MATHS 130 : Calculus


2023 Semester One (1233) (15 POINTS)

Course Prescription

A foundation for further mathematics courses, essential for students intending to major in Mathematics, Applied Mathematics, Statistics, Physics, or who want a strong mathematical component to their degree. Develops skills and knowledge in calculus of functions of a single variable. Recommended preparation: Merit or excellence in the Differentiation Standard 91578 at NCEA Level 3. Prerequisite: MATHS 208, or B- or higher in MATHS 108, or A- or higher in MATHS 110, or A+ in MATHS 102, or at least 18 credits in Mathematics at NCEA Level 3 including at least 9 credits at merit or excellence, or B in CIE A2 Mathematics, or 5 out of 7 in IB Mathematics: Analysis and Approaches (SL or HL)

Course Overview

MATHS 130 is a rigorous course in single-variable calculus and is an introduction to mathematical thinking and problem-solving. Students who successfully complete this course will be able to understand and construct logical mathematical arguments, and will be comfortable reading and using mathematical language and notation. In particular, they will be capable of using the language of sets and functions to describe mathematical objects, know how to calculate limits rigorously, understand how to differentiate and integrate functions and the theorems behind techniques for doing so, and will be able to use these operations to optimise and study the behaviour of a wide variety of objects.  

Course Requirements

No pre-requisites or restrictions

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
Capability 6: Social and Environmental Responsibilities
Graduate Profile: Bachelor of Science

Learning Outcomes

By the end of this course, students will be able to:
  1. Display mathematical competency in the topics covered in the syllabus (i.e., logic and calculus). (Capability 1, 2, 3 and 5)
  2. Demonstrate the skill of writing, analysing and solving problems involving limits, derivatives and integrals. (Capability 1, 2, 3 and 5)
  3. Display the skill of writing logical and mathematical arguments, using appropriate language and sufficient detail and structure. (Capability 1, 2 and 5)
  4. Display the ability to think critically about logical arguments and use basic techniques to solve problems. (Capability 1, 2, 3 and 5)
  5. Demonstrate an understanding of the fundamental theorem of calculus and its applications. (Capability 2 and 5)
  6. Develop the ability to work in a group and communicate mathematical ideas to others. (Capability 1, 4 and 6)
  7. Demonstrate an understanding of the wider social, economical and environmental context to which the techniques learnt apply. (Capability 1 and 6)


Assessment Type Percentage Classification
Tests 20% Individual Coursework
Assignments 20% Individual Coursework
Quizzes 5% Individual Coursework
Tutorials 5% Group Coursework
Final Exam 50% Individual Coursework
Assessment Type Learning Outcome Addressed
1 2 3 4 5 6 7
Final Exam


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

For further information on the Tuākana Maths programme, please visit

Key Topics

  • Set theory and proofs (2 weeks)
  • Functions (2 weeks)
  • Limits (2 weeks)
  • Sequences (1 week)
  • Differentiation (3 weeks)
  • Integration (2 weeks)

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

  • Lectures will 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.

  • There will be a course book for MATHS 130, which can be downloaded on Canvas or purchased from the Student Resource Centre. 
  • There will also be Canvas links to Khan academy tutorial videos relevant to the course content (and some prerequisites).

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.

It seems that adding some more straightforward and very elementary examples to the tutorials would benefit some students. This will be attended to.

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.


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 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


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.

Published on 07/03/2023 02:21 p.m.