MATHS 130 : Calculus


2020 Semester One (1203) (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+ or higher 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 or equivalent

Course Overview

Maths 130, alongside Maths 120 and Maths 162, forms a foundation for further study in mathematics at the University of Auckland. It is essential for students intending to major in Mathematics, Applied Mathematics, Statistics, Physics, or for anyone who wants a strong mathematical component to their degree.  

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.  

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. Be able to write, analyse and solve problems involving limits, derivatives and integrals. (Capability 1, 2, 3 and 5)
  3. Understand and 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. Understand and be able to use the fundamental theorem of calculus. (Capability 1, 2 and 5)
  6. Engage 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
Final Exam 50% Individual Examination
Test 20% Individual Test
Assignments 15% Individual Coursework
Tutorials 5% Individual Coursework
Team tasks 5% Group Coursework
Quizzes 5% Individual Coursework
Assessment Type Learning Outcome Addressed
1 2 3 4 5 6 7
Final Exam
Team tasks

A mark of at least 35% in the exam is required to pass the course.

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)

Learning Resources

A coursebook is available on Canvas and for purchase at the bookshop and/or student resource centre.

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, a 1 hour tutorial, 3 hours of reading and thinking about the content and 3 hours of work on assignments and/or test preparation.

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 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.

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.

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 at

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.

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.

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.

Published on 11/01/2020 03:09 p.m.