# Course Title: Use calculus

## Part B: Course Detail

Teaching Period: Term1 2012

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

Annabelle Lopez
Email:  annabelle.lopez@rmit.edu.au
Tel: 99254823

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 participate in individual and team problem solving activities related to typical engineering workplace problems. These activities involve class participation (discussions and oral presentations), prescribed exercises, homework, tutorials, application of theory to engineering problems and completion of calculations to industry standard, computer software application work in laboratory sessions (MATLAB, depending on availability of computer lab), tests and examination.

Teaching Schedule

This is an indicative teaching schedule. Refer to Online Blackboard announcements for changes.
Week 1 - Download/Explain course including assessments and policies/Revision of Pre Requisite course
Week 2 - Define derivatives, elementary algebraic function Differentiation – Product /quotient rule, Chain Rule
Week 3 - Differentiation – Chain Rule, Differentiation – Trigonometric Functions
Week 4 - Test 1
Week 5 - Differentiation – Ln and e functions / Differentiation – combinations
Week 6 - Differentiation Applications 1 / Differentiation Applications 2
Week 7 - Differentiation Applications 2
Week 8 - Test 2
Week 9 - Antiderivatives general/Antiderivatives various forms/Fundamental Theorem of Calculus
Week 10 - Fundamental Theorem of Calculus / Integrals General / Integrals Algebraic form/ Integrals other Forms
Week 11 - Integrals Exp and LN forms / Integrals Trig forms
Week 12 - Test 3
Week 13 - Integrals application - areas
Week 14 - Test 4
Week 15 - Major Assessment
Week 16 - Partly Self Directed-Inverse Fn & Graphing / Deferred Assessments and the like -Tests 1 & 2
Week 17 - Partly Self Directed-Implicit & Higher Derivatives / Deferred Assessments and the like -Tests 3 & 4
Week 18 - Finalising Results
This is an indicative teaching schedule. Refer to Online Blackboard announcements for changes.

Learning Resources

Prescribed Texts

References

 Fitzgerald G. F, Peckham I.A, Mathematical Methods for Engineers and Scientists, Fourth edition, 2005, Pearson Education Australia Other references will be given in class.

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

To be deemed competent students must demonstrate an understanding of all elements of a competency.

Students are advised that they are likely to be asked to personally demonstrate their assessment work to their teacher to ensure that the relevant competency standards are being met. Students will be provided with feedback throughout the course to check their progress.

Tests 1, 2, 3 and 4 all relate to competency based nature of C6093 program. Satisfactory completion of this competency based component requires a minimum of 80% in all minor tests 1, 2, 3 and 4. Satisfactory completion of this component entitles student to a ‘Pass’ for this course.

To obtain either “Credit’, ‘Distinction’ or ‘High Distinction’ for this course, student needs to take the Major Assessment in addition to having satisfactorily completed all Minor Tests.

Major Assessment is therefore not compulsory.

Assessment details:

Tests 1, 2, 3 and 4 – These assessments are used to indicate whether a student is competent (or not yet competent). These are written tests (closed book) to cover content so far. Satisfactory completion of this competency based component requires a minimum of 80% in all minor tests 1, 2, 3 and 4. Satisfactory completion of this component entitles student to a ‘Pass’ for this course.
These minor tests will focus on the students’ ability to solve problems and provide logical solutions to practical exercises. These tests collectively will have a weighting of 50% of the final overall assessment mark.

Major Assessment – This assessment is taken by students to obtain either “Credit’, ‘Distinction’ or ‘High Distinction’ for this course (in addition to having satisfactorily completed all Minor Tests).
This major assessment is a written test (closed book) to cover content so far. This will focus on the students’ ability to solve problems and provide logical solutions to practical exercises. These assessments will have a weighting of 50% of the final overall assessment mark.

Note: Students may not be entitled to any supplementary work. All assessments need to be passed.

Assessment Matrix

 Assessment Element Covered Test 1 1 Test 2 2  5 Test 3 3 Test 4 4  5 Major (Final) Assessment 1  2  3  4  5

Other Information

The underpinning knowledge and skills for this course are listed in the accreditation document and are available upon request from your instructor.
Study and learning Support:

Study and Learning Centre (SLC) provides free learning and academic development advice to you.
Services offered by SLC to support your 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/studyandlearningcentre to find more information about Study and learning Support

Disability Liaison Unit:

If you are suffering from long-term medical condition or disability, you should contact Disability Liaison Unit to seek advice and
support to complete your studies.

Please Refer http://www.rmit.edu.au/disability to find more information about services offered by Disability Liaison Unit

Late submission:

If you require an Extension of Submittable Work (assignments, reports or project work etc.) for 7 calendar days or less (from the original due date) and have valid reasons, 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. You 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 seek an Extension of Submittable Work for more than 7 calendar days (from the original due date) 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.

Submittable Work (assignments, reports or project work etc.) submitted late without approval of an extension will not be accepted or marked.

Special consideration:

Please Refer http://www.rmit.edu.au/browse;ID=riderwtscifm to find more information about special consideration

Plagiarism:

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

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

Other Information:

All email communications will be sent to your RMIT email address and you must regularly check your RMIT emails.

Course Overview: Access Course Overview