# MATHS 270 : Numerical Computation

## Science

### Course Prescription

Many mathematical models occurring in Science and Engineering cannot be solved exactly using algebra and calculus. Students are introduced to computer-based methods that can be used to find approximate solutions to these problems. The methods covered in the course are powerful yet simple to use. This is a core course for students who wish to advance in Applied Mathematics.

### 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

Prerequisite: MATHS 120 and 130, or 15 points from ENGGEN 150, ENGSCI 111, MATHS 108, 110, 150, 153, and 15 points from COMPSCI 101, 105, 130, INFOSYS 110, 120, MATHS 162, 199

### 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

By the end of this course, students will be able to:
1. Solve the types of problems covered in the course using standard numerical methods. (Capability 1, 2, 3, 4 and 5)
2. Demonstrate how to check the accuracy of numerical solutions calculated using the methods. (Capability 1, 2, 3 and 4)
3. Demonstrate the limitations of the methods. (Capability 1, 2 and 4)
4. Anlayse how finite precision affects the accuracy of numerical solutions. (Capability 1, 2 and 4)
5. 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
1 2 3 4 5
Assignments
Tutorials
Test
Final Exam

### Tuākana

Whanaungatanga and manaakitanga are fundamental principles of the Mathematics Tuākana programme which provides support for Māori and Pasifika students who are taking mathematics courses. The Tuākana Mathematics programme consists of workshops and drop-in times, and provides a space where you are able to work alongside our Tuākana tutors and other Māori and Pasifika students who are studying mathematics.

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

1. Numerical error and precision.
2. Iterative methods for nonlinear scalar equations.
3. Newton's method for systems of nonlinear algebraic equations.
4. Interpolation.
6. Initial value problems for ordinary differential equations.
7. Direct methods for systems of linear algebraic equations.
8. 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

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 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.

Attendance on campus is required for the test and exam.

The activities for the course are scheduled as a standard weekly timetable.

### Learning Resources

Recommended textbook

Guide to Scientific Computing

by Peter Turner

CRC Press, 2nd ed. (2000)

This textbook is very good, and the course makes extensive use of the book. You must read the textbook. There are several copies of the text available for Short Loan in the General Library; the university library also provides access the e-book version; or 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.

### Digital 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.

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.

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

### 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 .

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 your assessment is fair, and not compromised. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator, and if disruption occurs you should refer to the University Website for information about how to proceed.

• Level 1: Delivered normally as specified in delivery mode.
• Level 2: You will not be required to attend in person. All teaching and assessment will have a remote option.
• Level 3 / 4: All teaching activities and assessments are delivered remotely.

### 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 .

### 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 you may be asked to submit your 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. The final decision on the completion mode for a test or examination, and remote invigilation arrangements where applicable, will be advised to students at least 10 days prior to the scheduled date of the assessment, or in the case of an examination when the examination timetable is published.

Published on 22/12/2020 03:09 p.m.