33130 Subject Outline PDF

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SUBJECT OUTLINE 33130 Mathematical Modelling 1 Course area

UTS: Science

Delivery

Spring 2019; City

Credit points 6cp Result type

Grade and marks

Recommended studies: Extension 1 Mathematics

Subject coordinator Name: Dr Danica Solina Course Email queries: [email protected]

Teaching staff Lecturer: Gregory Cave Email: Gregory.Cave @uts.edu.au Tutors: to be advised.

Subject description This subject develops the knowledge and skills necessary for problem-solving and mathematical modelling at an introductory level. Differential calculus is applied to model situations in science and engineering that involve oscillations. Integral calculus is used to solve selected problems involving first- and second-order differential equations, and to calculate areas, volumes, lengths and other physical quantities. Vectors, matrix multiplication and determinants are introduced and applied to problem-solving and modelling. Sequences and series are reviewed and power series introduced where power series are used to approximate more functions.

Subject learning objectives (SLOs) Upon successful completion of this subject students should be able to: 1. Describe the relevance of mathematics to engineering and science and the role which engineering and science play in the development and evolution of mathematical ideas and methods 2. Apply mathematical tools and resources to model real world problems, especially in engineering and science 3. Demonstrate correct use of mathematical terminology and concepts, and show understanding of those concepts by describing them in both formal and informal language. 4. Achieve a high level of skill in the mathematical techniques covered in the subject content 5. Communicate mathematical knowledge clearly, logically and critically. 6. Use appropriate mathematical software to perform calculations and explore mathematical ideas relevant to the subject content, and demonstrate knowledge of the functions of this software by interpreting output.

Course intended learning outcomes (CILOs) This subject also contributes specifically to the development of following course intended learning outcomes: Problem-solving and design - engineering practice focuses on problem solving and design where artifacts are conceived, created, used, modified, maintained and retired (B.0) Abstraction and modelling - Abstraction, modelling, simulation and visualisation inform decision-making, and are underpinned by mathematics, as well as basic discipline sciences (C.0) Manage own time and processes effectively by prioritising competing demands to achieve personal goals, which is linked to EA Stage 1 Competencies: 3.5, 3.6 (D.1) 28/06/2019 (Spring 2019)

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Communicate effectively in ways appropriate to the discipline, audience and purpose, which is linked to EA Stage 1 Competency: 3.2 (E.1)

Contribution to the development of graduate attributes This subject contributes to the graduate profile of graduates from the Faculty of Engineering in many ways. Most obviously, it contributes to the mathematical and problem solving skills that form part of the list of Graduate Attributes under the headings : B. Problem solving and design:Engineering and IT practice focuses on problem solving and design where artifacts are conceived, created, used, modified, maintained and retired. 1. 2. 3. 4. 5. 6.

identify and apply relevant problem solving methodologies design components, systems and/or processes to meet required specifications synthesise alternative/innovative solutions, concepts and procedures apply decision making methodologies to evaluate solutions for efficiency, effectiveness and sustainability implement and test solutions, and demonstrate research skills.

C. Abstraction and modelling: Abstraction, modelling, simulation and visualisation inform decision making, and are underpinned by mathematics, as well as basic and discipline sciences. 1. apply abstraction, mathematics and/or discipline fundamentals to analysis, design and operation 2. develop models using appropriate tools such as computer software, laboratory equipment and other devices, and 3. evaluate model applicability, accuracy and limitations. D. Self management:Graduates must have capabilities for self-organisation, self-review, personal development and life-long learning. 1. manage their own time and processes effectively by prioritising competing demands to achieve personal goals ( manage self) E. Communication and coordination: Engineering and IT practice involves the coordination of a range of disciplinary and inter-disciplinary activities to arrive at problem and design solutions. 1. communicate effectively in ways appropriate to the discipline, audience and purpose

This subject contributes to the development of the following graduate attributes in Science: Graduate Attribute 1 - Disciplinary knowledge and its appropriate application A broad introduction to the most important and widely used concepts in mathematics is given. Graduate Attribute 2 - An Inquiry-oriented approach Throughout the subject mathematics is presented as a tool, which students are invited to use in the solution to real-world problems Graduate Attribute 3 - Professional skills and their appropriate application Throughout the subject mathematics is presented as a tool, which students are invited to use in the solution to real-world problems Graduate Attribute 6 - Communication skills Students will use formal and informal language to communicate knowledge clearly, logically and crtiically.

Teaching and learning strategies Lectures: Three hours of lectures in collaborative tiered lecture theatres. Tutorials: Students are expected to attend one two-hour tutorial per week. Expected Study time: 7.5 hours outside of class time. During lectures, students will be completing skeleton notes on paper by solving problems in pairs or small groups. 28/06/2019 (Spring 2019)

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Some of these problems will be available via UTSOnline for students to access and prepare before the class. The lecturer will demonstrate examples of the application of mathematical modelling to topics in Engineering and Science and students will have the opportunity to question and discuss the examples. In many cases, students will learn mathematical concepts and skills that are required as foundation knowledge in later Engineering and Science subjects. After lectures, students are expected to engage with material by reviewing lecture notes, attempting tutorial problems before attending tutorials. In the tutorials, students may be required to work in groups, as discussion of mathematical ideas helps students to learn. Students will be working through problems with the assistance of the tutor, who may also demonstrate mathematical modelling techniques and mathematical programming which the students can then investigate themselves. Students will get more value from the tutorials if they have attempted all tutorial problems before attending the tutorials. The second half of most tutorials will be used for Threshold Tests and feedback on the tests, which is described under “Assessment”. Feedback is given in the week after the first opportunity test only and students are required to attend the tutorial for feedback.

Content (topics) Matrix multiplication and determinants. Vectors and their application to physical problems. Complex numbers. Functions and their relationship to measurement and the interpretation of physical results. Differentiation. Differential equations arising from physical problems. Oscillatory motion. Trigonometric functions and inverse trigonometric functions. Integrals. Inverse functions. Hyperbolic functions. Methods of integration. Solution of differential equations by integration.Review of sequences and series and the use of power series to find an expression for a function. An introduction to Python and its use in mathematical modelling will be given if time permits.

Program Week/Session

Dates

Description

1

22 Jul

Lecture 1. Geometry in three dimensions. Vectors: definitions, components, dot product. Projections.Lines and planes, vector cross product. Notes: Tutorial 1: Information Assessment: Mathematics Threshold Test 1 - First Opportunity - This is based on assumed knowledge: 2 Unit Advanced Mathematics and some Ext 1. This takes place in your ASSIGNED tutorial class.

2

29 Jul

Lecture 2. Lines and planes, vector cross product continued. Triple products and applications. Notes: Tutorial 2: Vectors 1. Feedback on Mathematics Threshold Test 1 - First Opportunity....you will be able to check your paper but it must be returned. You will not be able to keep a copy so pay attention to issues you had.

3

5 Aug

Lecture 3. Functions and derivatives, including differentials, implicit differentiation, related rates. Exponential functions. Logarithmic differentiation. Newton's method. (Much of this is review). Complex numbers: introduction, notation, calculations, applications. Notes:

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Tutorial 3: Vectors 2 Assessment: Mathematics Threshold Test 1 - Second Opportunity - only for students who did not meet the minimum requirement in first opportunity. Maximum mark given is 80% (Threshold). This takes place in your ASSIGNED tutorial class. 5TH AUGUST is LAST DAY TO ENROL IN A SUBJECT

4

12 Aug

Lecture 4. *Complex numbers: introduction, notation, calculations, applications finalized. *Hyperbolic functions and inverse functions. Notes: Tutorial 4: Functions and Variables Assessment: Mathematics Threshold Test 2 - First Opportunity - Content Vectors. This takes place in your ASSIGNED tutorial class.

5

19 Aug

Lecture 5. Integration - concepts and Riemann Sums Notes: Tutorial 5: Complex Numbers and hyperbolic and inverse functions. Feedback on Mathematics Threshold Test 2 - First Opportunity. Tests must be returned to tutor. 23RD AUGUST - CENSUS DATE - LAST DAY to WITHDRAW WITHOUT ACADEMIC OR FINANCIAL PENALTY for a subject.

6

26 Aug

Lecture 6. Methods of integration: substitution, integration by parts, partial fractions. Notes: Tutorial 6: Integration 1 Assessment: Mathematics Threshold Test 2 - Second Opportunity This takes place in your ASSIGNED tutorial class.

7

2 Sept

Lecture 7. Differential equations: separable, and first order linear differential equations. Applications. Notes: Tutorial 7: Integration 2 Assessment: Mathematics Threshold Test 3 - First Opportunity - Covers lectures 3 - 5 and associated material

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This takes place in your ASSIGNED tutorial class.

StuVac

9 Sept

This week is for catching up on content, not a holiday!

8

16 Sept

Lecture 8. Introduction to second order differential equations. Notes: Tutorial 8: DEs, first order. Feedback on Mathematics Threshold Test 3 - First Opportunity. Tests must be returned to tutor.

9

23 Sept

Lecture 9. Extended Modelling: Oscillation problems. Damping and forced oscillations, resonance. Notes: Tutorial 9: 2nd Order DEs - Homogeneous case Assessment: Mathematics Threshold Test 3 - Second Opportunity This takes place in your ASSIGNED tutorial class

10

30 Sept

Lecture 10. Matrix Multiplication and determinants. Notes: Tutorial 10: 2nd Order DEs - Inhomogenous case Assessment: Mathematics Threshold Test 4 - First Opportunity - Covers lectures 6-8 and associated material This takes place in your ASSIGNED tutorial class.

11

7 Oct

Lecture 11. Series and power series. Notes: Monday is a public holiday therefore all Monday classes will be shifted by ONE week with a make-up class in StuVac on 21st October. Tutorial 11: Matrices and determinants Assessment: Mathematics Threshold Test 4 - Second Opportunity This takes place in your ASSIGNED tutorial class.

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12

14 Oct

Lecture 12. Threshold test 1,2,3 third opportunity will be held in lectures. Exact details will be released on the UTSonline announcement page. It is the responsibility of the student to be aware of this information. Notes: Tutorial 12: Power Series Assessment: Mathematics Threshold Test 4 - Third Opportunity This takes place in your ASSIGNED tutorial class

13

21 Oct

Monday 21st October. Make up sessions for Monday classes are running today owed to the 7th October public holiday. Makeup classes are official classes and will have the content that should have run the previous week including tests and are allowed under university rules.

Additional information STUDENT LEARNING SUPPORT: Students are encouraged to attend UPASS sessions – these are study sessions facilitated by experienced UTS students. Further details can be found at http://www.uts.edu.au/current-students/support/upass/upass . The Mathematics and Science Study Centre operates a Drop-in Room in Building 4, level 3, room 331 (CB04.03.331). Academic staff members are available in the Drop-in Room at the scheduled timetable for one-to-one assistance. Usually the centre is open at lunch time for the initial weeks of semester and then in the afternoons from week 3 of semester. Further details are at http://www.uts.edu.au/current-students/science/study-resources/mathematics-and-science-study-centre

Assessment Assessment in this subject is designed to ensure that basic and intermediate concepts and skills are mastered. Students demonstrate their mastery of basic+ skills by completing Threshold Tests. Students can practice for these tests by completing tutorial question and the additional basic level questions on UTSonline. Practice questions and online homework may include learning aides such as short videos. Full marks on all the Threshold Tests will result in a score of 50. In order to pass the subject however, students need: 1. At least 80% must be acheived in one attempt of Threshold Test 1 (worth 5%) 2. At least 70% must be achieved in one attempt of each of Threshold Tests 2, 3 and 4 (worth 15% each). 3. If the minimum requirement is not achieved in EACH of Threshold Tests 1, 2, 3 and 4 the student will not be eligible to sit for the final exam and their final exam paper will not be marked. 4. At least 40% must be achieved in the final exam. 5. An overall mark of 50+%. If an overal mark of 50+% is obtained but minimum requirements in an assessment are not acheived, an X grade fail may be awarded. Threshold Tests must be attempted in the student's assigned tutorial class. Marks obtained for a test attempted without an invigilator will be discounted. 28/06/2019 (Spring 2019)

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There are two opportunities allocated to each Threshold Test in the semester(see weekly timetable). Students may sit in both sessions in order to obtain the required minimum mark. Only in the first opportunity will marks in excess of the minimum requirement be awarded. Both opportunities for Threshold Test 1 will be organised before the census date for withdrawal for students who did not obtain 80%. Threshold Tests for the two opportunities are taken in your assigned tutorial. You must arrive early as extra time will not be given. For students who have sat either of the first two opportunities but did not achieve the minimum requirement, a third and final opportunity may be organised for the last week of semester. There will be no other sessions organised after the last day of formal face to face teaching. Special Consideration: Students who have missed a Threshold Test session owed to misadventure must apply for special consideration within 48 hours of the test. If special consideration is granted for the first or second opportunity, an alternate test will be scheduled for the student so they do not miss an opportunity. If special consideration is granted for the final opportunity of any test, a multiplier of 1.1 will be applied to the higher score of opportunity 1 or 2 for that test, and this mark will be awarded, not another test. If a student applies for special consideration for the third opportunity and has not sat either of the first two opportunities then they will receive zero for that test and fail the subject. It is in the interest of the student to attempt all opportunities.

Assessment task 1: Final examination Objective(s): This assessment task addresses subject learning objective(s): 1, 2, 3, 4, 5 and 6 This assessment task contributes to the development of course intended learning outcome(s): B.0, C.0 and E.1 Weight:

50%

Task:

Extended responses to several questions including seen and unseen problems. The final exam is a restricted open book exam in that you will be supplied with the equation sheet that has been available to you throughout the semester as a resource.

Length:

Two hours and ten minutes reading time.

Due:

In the formal examination period at the end of semester

Criteria:

Correct use of terminology Correct choice and use of problem solving strategies and procedures Accurate mathematical reasoning Correctly describe the relevance of mathematical modelling to engineering practice Accurately describe the role of engineering and science in the development and evolution of mathematical ideas and methods.

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Further The final exam is a restricted open book exam in that you will be supplied with the equation sheet information: that has been available to you throughout the semester as a resource. In order to pass the subject students need: 1. At least 80% must be achieved in one attempt of Threshold Test 1 2. At least 70% must be achieved in one attempt of each of Threshold Tests 2,3 and 4. 3. If the minimum requirement is not achieved in EACH of Threshold Tests 1, 2, 3 and 4 the student will not be eligible to sit for the final exam and their final exam paper will not be marked. 4. At least 40% must be achieved in the final exam. 5. An overall mark of 50+%. If an overall mark of 50+% is obtained but minimum requirements in an assessment are not achieved, an X grade fail may be awarded. Tests must be attempted in the student's assigned tutorial class. Marks obtained for a test attempted without an invigilator will be discounted.

Assessment task 2: Threshold Tests Objective(s): This assessment task addresses subject learning objective(s): 2, 3 and 4 This assessment task contributes to the development of course intended learning outcome(s): B.0, C.0 and D.1 Weight:

50%

Task:

Short responses to questions which require routine algorithms and problem solving. Samples of basic level questions on lecture material will be available online via UTSonline and more advanced material will be based on concepts from lectures and tutorials.

Length:

45 minutes

Due:

Full details on test content and when they will take place during the semester are given in the subject program.

Criteria:

Correct use of terminology Correct choice and use of problem solving strategies and procedures Accurate mathematical reasoning

Further In order to pass the subject however, students ...