# Course Title: Use mathematics for higher level engineering

## Part B: Course Detail

Teaching Period: Term2 2010

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: 8.0 The mass of a beam is determined using integration 8.1 The moment of a blade is determined though integration. 8.2 Bounded area is calculated using upper and lower Riemann Sum Element: Define and evaluate rate of change Performance Criteria: 3.0 Functions are examined for various limits 3.1 The derivative is defined from first principles 3.2 Non differentiable functions are examined Element: Exponential and Logarithmic functions are integrated Performance Criteria: 11.0 An inverse function is defined. 11.1 The properties of exponential and logarithmic functions are examined. 11.2 The function is derived and integrated 11.3 The function ln x is derived and integrated 11.4 Exponential and logarithmic functions are graphed using a computer application package 11.5 Growth and decay rates are calculated Element: Functions are graphed using the first and second derivative. Performance Criteria: 6.0 Critical values are used to define stationary and inflection points. 6.1 The angle of intersection between two curves is found using differentiation 6.2 A computer application package is used to graph functions Element: Functions are integrated using the properties of The Fundamental Theorem of Calculus Performance Criteria: 9.0 Definite integrals are derived and calculated. 9.1 Functions are integrated using the Second Fundamental Theorem of Calculus. 9.2 Functions are integrated using substitution 9.3 A Computer application package is used to calculate definite integrals Element: Graph simple functions Performance Criteria: 1.0 Numbers are identified as R 1.1 Absolute value is defined 1.2 Domain and range of functions are determined 1.3 Graphs of absolute value, quadratic and composite functions are drawn Element: Hyperbolic and Inverse Hyperbolic Functions are differentiated and integrated Performance Criteria: 13.0 Cosh x, sinh x, tanh x are defined. 13.1 The derivative of sinhx, coshx and tanhx are defined. 13.2 Engineering mathematics problems are solved using the derivative of Hyperbolic functions. 13.3 Inverse hyperbolic functions are differentiated and integrated Element: Inverse Trigonometric Functions are integrated Performance Criteria: 12.0 Inverse trigonometric functions are defined 12.1 The derivative of inverse trigonometric functions is determined. 12.2 The definite integral of inverse trigonometric functions is determined 12.3 Inverse trigonometric functions are graphed using a computer software application package. Element: Systems of linear equations are used to solve Engineering mathematics problems Performance Criteria: 2.0 Linear equations are represented as a matrix 2.1 Elementary row operations are applied to a matrix 2.2 Gaussian elimination is used to solve an augmented matrix 2.3 The solutions of a matrix are interpreted, 2.4 The transpose, inverse and determinant of a matrix up to 33 is determined and interpreted. 2.5 Matrices are solved using parameters 2.6 A software application package is used to solve and interpret linear systems. Element: The definite integral is applied to Engineering mathematics problems Performance Criteria: 10.0 The area between two curves is calculated 10.1 The volume of an ellipsoid is calculated 10.2 The length of an arc is calculated 10.3 Work done is calculated 10.4 Centre of mass and the first moment is calculated 10.5 Centroid of a plane region is calculated Element: The derivative of a function is used to calculate rates of change Performance Criteria: 4.0 Units are substituted into functions to calculate the rate of change 4.1The product, quotient and chain rule are used to find the derivative of a function Element: The derivatives of the six trigonometric functions are examined Performance Criteria: 5.0 Sinusoidal functions are graphed and interpreted. 5.1 First derivatives of sin, cos and tan are proved from first principles. 5.2 Implicit functions are derived. 5.3 Trigonometric functions are subject to second order differentiation 5.4 A computer application package is used to graph Trigonometric functions. Element: The maximum or minimum of functions in engineering situations is determined. Performance Criteria: 7.0 Relationships between functions are examined through related rates of change. 7.1 Maxima and minima problems are solved using related rates of change. 7.2 The mean value theorem is applied to differentiation

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

See Online Learning Hub for details.

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 written test (closed book) to cover content so far. This will focus on the students’ ability to solve problems and provide logical solutions to practical exercises. This test will have a weighting of approximately 45% of the final overall assessment mark.
Assessment 2 – This is a practical test (closed book) to cover content so far. This will focus on the students’ ability to solve problems and provide logical solutions to practical MATLAB exercises. This test will have a weighting of approximately 10% of the final overall assessment mark.
Assessment 3 – This is a collection of quizzes (closed book) to cover content so far. This will focus on the students’ ability to solve problems and provide logical solutions to practical exercises. This test will have a weighting of approximately 45% (altogether) of the final overall assessment mark.

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