# Course Title: Use mathematics for higher level engineering

## Part B: Course Detail

Teaching Period: Term2 2011

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

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: Antiderivatives or (indefinite integrals) are used to relate density, mass and moment. 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: Define and evaluate rate of change 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 2.6 The transpose, inverse and determinant of a matrix up to 3×3 is determined and interpreted. 2.7 Matrices are solved using parameters. 2.8 A software application package is used to solve and interpret linear systems. Element: Exponential and Logarithmic functions are integrated 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: Functions are graphed using the first and second derivative. 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: Functions are integrated using the properties of The Fundamental Theorem of Calculus 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: Graph simple functions 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: Hyperbolic and Inverse Hyperbolic Functions are differentiated and integrated 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: Inverse Trigonometric Functions are integrated 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: Systems of linear equations are used to solve Engineering mathematics problems 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: The definite integral is applied to Engineering mathematics problems 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: The derivative of a function is used to calculate rates of change 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: The derivatives of the six trigonometric functions are examined 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: The maximum or minimum of functions in engineering situations is determined. 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 participate in individual and team problem solving activities related to typical engineering workplace problems. These activities involve class participation (discussions and oral presentations), prescribed exercises, homework, tutorials, application of theory to engineering problems and completion of calculations to industry standard, computer software application work in laboratory sessions (MATLAB, depending on availability of computer lab), tests and examination.

Teaching Schedule

This is an indicative teaching schedule. Refer to Online Blackboard announcements for changes.
Week 2 - Lecture: matrices, determinants, (implicit, higher derivatives, all other differentiation)
Week 3 - Consultation: matrices, determinants, implicit, higher derivatives, all other differentiatiion
Week 4 - Consultation: matrices, determinants, implicit, higher derivatives, all other differentiatiion
Week 5 - Oral Assessment and assignment 1 due First Group
Week 6 - Oral Assessment and assignment 1 due Second Group
Week 7 - Oral Assessment and assignment 1 due Third Group
Week 8 - Oral Assessment and assignment 1 due Fourth Group
Week 9 - Lecture: centroids & moments of inertia
Week 10 Lecture: differentiation & integration of inverse functions
Week 11 Consultation: applications, inverse functions, graphing
Week 12 – Consultation: applications, inverse functions, graphing
Week 13 - Oral Assessment and assignment 2 due Third Group
Week 14 Oral Assessment and assignment 2 due Fourth Group
Week 15 - Oral Assessment and assignment 2 due First Group
Week 16 - Oral Assessment and assignment 2 due Second Group
Week 17 - Deferred Assessments
Week 18 - Finalising Results

This is an indicative teaching schedule. Refer to Online Blackboard announcements for changes.

Learning Resources

Prescribed Texts

References

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

Other Resources

1. Hibbeler R. C., Engineering Mechanics: Statics, 11th Ed., 2007.
2. Fitzgerald G. F, Tables, RMIT Notes in Mathematics, 1995.
3. Thomas, G, & Finney, R Calculus and Analytical Geometry, 7th Ed., Addison – Wesley.
4. An Introduction to Applied Numerical Analysis, PSW – Kent, 1992.

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

To be deemed competent students must demonstrate an understanding of all elements of a competency.
Students are advised that they are likely to be asked to personally demonstrate their assessment work to their teacher to ensure that the relevant competency standards are being met. Students will be provided with feedback throughout the course to check their progress.

Assessment details:
Assessment 1 – This is a combination of assignment and oral assessment, to cover content so far. This will focus on the students’ ability to solve problems and provide logical solutions to practical exercises. This assessment will have a weighting of approximately 50% of the final overall assessment mark.

General topics covered are: matrix algebra, differentiation of functions including implicit differentiation and higher derivatives.

Assessment 2 – This is a combination of assignment and oral assessment, to cover content so far. This will focus on the students’ ability to solve problems and provide logical solutions to practical exercises. This assessment will have a weighting of approximately 50% of the final overall assessment mark.

General topics covered are: applications, differentiation/integration of inverse functions and graphing.

Note: Students will not be entitled to any supplementary work. All assessments need to be passed.

Assessment Matrix

Other Information

The underpinning knowledge and skills for this course are listed in the accreditation document and are available upon request from your instructor.

Course Overview: Access Course Overview