# Course Title: Apply calculus in engineering situations

## Part B: Course Detail

Teaching Period: Term1 2011

Course Code: MATH5323C

Course Title: Apply calculus in engineering situations

School: 130T Vocational Engineering

Campus: City Campus

Program: C6107 - Advanced Diploma of Engineering

Course Contact: Steven Bevan

Course Contact Phone: +61 3 9925 4468

Course Contact Email: steven.bevan@rmit.edu.au

Name and Contact Details of All Other Relevant Staff

Nancy Varughese - Coordinator

Building 51 Level 6 Room 04

Tel: +61 3 9925 4713

email:  nancy.varughese@rmit.edu.au

Brian Hayes

Building 51 Level 7 Room 05

Tel: +61 3 9925 4745

brihaye@rmit.edu.au

Tatjana Grozdanovski

Building 51 Level 6 Room 04

Tel: +61 3 9925 4689

Nominal Hours: 80

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

Pre-requisite  MEM30012A - Apply mathematical techniques in manufacturing, engineering or related situations

Course Description

This unit covers the application of calculus concepts and techniques to solve problems in engineering situations. It includes finding the derivatives from first principles, using the rules of differentiation to find first and second derivatives of functions, applying integral calculus to functions, and applying differential and integral calculus techniques to solve engineering problems.

National Codes, Titles, Elements and Performance Criteria

 National Element Code & Title: MEM23002A Apply calculus in engineering situations Element: Apply differentiation techniques to engineering applications. Element: Apply integration techniques to engineering applications.

Learning Outcomes

Element 1:       Apply differentiation techniques to engineering applications.

Performance Criteria 1.1:     Solve engineering problems using the rules of differentiation.

Element 2:        Apply integration techniques to engineering applications.

Performance Criteria  2.1:     Use integration techniques to obtain integrals of algebraic, trigonometric and exponential functions, and evaluate definite integrals.

Performance Criteria  2.2:      Solve engineering problems using the rules of integration.

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 (1.5 hrs) 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.  End-Semester Test (1.5 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

To successfully complete this course, the student is required to demonstrate competency in written assessment tasks and project tasks to engineering standards.

NYC - Not yet competent

CA - Competence Achieved

CC - Competence with Credit

CDI - Competence with Distinction

CHD - Competence with High Distinction

Students are required to complete three different types of assessment tasks, quizzes worth 20% in total, one project worth 20% and tests worth 60%.
Successful completion is achieved if the student attains at least 50% of total mark for each type of 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                     30%
Project                                           Element 1, 2                 20%
End-Sem Test                             Element 1, 2                  30%

Assessment Matrix

Quizzes                                                          Element 1 and 2              20%
Mid-Sem Test                                               Element 1                         30%
Project                                                            Element 1, 2                     20%
End-Sem Test                                              Element 1, 2                     30%

Other Information