Course Title: Aerospace Mathematics 1

Part B: Course Detail

Teaching Period: Term1 2011

Course Code: MATH5156

Course Title: Aerospace Mathematics 1

School: 155T Vocational Health and Sciences

Campus: City Campus

Program: C6011 - Advanced Diploma of Engineering (Aerospace)

Course Contact: Nancy Varughese

Course Contact Phone: +61 3 9925 4713

Course Contact Email: nancy.varughese@rmit.edu.au

Name and Contact Details of All Other Relevant Staff

Brian Hayes

Building 51 Level 7 Room 05

Tel: +61 3 9925 4745

brihaye@rmit.edu.au

Tatjana Grozdanovski

Building 51 Level 5 Room 04

Tel: +61 3 9925 4689

Nominal Hours: 40

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

A pass in MEM30012A Apply mathematical techniques in manufacturing, engineering or related situations or
Year 11 mathematical methods 1 and 2, or equivalent

Course Description

This unit covers the selection and application of calculus techniques to resolve engineering problems. It includes finding derivatives from first principles, using rules of derivatives to find first and second derivatives of functions; applying integral calculus to functions; applying differential and integral calculus to engineering problems.

National Codes, Titles, Elements and Performance Criteria

 National Element Code & Title: VBH154 Aerospace Mathematics 1 Element: 1. Apply differentiation techniques to engineering applications. 2. Apply integration techniques to engineering applications.

Learning Outcomes

1. Apply differentiation techniques to engineering applications.

1. 1 Differentiate polynomial functions by first principles.
1.2. Differentiate polynomials, trigonometric, logarithmic and exponential functions using the rules of differentiation.
1.3  Use the chain, product and quotient rule of differentiation to all functions in 1.2 above.

1.4 Application of differentiation to solving engineering problems.

2. Apply integration techniques to engineering applications.

2.1 Integrate polynomials, trigonometric, and exponential functions using the rules of integration.
2.2 Evaluate definite integrals of functions above in 2.1, and find areas.

2.3  Application of ntegration techniques to solve engineering problems.

Details of Learning Activities

Learning activities include class exercises using mathematical techniques of differentiation and integration to solve engineering problems.

In addition to written tests and class exercises, the students are required to work on a project to solve engineering problems.

Teaching Schedule

This course involves the delivery of following key topics over 17 sessions (9-10 Weeks).

Session 1. Limits, differentiation by First Principles – Polynomial functions by first principle
Session 2 . Differentiation of functions by rule – First and second derivatives of Polynomials, trigonometric, exponential and logarithmic functions
Session 3. Chain rule, Product rule, Quotient rule Apply the 3 rules to all types of functions covered in session 2  (QUIZ 1 on limits, first principles and differentiation rule)
Session 4 . Parametric differentiation, Implicit differentiation Solve engineering problems using the principles of differentiation

Session 5. Use differential calculus to find stationary points, and maxima and minima application. Solve engineering problems using the principles of differentiation

Session 6 .Application of differentiation to rates of change, equations of tangents and normal and rectilinear motion Solve engineering problems using the principle of  differentiation  (QUIZ 2 applications of differentiation).

Session 7. Newton’s method for solving equations Solve engineering problems using the principles of differentiation
Session 8.  Revision
Session 9  Mid semester test (1 hr) Covering Element 1
Session 10. Integration - Find the indefinite integral of Polynomials, trigonometric and exponential functions (Hand out Project )
Session 11. Integration - Evaluate definite integral of Polynomials, trigonometric and exponential functions, and hence find the area .

Session 12.  Applications of Simpson’s rule Solve engineering problems using the principles of integration (QUIZ 3 on Simpsons rule and applications)
Session 13.  Area between 2 curves .Solve engineering problems using the principles of integration
Session 14.  Application of integration to distance travelled and rectilinear motion Solve engineering problems using the principles of integration (Project DUE).
Session 15.  Revision .Solve engineering problems using the principles of integration (QUIZ 4 applications of integration).

Session 16. Revision. Solve engineering problems using the principles of differentiation and integration.
Session 17.  Final exam (2 hrs) Covering Element 1 and 2

Learning Resources

Prescribed Texts

 There are no prescribed Textbooks. Class notes and references will be provided to students

References

 1.     G. F. Fitz-Gerald and I. A. Peckham, Mathematical Methods for Engineers and Scientists. 2.      K.A. Stroud, Engineering Mathematics fifth edition.

Other Resources

An approved Graphics Calculator

Overview of Assessment

Assessment may incorporate a variety of methods including written/oral activities and demonstration of mathematical problem solving skills to solve engineering problems. Participants are advised that they are likely to be asked to personally demonstrate their assessment activities to their teacher/assessor. Feedback will be provided throughout the course.

Participants are required to complete four types of assessment tasks. There are four quizzes worth 20% in total, one closed book test worth 20%, one project worth 20% and one closed book exam worth 40%.
Successful completion is achieved if the student attains at least 50% of total mark for each assessment task AND his/her accumulation of marks is NOT less than 50% of all the assessment tasks.

Quizzes                                         Element 1 and 2          20%
Mid-Sem Test                              Element 1                     20%
Project                                           Element 1, 2                 20%
Exam                                             Element 1, 2                  40%

Assessment Matrix

Quizzes                                                          Element 1 and 2              20%
Mid-Sem Test                                               Element 1                         20%
Project                                                            Element 1, 2                     20%
Exam                                                              Element 1, 2                     40%

Other Information