# Course Title: Use calculus

## Part B: Course Detail

Teaching Period: Term2 2013

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)

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. Differentiate algebraic, exponential and natural logarithmic functions and use the results to solve problems 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. Interpret the concept of a derivative graphically and as a rate of change, and solve applied problems 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. Simple differential equations are solved by determining the antiderivatives of algebraic, exponential and natural logarithmic functions 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. Analytical and applied problems are solved by evaluating definite integrals and interpreting their meaning 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. Applied problems are solved using derivatives and anti-derivatives of trigonometric functions 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

 Week Number Topic Delivered Assessment Task 1 Download/Explain course including assessments,  policies/Revision of Pre Requisite course and Introduction to the competency 2 Define derivatives, elementary algebraic function Differentiation – Product rule Element 1 3 Differentiation – quotient rule Elements 1&2 4 Differentiation – Ln and e functions / Differentiation – combinations Elements 1&2 5 Test 1 25% of total assesment 6 Differentiation – Chain Rule, Differentiation – Trigonometric Functions Elements 1&2 7 Differentiation Applications to engineering problems Elements 1&2 8 Further application to Differentiation 25% of total assesment 9 Test 2 25% of total assesment 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 Elements 3&4 11 Integrals Exp and LN forms / Integrals Trig forms Elements 3&4 12 methods of integration - substitution and partial integration   methods of integration - rational integration and other trigonometric integrations Elements 3&4 13 Test 3 25% of total assesment 14 methods of integration - rational integration and other trigonometric integrations Elements 4&5 15 Integrals application - areas and volumes Elements 4&5 16 Integrals application - practical engineering problems Elements 4&5 17 Test 3 25% of total assesment 18 Final results Elements 1,2,3,4&5

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 task 1 (test 1): 25%
This assessment demonstrates an understanding with applications of mathematics involving engineering problems which are covered from week 1 to week 4. The time allowed for this test is no more that 1 hour and 15 minutes reading time.

Assessment task 2 (test 2): 25%
This assessment demonstrates an understanding with applications of mathematics involving engineering problems which are covered from week 5 to week 8. The time allowed for this test is no more that 1 hours and 15 minutes reading time.

Assessment task 3 (test 3 ): 25%
This assessment demonstrates an understanding with applications of mathematics involving engineering problems which are covered from week 9 to week 12. The time allowed for this test is no more that 1 hour and 15 minutes reading time

Assessment task 4 (Final Exam): 25%
This assessment demonstrates an understanding with applications of differential calculus,, integral calculus and problems with engineering applications, which is covered from week 13 to week 16. The time allowed for this test is no more that 1 hour and 15 minutes reading time.

CHD- Competent with High Distinction
CDI- Competent with Distinction
CC- Competent with Credit
NYC- Not Yet Competent
DNS- Did Not Submit for Assessment. (This grade is only to be used where the student’s attendance in the course has been ‘confirmed’ (but they have not participated in any form of assessment and did not withdraw by the census date).

Assessment Matrix

 Element Covered Assessment Task Proportion of Final Assessment Submission Time 1&2 test 1 25% Week 5 1&2 test 2 25% Week 9 3,4&5 test 3 25% Week 13 3,4&5 test 4 25% Week 17 or 18

Other Information

Minimum student directed hours are 12 in addition to 48 scheduled teaching hours.

- Student directed hours involve completing activities such as reading online resourses, assignements, notes and other learning material, preparation for test and exam and individual student - teacher course related consultation.

Study and learning Support:

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 of the students are:

assignment writing, thesis writing and study skills advice
maths and science developmental support and advice
English language development