Introduction to Calculus


Classical mechanics, the basis for Newtonian physics, and much of engineering, are founded on and made rigorous by calculus. This is a gateway course to most of the mathematically rigorous intellectual disciplines. At its centre are two perspicuous geometry problems: what straight line segment best approximates a small portion of a given curve and how can one define the area of a region if its boundary is a curve and thus cannot be paved over exactly with rectangular tiles no matter how tiny? Astonishingly enough these problems are not unrelated – roughly speaking each is the 'reverse' of the other, though it takes some time to explain what that means and how it happens.

(Mysterious hint: The word "curve" appears in the statement of each of the problems, but there are two curves under consideration, one for the first problem and a different one for the second.)

Programme details

Course starts: 15 Jan 2024

Week 0: Course orientation

Week 1: Graphing and limits

Week 2: Differentiation

Week 3: More differentiation

Week 4: Max-min/optimisation problems

Week 5: Integration and areas bounded by curves

Week 6: More Integration

Week 7: Applications of the calculus, optimisation of functions of two or more independent variables

Week 8: More integration

Week 9: Partial derivatives and the Lagrange multiplier

Week 10: Miscellanea

Digital Certification

To complete the course and receive a certificate, you will be required to attend and participate in at least 80% of the live sessions on the course and pass your final assignment. Upon successful completion, you will receive a link to download a University of Oxford digital certificate. Information on how to access this digital certificate will be emailed to you after the end of the course. The certificate will show your name, the course title and the dates of the course you attended. You will be able to download your certificate or share it on social media if you choose to do so.


Description Costs
Course Fee £257.00
Take this course for CATS points £10.00


If you are in receipt of a UK state benefit, you are a full-time student in the UK or a student on a low income, you may be eligible for a reduction of 50% of tuition fees. Please see the below link for full details:

Concessionary fees for short courses


Dr Vasos Pavlika

Dr Vasos Pavlika is Associate Professor (Education) at University College London, he also teaches Mathematics and Statistics at the LSE (University of London), as well as Online at: SOAS, University of London (Mathematical Economics), Goldsmiths College (Computing and Data Science), University of London and the Open University (Applied Mathematics). He has been a lecturer in the Department for Continuing Education, Oxford since 2004. Vasos is the Director of Studies in the Physical Studies in the Department for Continuing Education, Oxford as well a tutor in the Department of Continuing Education at the University of Cambridge.

Course aims

Open students' eyes to the foundations of rigorous quantitative science and students' ears to the vocabulary in which it is expressed. Provide experience working out basic problems formulated in this vocabulary.

Course Objectives:

  • To learn how to differentiate, how to integrate, when to do either, and how to interpret the results.
  • Learn how to find optimal solutions. 

Teaching methods

Students will have access to a pre-recorded lecture to be watched in advance of the weekly online session.

Learning outcomes

By the end of this course students will be expected to:

  • be able to differentiate and integrate non-exotic expressions, interpret the results, and invoke the standard theorems when they apply.

After attending this course, students will know how to:

  • differentiate partially;
  • determine definite and indefinite integrals;
  • solve simple 1st order ordinary differential equations of the separable of variable type.

Assessment methods

Short tests - A set of exercises (an assignment) will be set in week 5 which will constitute the assessment for the award of the 10 CATs points. Alternatively the students can submit a portfolio of exercises which will arise from solving the homework exercises that will be set at the end of each week. 

Students must submit a completed Declaration of Authorship form at the end of term when submitting your final piece of work. CATS points cannot be awarded without the aforementioned form - Declaration of Authorship form


We will close for enrolments 7 days prior to the start date to allow us to complete the course set up. We will email you at that time (7 days before the course begins) with further information and joining instructions. As always, students will want to check spam and junk folders during this period to ensure that these emails are received.

To earn credit (CATS points) for your course you will need to register and pay an additional £10 fee per course. You can do this by ticking the relevant box at the bottom of the enrolment form or when enrolling online.

Please use the 'Book' or 'Apply' button on this page. Alternatively, please complete an enrolment form (Word) or enrolment form (Pdf).

Level and demands

GCSE mathematics, algebra, and graphing experiences.

Before attending this course, prospective students will know:

  • what a linear equation is;
  • what a quadratic equation is and how to solve it;
  • how to sketch polynomial functions.

Students who register for CATS points will receive a Record of CATS points on successful completion of their course assessment.

To earn credit (CATS points) you will need to register and pay an additional £10 fee per course. You can do this by ticking the relevant box at the bottom of the enrolment form or when enrolling online.

Coursework is an integral part of all weekly classes and everyone enrolled will be expected to do coursework in order to benefit fully from the course. Only those who have registered for credit will be awarded CATS points for completing work at the required standard.

Students who do not register for CATS points during the enrolment process can either register for CATS points prior to the start of their course or retrospectively from the January 1st after the current full academic year has been completed. If you are enrolled on the Certificate of Higher Education you need to indicate this on the enrolment form but there is no additional registration fee.

Most of the Department's weekly classes have 10 or 20 CATS points assigned to them. 10 CATS points at FHEQ Level 4 usually consist of ten 2-hour sessions. 20 CATS points at FHEQ Level 4 usually consist of twenty 2-hour sessions. It is expected that, for every 2 hours of tuition you are given, you will engage in eight hours of private study.

Credit Accumulation and Transfer Scheme (CATS)