Calculus: Introduction



Overview

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.)

This course combines online study with a weekly 1-hour live webinar led by your tutor. Find out more about how our short online courses are taught.

Programme details

This course begins on the 15 Sep 2025 which is when course materials are made available to students. Students should study these materials in advance of the first live meeting which will be held on 22 Sep 2025, 6:30-7:30pm (UK time).

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

Certification

Credit Application Transfer Scheme (CATS) points 

Coursework is an integral part of all online courses and everyone enrolled will be expected to do coursework. All those enrolled on an online courses are registered for credit and will be awarded CATS points for completing work at the required standard.

See more information on CATS points

Digital credentials

All students who pass their final assignment will be eligible for a digital Certificate of Completion. 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. 

Please note that assignments are not graded but are marked either pass or fail. 

Credit Application Transfer Scheme (CATS) points 

Coursework is an integral part of all online courses and everyone enrolled will be expected to do coursework. All those enrolled on an online courses are registered for credit and will be awarded CATS points for completing work at the required standard.

See more information on CATS points

Digital credentials

All students who pass their final assignment will be eligible for a digital Certificate of Completion. 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. 

Please note that assignments are not graded but are marked either pass or fail. 

Credit Application Transfer Scheme (CATS) points 

Coursework is an integral part of all online courses and everyone enrolled will be expected to do coursework. All those enrolled on an online courses are registered for credit and will be awarded CATS points for completing work at the required standard.

See more information on CATS points

Digital credentials

All students who pass their final assignment will be eligible for a digital Certificate of Completion. 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. 

Please note that assignments are not graded but are marked either pass or fail. 

Credit Application Transfer Scheme (CATS) points 

Coursework is an integral part of all online courses and everyone enrolled will be expected to do coursework. All those enrolled on an online courses are registered for credit and will be awarded CATS points for completing work at the required standard.

See more information on CATS points

Digital credentials

All students who pass their final assignment will be eligible for a digital Certificate of Completion. 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. 

Please note that assignments are not graded but are marked either pass or fail. 

Fees

Description Costs
Course Fee £360.00

Funding

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

Tutor

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

  • To 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.
  • 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

Learning takes place on a weekly schedule. At the start of each weekly unit, students are provided with learning materials on our online platform, including one hour of pre-recorded video, often supplemented by guided readings and educational resources. These learning materials prepare students for a one-hour live webinar with an expert tutor at the end of each weekly unit which they attend in small groups. Webinars are held on Microsoft Teams, and provide the opportunity for students to respond to discussion prompts and ask questions. The blend of weekly learning materials that can be worked through flexibly, together with a live meeting with a tutor and their peers, maximise learning and engagement through interaction in a friendly, supportive environment.

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

You will be set independent formative and summative work for this course. Formative work will be submitted for informal assessment and feedback from your tutor, but has no impact on your final grade. The summative work will be formally assessed as pass or fail.

Application

Please use the 'Book' or 'Apply' button on this page. Alternatively, please complete an Enrolment form for short courses | Oxford University Department for Continuing Education

 

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.

The Department's short online courses are taught at FHEQ Level 4, i.e. first year undergraduate level. FHEQ level 4 courses require approximately 10 hours study per week, therefore a total of about 100 study hours.

English Language Requirements

We do not insist that applicants hold an English language certification, but warn that they may be at a disadvantage if their language skills are not of a comparable level to those qualifications listed on our website. If you are confident in your proficiency, please feel free to enrol. For more information regarding English language requirements please follow this link: https://www.conted.ox.ac.uk/about/english-language-requirements

Terms & conditions for applicants and students

Information on financial support