Course Title: Use calculus

Part B: Course Detail

Teaching Period: Term1 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 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

WeekTopic Delivered                                                                                                                                             Elements /
Performance Criteria      
1Download/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
2Define derivatives, elementary algebraic function Differentiation – Product rule1.3,1.4
3Differentiation – quotient rule1.5,1.6,1.7
4Differentiation – Ln and e functions / Differentiation – combinations1.8, 2.1
5Differentiation – Chain Rule, Differentiation – Trigonometric Functions2.2, 2.3, 2.4
6Differentiation Applications to engineering problems

1.1, 1.2, 1.3
1.4, 1.5, 1.6
1.7, 1.8

7Further application to Differentiation

2.1, 2.2
2.3, 2.4

8Practice Test and revision1.1, 1.2, 1.3 1.4, 1.5, 1.6, 1.7, 1.8, 2.1, 2.2, 2.3, 2.4
9Closed 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
10Antiderivatives 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
 
11Integrals Exp and LN forms / Integrals Trig forms3.1, 3.2
4.1, 4.2
12methods of integration - substitution and partial integration3.3, 3.4
4.3, 4.4
13methods of integration - rational integration
and other trigonometric integrations
3.1,3.2, 3.3,3.4
4.1, 4.2
14methods of integration - trigonometric integrations4.1, 4.2, 4.3,4.4
15Integrals application - areas and volumes

5.1,5.2,5.3, 5.4

16Integrals application - practical engineering problems5.5, 5.6, 5.7
17Practice 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

18Closed book Exam
(worth 50% of total mark)
 
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
Assessments1.11.21.31.41.51.61.71.82.12.22.32.4
Assignmentxxxxxxxxxxxx
Testxxxxxxxxxxxx
Exam             

 

 

 EAX110B Elements & Performance Criteria
Assessments3.13.23.33.44.14.24.34.45.15.25.35.45.55.65.7
Assignmentxxxxxxxxxxxxxxx
Test               
Exam xxxxxxxxxxxxxxx

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.

Course Overview: Access Course Overview