# Course Title: Use calculus

## Part B: Course Detail

Teaching Period: Term2 2015

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

Program Manager
Mr. Ahmet Ertuncay
Tel. +61 3 9925 8375
Email: ahmet.ertuncay@rmit.edu.au

Ms. Annabelle Lopez
Tel. +61 3 9925 4823
Email: annabelle.lopez@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)

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. 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 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 in 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 exp functions / Differentiation – combinations. Assignment part A (5 marks, 5% of total mark) due. 1.8, 2.1 5 Differentiation – Chain Rule, Differentiation – Trigonometric Functions, applications Assignment handed out (worth 15% of total marks, due in week 16). 2.2, 2.3, 2.4 6 Test (Closed book, worth 30% of total mark) Topics covered in Test include but not limited to: all rules of differentiation including linearity, product, quotient, trigonometric, logarithmic, exponential, elementary algebraic, chain & all combinations PLUS applications of differentiation. 1.1, 1.2, 1.3 1.4, 1.5, 1.6 1.7, 1.8 7 Differentiation Applications in engineering 2.1, 2.2 2.3, 2.4 8 Applications of Differentiation. 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 Further applications of Differentiation. 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. 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, revision. 3.3, 3.4 4.3, 4.4 13 Methods of integration - rational integration and other trigonometric integrations, revision. 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. 5.1,5.2,5.3, 5.4 16 Integrals application - practical engineering problems, Revision for Exam. Assignment 1 (15% of total mark) due. 5.5, 5.6, 5.7 17 Exam (Closed book, worth 50% of total mark).  Topics covered in Exam include but not limited to: Anti derivatives of various forms, Integrals of various forms eg exp, log, trigonometric etc, Using table of integrals/anti derivatives, Various methods of integration eg substitution, partial integration, integrating rational functions, Applications of integration and graphing 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 Feedback maybe available. 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

• Assignments, 20% (5% + 15%)
• 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.

Credit Transfer and/or Recognition of Prior Learning (RPL):

You may be eligible for credit towards courses in your program if you have already met the learning/competency outcomes through previous learning and/or industry experience. To be eligible for credit towards a course, you must demonstrate that you have already completed learning and/or gained industry experience that is:

• Relevant
• Current
• Satisfies the learning/competency outcomes of the course

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

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.

Late Submission:

If you require an Extension of Submittable Work (assignments, reports or project work etc.) for seven calendar days or less (from the original due date) and have valid reasons, you must complete 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 two working days of the date of lodgement as to whether the extension has been granted.

If you seek an Extension of Submittable Work for more than seven 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 two 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: