Course Title: Use calculus

Part B: Course Detail

Teaching Period: Term2 2010

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

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 basic formulae 3.2 The antiderivatives of composite functions are determined using each 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 - Define derivatives, elementary algebraic function
Week 2 - Differentiation – Product /quotient rule
Week 3 - Differentiation - Chain Rule
Week 4 - Differentiation – Ln and e functions
Week 5 - Differentiation – Trigonometric functions
Week 6 - Differentiation - Combinations
Week 7 - Differentiation Applications 1
Week 8 - Differentiation Applications 2
Week 9 - Test 1 (Assessment 1)
Week 10 - Antiderivatives general
Week 11 - Antiderivatives various forms
Week 12 - Fundamental Theorem of Calculus
Week 13 - Integrals general
Week 14 - Integrals algebraic form
Week 15 - Integrals Exp and Ln forms
Week 16 - Integrals Trig forms
Week 17 - Integrals application – areas
Week 18 - Test 2 (Assessment 2)
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

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.

Assessment details:
Assessment 1 – This 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. This test will have a weighting of 50% of the final overall assessment mark.
Assessment 2 – This 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. This test will have a weighting of 50% of the final overall assessment mark.
Note regarding Assessments: Option to assess via topic quizzes covering the same elements of competency is available.

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

Assessment Matrix

Other Information

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

Course Overview: Access Course Overview