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ENGSCI 314 : Mathematical Modelling 3ES
Engineering
2023 Semester One (1233) (15 POINTS)
Course Prescription
Course Overview
This course provides valuable skills in differential equations and statistics to support degrees in Engineering Science and Biomedical Engineering.
One half of the course focuses on the theory and use of differential equations for the modelling of physical phenomena including diffusion of heat and mechanical vibrations. Students learn how to set a problem up by appropriate choice of equation(s), boundary conditions and initial conditions and how to solve it. This is followed by an introduction to the calculus of variations; useful for finding the equations of motion of vibrating systems.
The other half is a practical course in statistical data analysis with a heavy emphasis on interpretation and communication of statistical findings. The core of the course covers linear models but the course also includes an introduction to logistic regression. The course is taught using the R computing environment with an emphasis on reproducible research. It enables them to answer many of the commonly encountered quantitative scientific questions of interest.
Capabilities Developed in this Course
| Capability 1: | Disciplinary Knowledge and Practice |
| Capability 2: | Critical Thinking |
Learning Outcomes
- Write the characteristic equation for an ODE and identify the correct form for particular solutions. Know the difference between homogeneous and non-homogeneous boundary conditions. Solve a partial differential equation using the separation of variables method. Understand the basics of calculus of variations. (Capability 1.1 and 2.1)
- Identify key simplifying assumptions and interpret them from a modeling perspective. (Capability 1.1 and 2.1)
- Demonstrate an understanding of how to dissect a problem so that it can be solved by combining solutions, such as the steady state and the transient solutions to a heat equation. (Capability 1.1 and 2.1)
- Critically evaluate a problem of a statistical nature and proceed towards its solution. (Capability 1.1 and 2.1)
Assessments
| Assessment Type | Percentage | Classification |
|---|---|---|
| Test | 20% | Individual Test |
| Final Exam | 50% | Individual Examination |
| Assignments | 30% | Individual Coursework |
| 3 types | 100% |
| Assessment Type | Learning Outcome Addressed | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | |||||||
| Test | ||||||||||
| Final Exam | ||||||||||
| Assignments | ||||||||||
To pass the course, students must score a minimum of 50% overall as well as a minimum of 50% in the test and exam considered together (i.e., a minimum of 35/70 from the combined test and exam marks).
Workload Expectations
This course is a standard 15 point course and students are expected to spend 10 hours per week involved in each 15 point course that they are enrolled in.
For this course, you can expect, on average per week, 3 hours of lectures, 1 hour of tutorial, 3 hours of reading and thinking about the content, and 3 hours of work on assignments and/or test preparation.
Delivery Mode
Campus Experience
Attendance is expected at scheduled activities including lectures and tutorials to complete components of the course.
Lectures will be available as recordings.
Attendance on campus is required for the test.
The activities for the course are scheduled as a standard weekly timetable.
Learning Resources
Course materials are made available in a learning and collaboration tool called Canvas which also includes reading lists and lecture recordings (where available).
Please remember that the recording of any class on a personal device requires the permission of the instructor.
Health & Safety
Student Feedback
At the end of every semester students will be invited to give feedback on the course and teaching through a tool called SET or Qualtrics. The lecturers and course co-ordinators will consider all feedback and respond with summaries and actions.
Your feedback helps teachers to improve the course and its delivery for future students.
Class Representatives in each class can take feedback to the department and faculty staff-student consultative committees.
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Academic Integrity
The University of Auckland will not tolerate cheating, or assisting others to cheat, and views cheating in coursework as a serious academic offence. The work that a student submits for grading must be the student's own work, reflecting their learning. Where work from other sources is used, it must be properly acknowledged and referenced. This requirement also applies to sources on the internet. A student's assessed work may be reviewed against online source material using computerised detection mechanisms.
Class Representatives
Class representatives are students tasked with representing student issues to departments, faculties, and the wider university. If you have a complaint about this course, please contact your class rep who will know how to raise it in the right channels. See your departmental noticeboard for contact details for your class reps.
Inclusive Learning
All students are asked to discuss any impairment related requirements privately, face to face and/or in written form with the course coordinator, lecturer or tutor.
Student Disability Services also provides support for students with a wide range of impairments, both visible and invisible, to succeed and excel at the University. For more information and contact details, please visit the Student Disability Services’ website http://disability.auckland.ac.nz
Special Circumstances
If your ability to complete assessed coursework is affected by illness or other personal circumstances outside of your control, contact a member of teaching staff as soon as possible before the assessment is due.
If your personal circumstances significantly affect your performance, or preparation, for an exam or eligible written test, refer to the University’s aegrotat or compassionate consideration page https://www.auckland.ac.nz/en/students/academic-information/exams-and-final-results/during-exams/aegrotat-and-compassionate-consideration.html.
This should be done as soon as possible and no later than seven days after the affected test or exam date.
Learning Continuity
In the event of an unexpected disruption, we undertake to maintain the continuity and standard of teaching and learning in all your courses throughout the year. If there are unexpected disruptions the University has contingency plans to ensure that access to your course continues and course assessment continues to meet the principles of the University’s assessment policy. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator/director, and if disruption occurs you should refer to the university website for information about how to proceed.
Student Charter and Responsibilities
The Student Charter assumes and acknowledges that students are active participants in the learning process and that they have responsibilities to the institution and the international community of scholars. The University expects that students will act at all times in a way that demonstrates respect for the rights of other students and staff so that the learning environment is both safe and productive. For further information visit Student Charter https://www.auckland.ac.nz/en/students/forms-policies-and-guidelines/student-policies-and-guidelines/student-charter.html.
Disclaimer
Elements of this outline may be subject to change. The latest information about the course will be available for enrolled students in Canvas.
In this course students may be asked to submit coursework assessments digitally. The University reserves the right to conduct scheduled tests and examinations for this course online or through the use of computers or other electronic devices. Where tests or examinations are conducted online remote invigilation arrangements may be used. In exceptional circumstances changes to elements of this course may be necessary at short notice. Students enrolled in this course will be informed of any such changes and the reasons for them, as soon as possible, through Canvas.