MATHS 270 : Numerical Computation
Science
2023 Semester Two (1235) (15 POINTS)
Course Prescription
Course Overview
MATHS 270 introduces the methods frequently used to find numerical solutions to problems that arise in Applied Mathematics. The topics covered include methods for solving linear and nonlinear algebraic equations, interpolation, differentiation, integration and the numerical solution of ordinary differential equations. The numerical calculations in the course are performed using MATLAB. MATHS 270 is a required course for the major in Applied Mathematics. After successfully completing MATHS 270, students will be well prepared for the Stage III courses in Applied Mathematics that require computational techniques.
Course Requirements
Capabilities Developed in this Course
| Capability 1: | Disciplinary Knowledge and Practice |
| Capability 2: | Critical Thinking |
| Capability 3: | Solution Seeking |
| Capability 4: | Communication and Engagement |
| Capability 5: | Independence and Integrity |
Learning Outcomes
- Solve the types of problems covered in the course using standard numerical methods. (Capability 1, 2, 3, 4 and 5)
- Demonstrate how to check the accuracy of numerical solutions calculated using the methods. (Capability 1, 2, 3 and 4)
- Demonstrate the limitations of the methods. (Capability 1, 2 and 4)
- Analyse how finite precision affects the accuracy of numerical solutions. (Capability 1, 2 and 4)
- Demonstrate how to implement the methods in Matlab. (Capability 1 and 4)
Assessments
| Assessment Type | Percentage | Classification |
|---|---|---|
| Assignments | 20% | Individual Coursework |
| Tutorials | 10% | Group & Individual Coursework |
| Test | 20% | Individual Test |
| Final Exam | 50% | Individual Examination |
| 4 types | 100% |
| Assessment Type | Learning Outcome Addressed | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||||||
| Assignments | ||||||||||
| Tutorials | ||||||||||
| Test | ||||||||||
| Final Exam | ||||||||||
Tuākana
Tuākana Science is a multi-faceted programme for Māori and Pacific students providing topic specific tutorials,
one-on-one sessions, test and exam preparation and more. Explore your options at
https://www.auckland.ac.nz/en/science/study-with-us/pacific-in-our-faculty.html
https://www.auckland.ac.nz/en/science/study-with-us/maori-in-our-faculty.html
https://www.auckland.ac.nz/en/science/study-with-us/pacific-in-our-faculty.html
https://www.auckland.ac.nz/en/science/study-with-us/maori-in-our-faculty.html
Key Topics
- Numerical error and precision.
- Iterative methods for nonlinear scalar equations.
- Newton's method for systems of nonlinear algebraic equations.
- Interpolation.
- Quadrature and numerical differentiation.
- Initial value problems for ordinary differential equations.
- Direct methods for systems of linear algebraic equations.
- Iterative methods for systems of linear algebraic equations.
Special Requirements
You will either need a home computer to run MATLAB on, or you will need to be regularly on campus to make use of the University of Auckland's computer labs to work on any assignment tasks that use MATLAB.
You can find details about our computer labs here: https://www.library.auckland.ac.nz/services/it-essentials/computer-facilities
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 each week of this course, you can expect 3 hours of lectures, a 1-hour 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 for scheduled lectures, and it is required for scheduled tutorials, which includes working in groups.
- Lectures will be recorded, but we cannot guarantee that recordings of all lectures will be available. Lecture recordings should be used as an additional resource, not as a replacement for lectures. Tutorials will not be available as recordings.
- 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.
Recommended Text:
- Guide to Scientific Computing by Peter Turner. CRC Press, 2nd ed. (2000)
You must read the textbook, as the course makes extensive use of it. There are several copies of the text available for Short Loan in the General Library and the university library provides access to the e-book version. Alternatively, you can purchase you own copy from Ubiq or second-hand from online websites.
Maths 270 also makes use of the numerical computing environment and programming language MATLAB and the course includes teaching you how to code in MATLAB. You can download MATLAB for home use by following the instructions here: https://www.software.auckland.ac.nz/en/matlab.html
Student Feedback
During the course Class Representatives in each class can take feedback to the staff responsible for the course and staff-student consultative committees.
At the end of the course 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.
Your feedback helps to improve the course and its delivery for all students.
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.
Copyright
The content and delivery of content in this course are protected by copyright. Material belonging to others may have been used in this course and copied by and solely for the educational purposes of the University under license.
You may copy the course content for the purposes of private study or research, but you may not upload onto any third party site, make a further copy or sell, alter or further reproduce or distribute any part of the course content to another person.
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.
The delivery mode may change depending on COVID restrictions. Any changes will be communicated through Canvas.
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.