# Course Title: Mathematics for university engineering

## Part B: Course Detail

Teaching Period: Term1 2008

Course Code: CIVE5625

Course Title: Mathematics for university engineering

School: 130T Infra, Electrotec & Build Serv

Campus: City Campus

Program: C6066 - Advanced Diploma of Civil Engineering (Structural Design)

Course Contact : Tony Skinner Program Coordinator

Course Contact Phone: (03) 9925 4444

Course Contact Email:tony.skinner@rmit.edu.au

Name and Contact Details of All Other Relevant Staff

Program Coordinator:
Mr Tony Skinner
Tel. 9925 4444
Fax. 99254377
Email: tony.skinner@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

EAX110 – Use calculus
EDX130 – Use mathematics at technician level
EDX140 – Use, quadratic, exponential, logarithmic and trigonometric functions and matrices

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 mathematics at university.

National Codes, Titles, Elements and Performance Criteria

 National Element Code & Title: EAX095 Mathematics for university engineering Element: Anti-derivatives or (indefinite integrals) are used to relate density, mass and moment Performance Criteria: 1.0The mass of a beam is determined using integration 1.1 The moment of a blade is determined though integration. 1.2 Bounded area is calculated using upper and lower Riemann Sum Element: Define and evaluate rate of change Performance Criteria: 2.0 Functions are examined for various limits 2.1 The derivative is defined from first principles 2.2 Non differentiable functions are examined Element: Exponential and Logarithmic functions are integrated Performance Criteria: 3.0An inverse function is defined. 3.1 The properties of exponential and logarithmic functions are examined. 3.2 The function is derived and integrated 3.3 The function lnx is derived and integrated 3.4 Exponential and logarithmic functions are graphed using a computer application package 3.5 Growth and decay rates are calculated Element: Functions are graphed using the first and second derivative Performance Criteria: 4.0 Critical values are used to define stationary and inflection points. 4.1 The angle of intersection between two curves is found using differentiation 4.2 A computer application package is used to graph functions Element: Functions are integrated using the properties of The Fundamental Theorem of Calculus Performance Criteria: 5.0Definite integrals are derived and calculated. 5.1 Functions are integrated using the Second Fundamental Theorem of Calculus. 5.2 Functions are integrated using substitution 5.3 A Computer application package is used to calculate definite integrals Element: Graph simple functions Performance Criteria: 6.0 Numbers are identified as R 6.1 Absolute value is defined 6.2 Domain and range of functions are determined 6.3 Graphs of absolute value, quadratic and composite functions are drawn Element: Hyperbolic and Inverse Hyperbolic Functions are differentiated and integrated Performance Criteria: 7.0Coshx, sinhx, tanhx are defined. 7.1 The derivative of sinhx, coshx and tanhx are defined. 7.2 Engineering mathematics problems are solved using the derivative of Hyperbolic functions. 7.3 Inverse hyperbolic functions are differentiated and integrated Element: Inverse Trigonometric Functions are integrated Performance Criteria: 8.0 Inverse trigonometric functions are defined 8.1 The derivative of inverse trigonometric functions is determined. 8.2 The definite integral of inverse trigonometric functions is determined 8.3 nverse trigonometric functions are graphed using a computer software application package. Element: Systems of linear equations are used to solve Engineering mathematics problems Performance Criteria: 9.0 Linear equations are represented as a matrix 9.1 Elementary row operations are applied to a matrix 9.2 Gaussian elimination is used to solve an augmented matrix 9.3 The solutions of a matrix are interpreted, 9.4 The transpose, inverse and determinant of a matrix up to 33 is determined and interpreted. 9.5 Matrices are solved using parameters 9.6 A software application package is used to solve and interpret linear systems. Element: The definite integral is applied to Engineering mathematics problems Performance Criteria: 10.0The 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: 11.0 Units are substituted into functions to calculate the rate of change 11.1 The 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: 12.0 Sinusoidal functions are graphed and interpreted. 12.1 First derivatives of sin, cos and tan are proved from first principles. 12.2 Implicit functions are derived. 12.3 Trigonometric functions are subject to second order differentiation 12.4 A computer application package is used to graph Trigonometric functions. Element: The maximum or minimum of functions in engineering situations is determined Performance Criteria: 13.0 Relationships between functions are examined through related rates of change. 13.1 Maxima and minima problems are solved using related rates of change. 13.2 The mean value theorem is applied to differentiation

Learning Outcomes

Anti-derivatives or (indefinite integrals) are used to relate density, mass and moment
Define and evaluate rate of change

Exponential and Logarithmic functions are integrated
Functions are graphed using the first and second derivative

Functions are integrated using the properties of The Fundamental Theorem of Calculus

Graph simple functions

Hyperbolic and Inverse Hyperbolic Functions are differentiated and integrated

Inverse Trigonometric Functions are integrated

Systems of linear equations are used to solve Engineering mathematics problems
The definite integral is applied to Engineering mathematics problems

The derivative of a function is used to calculate rates of change.

The derivatives of the six trigonometric functions are examined

The maximum or minimum of functions in engineering situations is determined

Details of Learning Activities

• Differentiate and integrate algebraic, trigonometric, exponential and logarithmic, and hyperbolic functions.
• Solve maxima and minima engineering problems using differentiation.
• Demonstrate with applications the density, mass, moment and area using integration.
• Apply the matrices theory in order to solve a system of linear equations.
Participate in individual and team problem solving calculation activities completed to industry standard related to typical engineering problems requiring:
• Graph simple functions by using the derivatives
• Applying the indefinite integrals to relate density, mass and moment.
• Using the definite integral to Engineering mathematics problems
• Solving integrals involving exponential and logarithmic equations
• Applying the integration to Hyperbolic and Inverse Hyperbolic Functions

Teaching Schedule

See Online Learning Hub for details.

Learning Resources

Prescribed Texts

 Fitzgerald G. F, Peckham I.A, Mathematical Methods for Engineers and Scientists, third edition, 2002, Pearson Education Australia

References

 1. Fitzgerald G. F, Tables, RMIT Notes in Mathematics, 1995. 2. Thomas, G, & Finney, R Calculus and Analytical Geometry, 7th Ed., Addison – Wesley. An Introduction to Applied Numerical Analysis, PSW – Kent, 1992.

Other Resources

Overview of Assessment

The assessment comprises a combination of Assignments and Tests.
The students are required to complete:
Written Assignment 1 10% of the total marks
Written Test 1 40% of the total marks
Written Assignment 2 10% of the total marks
Written Test 2 40% of the total marks

• Vector and Matrix algebra, determinants, and systems of linear equations are assessed with Assignment 1 and Test 1.
• Differential and Integral calculus (functions of multiple variables, the double integral) and its applications (the rate of change, the density, mass, moment and area using integration) are assessed with Assignment 2 and Test 2.