MATHS 208 : General Mathematics 2
Science
2025 Summer School (1250) (15 POINTS)
Course Prescription
Course Overview
The course explores calculus, linear algebra, and differential equations in depth, and the connections between the areas are indicated. The course is designed to provide an understanding of many of the mathematical concepts and methods involved in more advanced subjects in Economics, Finance, Statistics, Operations Research, Computer Science, and many other areas. The course also serves as suitable preparation for MATHS 120/130, and thus can be used as a pathway into the mathematics major.
This course could be of interest to students majoring in Economics, Finance, Statistics, Computer Science, Data Science, Operations Research, Chemistry, and other science and commerce majors. Skills and knowledge gained after completion of this course could be beneficial to professionals from a variety of sectors, in particular, those that experience fast growth driven by the new technological advances.
Course Requirements
Capabilities Developed in this Course
| Capability 1: | People and Place |
| Capability 2: | Sustainability |
| Capability 3: | Knowledge and Practice |
| Capability 4: | Critical Thinking |
| Capability 5: | Solution Seeking |
| Capability 6: | Communication |
| Capability 7: | Collaboration |
| Capability 8: | Ethics and Professionalism |
Learning Outcomes
- Compute partial derivatives, directional derivatives, and gradients and use them to solve problems in multivariable calculus. (Capability 3, 4 and 5)
- Apply convergence tests to study sequences, series, and power series, as well as, compute and manipulate Taylor series and Taylor polynomials. (Capability 3, 4 and 5)
- Use the theory of vector spaces to solve problems involving linear algebra. (Capability 3, 4 and 5)
- Use integration techniques (e.g., separation of variables, integrating factors, and characteristic equations) to solve differential equations and systems of differential equations, as well as, apply numerical and qualitative techniques to study first order differential equations. (Capability 3, 4 and 5)
- Use mathematical notation and terminology logically and correctly. (Capability 2, 4 and 6)
- Engage in group discussions and critical interactions. (Capability 1, 3, 6, 7 and 8)
Assessments
| Assessment Type | Percentage | Classification |
|---|---|---|
| Coursework | 20% | Individual Coursework |
| Test | 20% | Individual Test |
| Quizzes | 10% | Individual Coursework |
| Final Exam | 50% | Individual Examination |
| 4 types | 100% |
| Assessment Type | Learning Outcome Addressed | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | |||||
| Coursework | ||||||||||
| Test | ||||||||||
| Quizzes | ||||||||||
| Final Exam | ||||||||||
A minimum of 35% on the final exam is required to pass the course.
Key Topics
- Multivariable functions, the chain rule, implicit differentiation, directional derivative, Hessian matrix, constrained optimisation.
- Sequences, series, Taylor polynomials, power series, integration using substitution and integration by parts.
- Linear system of equations, vector spaces, subspace, linear independence, bases, dimension.
- Inner products, orthogonality, the Gram-Schmidt process, least-square solutions.
- Eigenvalues, eigenvectors, diagonalisation, Markov chains and dynamical systems.
- First order differential equations, system of first order homogeneous linear differential equations, second order homogeneous linear differential equations.
Special Requirements
This course has one test, which will be conducted in the evening outside of normal lecture hours.
Workload Expectations
This course is a standard 15-point course and students are expected to spend 20 hours per week involved in each 15-point course that they are enrolled in during the summer semester. For each week of this course, you can expect 6 hours of lectures, 2 hours of tutorial, 6 hours of reading and thinking about the content and 6 hours of work on assignments and/or test preparation.
Delivery Mode
Campus Experience
Attendance is expected for scheduled events including Lectures and Tutorials.
Lectures will be available as recordings. There will not be live online events.
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.
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, tests and examinations 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. A student's assessed work may be reviewed against electronic source material using computerised detection mechanisms. Upon reasonable request, students may be required to provide an electronic version of their work for computerised review.
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 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.
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 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.