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)
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 1 Download/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 2 Domain and range of functions are determined. Graphs of absolute value, quadratic and composite functions are drawn 1.3, 1.4 3 Linear Algebra: Linear equations are represented as a matrix. Matrix Algebra Definition and Matrix Algebra Elementary row operations 2.1,2.2,2.3 4 Matrix Algebra The Transpose, the Inverse of a matrix 2.4,2.5,2.6 5 Matrix Algebra The Inverse of a matrix 2.5, 2.6,2.7 6 Determinants of a matrix Application of matrix algebra to solving linear systems. 2.1,2.2,2.3,2.4,2.5 7 Solutions of linear equations Application of matrix algebra to real life problems. Engineering Applications 2.3,2.4,2.5,2.6,2.7 8 Practice 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 9 Closed 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 10 Functions of multiple Variables Graphs, level curves and surfaces 3.1,3.2,3.3,3.4 4.1,4.2,4.3,4.4 11 Partial derivatives, product rule, Quotient rule 5.1,5.2,5.3,5.4,5.5 12 Partial derivatives, chain rule; directional derivative Maxima and minima 6.1,6.2,6.3 7.1,7.2,7.3 13 Application of partial derivatives Define and evaluate rate of change 8.1,8.2,8.3 9.1,9.2,9.3,9.4 14 The 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 15 Applications 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 16 Practice 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 17 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 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

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

Assessment Matrix

 EAX095B Elements & Performance Criteria Assessments 1.1 1.2 1.3 1.4 2.1 2.2 2.3 2.4 2.5 2.6 2.7 Assignment x x x x x x x x x x x Test x x x x x x x x x x x Exam

 EAX095B Elements & Performance Criteria Assessments 3.1 3.2 3.3 4.1 4.2 5.1 5.2 5.3 5.4 5.5 6.1 6.2 6.3 7.1 7.2 7.3 Assignment x x x x x x x x x x x x x x x x Test Exam x x x x x x x x x x x x x x x x

 EAX095B Elements & Performance Criteria Assessments 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 Assignment x x x x x x x x x x x x x x x x x x Test Exam x x x x x x x x x x x x x x x x x x

 EAX095B Elements & Performance Criteria Assessments 11.5 11.6 12.1 12.2 12.3 12.4 13.1 13.2 13.3 13.4 Assignment x x x x x x x x x x Test Exam x x x x x x x x x x

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