5,2.6
5Matrix Algebra
The Inverse of a matrix
 2.5, 2.6,2.7
6Determinants of a matrix
Application of matrix algebra to solving linear systems.

2.1,2.2,2.3,2.4,2.5

7Solutions of linear equations
Application of matrix algebra to real life problems. Engineering Applications

2.3,2.4,2.5,2.6,2.7
 

8Practice Test and revision

1.1,1.2,1.3,1.4
2.1,2.2,2.3,2.4,2.5,2.6,2.7

9Closed book Test 
(worth 30% of total mark)

1.1,1.2,1.3,1.4
2.1,2.2,2.3,2.4,2.5,2.6,2.7 

10Functions of multiple Variables
Graphs, level curves and surfaces
3.1,3.2,3.3,3.4
4.1,4.2,4.3,4.4
11Partial derivatives, product rule, Quotient rule5.1,5.2,5.3,5.4,5.5
12Partial derivatives, chain rule; directional derivative
Maxima and minima
6.1,6.2,6.3
7.1,7.2,7.3
13Application of partial derivatives
Define and evaluate rate of change
8.1,8.2,8.3
9.1,9.2,9.3,9.4
14The Exponential and Logarithmic functions
Differentiation and integration of Exponential and Logarithmic functions
Hyperbolic Functions
Inverse Hyperbolic Functions

10.1,10.2,10.3,10.4,10.5,10.6,10.7

11.1,11.2,11.3,11.4,11.5,11.6
 

15Applications of Exponential, Logarithmic, Hyperbolic and Invers Hyperbolic functions into engineering problems
Revision
12.1,12.2,12.3,12.4
13.1,13.2,13.3,13.4
16Practice Exam and revision

3.1,3.2,3.3,3.4
4.1,4.2,4.3,4.4
5.1,5.2,5.3,5.4,5.5
6.1,6.2,6.3
7.1,7.2,7.3
8.1,8.2,8.3
9.1,9.2,9.3,9.4
10.1,10.2,10.3,10.4,10.5,10.6,10.7
11.1,11.2,11.3,11.4,11.5,11.6
12.1,12.2,12.3,12.4
13.1,13.2,13.3,13.4

17Closed book Exam
(worth 50% of total mark)
 (week 17 or 18)
3.1,3.2,3.3,3.4
4.1,4.2,4.3,4.4
5.1,5.2,5.3,5.4,5.5
6.1,6.2,6.3
7.1,7.2,7.3
8.1,8.2,8.3
9.1,9.2,9.3,9.4
10.1,10.2,10.3,10.4,10.5,10.6,10.7
11.1,11.2,11.3,11.4,11.5,11.6
12.1,12.2,12.3,12.4
13.1,13.2,13.3,13.4
18 Closed book Exam
(worth 50% of total mark)
(week 17 or 18)
 3.1,3.2,3.3,3.4
4.1,4.2,4.3,4.4
5.1,5.2,5.3,5.4,5.5
6.1,6.2,6.3
7.1,7.2,7.3
8.1,8.2,8.3
9.1,9.2,9.3,9.4
10.1,10.2,10.3,10.4,10.5,10.6,10.7
11.1,11.2,11.3,11.4,11.5,11.6
12.1,12.2,12.3,12.4
13.1,13.2,13.3,13.4


Learning Resources

Prescribed Texts

Fitzgerald G. F, Peckham I.A, Mathematical Methods for Engineers and Scientists, fourth edition, 2005, Pearson Education Australia

1-74009-733-5


References


Other Resources


Overview of Assessment

Assessment are conducted in both theoretical and practical aspects of the course according to the performance criteria set out in the National Training Package. Students are required to undertake summative assessments that bring together knowledge and skills.

To successfully complete this course you will be required to demonstrate competency in each assessment tasks detailed under the Assessment Task Section.


Your assessment for this course will be marked using the following table

NYC (<50%)
Not Yet Competent

CAG (50-59%)
Competent - Pass

CC (60-69%)
Competent - Credit

CDI (70-79%)
Competent - Distinction

CHD (80-100%)
Competent - High Distinction


Assessment Tasks

• Assignment, 20%
• Test, 30%
• Exam , 50%
 


Assessment Matrix

 

 EAX095B Elements & Performance Criteria
Assessments1.11.21.31.42.12.22.32.42.52.62.7
Assignmentxxxxxxxxxxx
Testxxxxxxxxxxx
Exam            

 

 EAX095B Elements & Performance Criteria
Assessments3.13.23.34.14.25.15.25.35.45.56.16.26.37.17.27.3
Assignmentxxxxxxxxxxxxxxxx
Test                
Exam xxxxxxxxxxxxxxxx

 

 

 EAX095B Elements & Performance Criteria
Assessments 8.18.28.39.19.29.39.410.110.210.310.410.510.610.711.111.211.311.4
Assignmentxxxxxxxxxxxxxxxxxx
Test                  
Exam xxxxxxxxxxxxxxxxxx

 

 EAX095B Elements & Performance Criteria
Assessments11.511.612.112.212.312.413.113.213.313.4
Assignmentxxxxxxxxxx
Test          
Exam xxxxxxxxxx

Other Information

• Student directed hours involve completing activities such as reading online resources, assignment, individual student-teacher course-related consultation. Students are required to self-study the learning materials and complete the assigned out of class activities for the scheduled non-teaching hours. The estimated time is 12 hours outside the class time.

Course Overview: Access Course Overview