Course Title: Use calculus

Part B: Course Detail

Teaching Period: Term2 2014

Course Code: MATH5318

Course Title: Use calculus

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

Dr Elmas Aliu
+61 3 9925 4360
elmas.aliu@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

EDX130B Use technical mathematics (basic)
EDX140B Use technical mathematics (advanced)

Course Description

This unit covers the competency to differentiate and integrate functions related to practical problems common to the Civil and Mechanical engineering disciplines.


National Codes, Titles, Elements and Performance Criteria

National Element Code & Title:

EAX110B Use calculus

Element:

1. Differentiate algebraic, exponential and natural logarithmic functions and use the results to solve problems

Performance Criteria:

1.1 Define the derivative of a function f as the slope of the limiting positive of a secant to a curve using.
1.2 Elementary algebraic functions are differentiated using the rules
1.3 Algebraic functions are differentiated using the product rule.
1.4 Algebraic functions are differentiated using the quotient rule
1.5 Algebraic functions are differentiated use the chain rule
1.6 Natural logarithmic (base e) and exponential functions are differentiated using the chain rule.
1.7 Algebraic, logarithmic and exponential functions are differentiated using a combination of the product, quotient and chain rule.
1.8 Functions drawn from applied situations are differentiated and the results interpreted
 

Element:

2. Interpret the concept of a derivative graphically and as a rate of change, and solve applied problems

Performance Criteria:

2.1 Applied problems involving algebraic, logarithmic and exponential functions are solved by interpreting the derivative as an instantaneous rate of change of a quantity at a time t.
2.2 The equation of a tangent to a curve is determined by using the derivative as a function, which gives the slope of the tangent at a point on the curve.
2.3 Elementary optimization problems are solved using the zero property of a tangent to a curve at the minimum or maximum of the function.
2.4 Applied problems are solved using the derivative of a function and the results interpreted.
 

Element:

3. Simple differential equations are solved by determining the antiderivatives of algebraic, exponential and natural logarithmic functions

Performance Criteria:

3.1 The antiderivatives of elementary functions are determined using the following basic formulae
3.2 The antiderivatives of composite functions are determined using each of the following standard antiderivatives.
3.3 The general solutions of differential equations of the form are found using the anti-derivatives from above.
3.4 General differential equations of the form where where can be found using the standard anti-derivatives.
 

Element:

4. Analytical and applied problems are solved by evaluating definite integrals and interpreting their meaning

Performance Criteria:

4.1 Definite integrals are evaluated using the Fundamental Theorem of Calculus where
4.2 Evaluate the areas of particular functions using the properties of definite integrals
4.3 Particular solutions of differential equations are calculated using initial conditions and definite integrals
4.4 Applied problems are solved using definite integrals
4.5 Differential equations of the type in section 3 are solved and the solutions interpreted
 

Element:

5. Applied problems are solved using derivatives and anti-derivatives of trigonometric functions

Performance Criteria:

5.1 Trigonometric functions in combination and composition with algebraic, exponential and logarithmic functions are differentiated using one or more of the sum, product, quotient and chain rules.
5.2 Where the first quantity is a function with one variable
only determine the instantaneous rate of change of one quantity with respect to another quantity
5.3 The antiderivative of a trigonometric function combined and composed with algebraic, exponential and reciprocal elements, is determined.
5.4 Elementary optimisation problems are solved using the fact that the value of the first derivative is zero at the maximum or minimum point of the function
5.5 The definite integral of a trigonometric function is evaluated.
5.6 Elementary differential equations of the form are solved where f involves a trigonometric function.
5.7 Applied problems involving trigonometric functions are solved.
 

Learning Outcomes


• Develop analytical and logical thinking skills
• Apply mathematical principles and skills in relation to:
- derivatives and anti-derivatives,
- solution of differential equations
- rate of change,
- definite integrals
• Perform calculations to industry standard


Details of Learning Activities

You will involve in the following learning activities to meet requirements for this course

• Tutorial
• Work simulation activities


Teaching Schedule

Week Topic Delivered                                                                                                                                                  Elements / 
Performance Criteria       
1 Download/Explain course including assessments, policies/Revision of Pre Requisite course and Introduction to the competency
Assignment (part A) handed out (worth 5% of total mark) due date end of week 4.		 1.1,1.2
2 Define derivatives, elementary algebraic function Differentiation – Product rule 1.3,1.4
3 Differentiation – quotient rule 1.5,1.6,1.7
4 Differentiation – Ln and e functions / Differentiation – combinations 1.8, 2.1
5 Differentiation – Chain Rule, Differentiation – Trigonometric Functions 2.2, 2.3, 2.4
6 Differentiation Applications to engineering problems

1.1, 1.2, 1.3,1.4, 1.5, 1.6,
1.7, 1.8
7 Further application to Differentiation

2.1, 2.2, 2.3, 2.4
8 Practice Test and revision 1.1, 1.2, 1.3 1.4, 1.5, 1.6, 1.7, 1.8, 2.1, 2.2, 2.3, 2.4
9 Closed book Test
(worth 30% of total mark)		 1.1, 1.2, 1.3 1.4, 1.5, 1.6
1.7, 1.8, 2.1, 2.2, 2.3, 2.4
10 Antiderivatives general/Antiderivatives various forms/Fundamental Theorem of Calculus
Fundamental Theorem of Calculus / Integrals General / Integrals Algebraic form/ Integrals other Forms
Integrals Exp and LN forms / Integrals Trig forms		 3.1, 3.2 3.3,3.4
4.1, 4.2, 4.3,4.4
 
11 Integrals Exp and LN forms / Integrals Trig forms 3.1, 3.2
4.1, 4.2
12 methods of integration - substitution and partial integration 3.3, 3.4
4.3, 4.4
13 methods of integration - rational integration
and other trigonometric integrations
 		 3.1,3.2, 3.3,3.4
4.1, 4.2
14 methods of integration - trigonometric integrations 4.1, 4.2, 4.3,4.4
15

Integrals application - areas and volumes
practical engineering problems

5.1,5.2,5.3, 5.4,
5.5, 5.6, 5.7
16 Practice Exam and revision 3.1,3.2, 3.3,3.4
4.1, 4.2, 4.3, 4.4, 4.5
5.1, 5.2, 5.3,5.4, 5.5, 5.6, 5.7
17

Closed book Exam
(worth 50% of total mark)

(week 17 or 18)

3.1,3.2, 3.3,3.4
4.1, 4.2, 4.3, 4.4, 4.5
5.1, 5.2, 5.3,5.4, 5.5, 5.6, 5.7
18 Closed book Exam
(worth 50% of total mark)
 (week 17 or 18)
 		 3.1,3.2, 3.3,3.4
4.1, 4.2, 4.3, 4.4, 4.5
5.1, 5.2, 5.3,5.4, 5.5, 5.6, 5.7


Learning Resources

Prescribed Texts

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

1-74009-733-5

References

Glyn James, Modern Engineering Mathematics, fourth edition, Pearson Education Australia

9780132391443

Other Resources


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


Assessment Tasks

• Assignment, 20%
• Test, 30%
• Exam, 50%
 


Assessment Matrix

 

  EAX110B Elements & Performance Criteria
Assessments 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 2.1 2.2 2.3 2.4
Assignment x x x x x x x x x x x x
Test x x x x x x x x x x x x
Exam                        

 

  EAX110B Elements & Performance Criteria
Assessments 3.1 3.2 3.3 3.4 4.1 4.2 4.3 4.4 5.1 5.2 5.3 5.4 5.5 5.6 5.7
Assignment x x x x x x x x x x x x x x x
Test                              
Exam x x x x x x x x x x x x x x x

Other Information

• Student directed hours involve completing activities such as reading online resources, assignment, individual student-teacher course-related consultation. Students are required to self-study the learning materials and complete the assigned out of class activities for the scheduled non-teaching hours. The estimated time is 12 hours outside the class time.

Study and Learning Support:
The Study and Learning Centre (SLC) provides free learning and academic development advice to all RMIT students.
Services offered by SLC to support numeracy and literacy skills are:

* Assignment writing, thesis writing and study skills advice
* Maths and science developmental support and advice
* English language development

Please refer http://www.rmit.edu.au/students/studyandlearningcentre to find more information

Disability Liaison Unit:
If you have a disability or long-term medical condition you should contact the DLU to seek advice and support.

Please Refer http://www.rmit.edu.au/disability to find more information about their services

Late submission:
If you require an extension for 7 calendar days or less (from the original due date) you must complete and lodge an Application for Extension of Submittable Work (7 Calendar Days or less) form and lodge it with the Senior Educator/ Program Manager.
The application must be lodged no later than one working day before the official due date. The student will be notified within no more than 2 working days of the date of lodgment as to whether the extension has been granted.

If you require an extension of more than 7 calendar days (from the original due date) you must lodge an Application for Special Consideration form under the provisions of the Special Consideration Policy, preferably prior to, but no later than 2 working days after the official due date.

Assignments submitted late without approval of an extension will not be accepted nor marked.

Special consideration:

Please Refer http://www.rmit.edu.au/students/specialconsideration to find more information

Plagiarism:
Plagiarism is a form of cheating and it is a very serious academic offence that may lead to expulsion from the University.

Please Refer: www.rmit.edu.au/academicintegrity to find more information.

Other Information:
All email communications will be sent to your RMIT email address and it is recommended that you check it regularly.

Course Overview: Access Course Overview