MATHS 130 : Calculus


2021 Semester One (1213) (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; more generally, along with Maths 120 it is an introduction to mathematical thinking and problem-solving. Students who successfully complete this course will be able to understand and write 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.  

MATHS 130 is a prerequisite for MATHS 250 and must be taken by all students majoring in mathematics. 

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. Capable to write, analyse and solve problems involving limits, derivatives and integrals. (Capability 1, 2, 3 and 5)
  3. Be able to write logical and mathematical arguments, using appropriate language and sucient detail and structure. (Capability 1, 2 and 5)
  4. Think critically about logical arguments, and use basic techniques to solve problems. (Capability 1, 2, 3 and 5)
  5. Be able to use the fundamental theorem of calculus. (Capability 2 and 5)
  6. Engaging in group work and communicating mathematical ideas to others. (Capability 1, 4 and 6)
  7. Be aware of the wider social, economical and environmental context to which the techniques learnt apply. (Capability 1 and 6)


Assessment Type Percentage Classification
Assignments 30% Group & Individual Coursework
Test 15% Individual Test
Final Exam 55% Individual Examination
Assessment Type Learning Outcome Addressed
1 2 3 4 5 6 7
Final Exam


Māori and Pasifika students are encouraged to participate in the Maths Tuākana Programme and use their free drop-in tutorial sessions. 

Key Topics

Topics covered in Maths 130:

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

Special Requirements


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 3 hours of lectures and 1 hour tutorial per week. You should also allocate 3 hours of reading and thinking about the content and 3 hours on assignments and/or test per week.

Delivery Mode

Campus Experience

Attendance is expected at scheduled activities including tutorials to receive credit for components of the course.

Lectures will be available as recordings. Other learning activities including tutorials will not be available as recordings.

The course will include live online events including tutorials.

Attendance on campus is required for the test/exam.

Learning Resources

There will be a course book for MATHS 130 and it 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.

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.

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.


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


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 26/01/2021 09:28 a.m.