Short course
Calculus: Introduction
Course status:
Applications being accepted
Location:
Online
Dates:
13/01/2027 - 24/03/2027
Study format:
Online - live
Fees:
£430.00
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.)
Book this course
Book your place online using the button below.
Programme details
This course begins on the 13 Jan 2027 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 20 Jan 2027, 6:00-7:00pm (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
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.
This course is offered at FHEQ level 4 (first year undergraduate level), and you will be expected to engage in independent study in preparation for your assignments. Our 10-week Short Online Courses come with an expected total commitment of 100 study hours.
English Language Requirements
We do not insist that applicants hold an English language certification, but we 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 see here.
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.
IT requirements
Any standard web browser can be used to access course materials on our virtual learning environment, but we recommend Google Chrome. We also recommend that students join the live webinars on Microsoft Teams using a laptop or desktop computer rather than a phone or tablet due to the limited functionality of the app on these devices.
Programme details
This course begins on the 13 Jan 2027 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 20 Jan 2027, 6:00-7:00pm (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
Teaching methods
This course takes place over 10 weeks, with a weekly learning schedule and weekly live webinar held on Microsoft Teams. Shortly before a course commences, students are provided with access to an online virtual learning environment, which houses the course content, including video lectures, complemented by readings or other study materials. Any standard web browser can be used to access these materials, but we recommend Google Chrome. Working through these materials over the course of the week will prepare students for a weekly 1-hour live webinar you will share with your expert tutor and fellow students. All courses are structured to amount to 100 study hours, so that on average, you should set aside 10 hours a week for study. Although the course finishes after 10 weeks, all learning materials remain available to all students for 12 months after the course has finished.
All courses are led by an expert tutor. Tutors guide students through the course materials as part of the live interactions during the weekly webinars. Tutors will also provide individualised feedback on your assignments. All online courses are taught in small student cohorts so that you and your peers will form a mutually supportive and vibrant learning community for the duration of the course. You will learn from your fellow students as well as from your tutor, and they will learn from you.
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.
Dr Niccolò Salvatori
Niccolò Salvatori completed a Ph.D. in Pure Mathematics at KCL in 2017 on logarithmic structures of Topological Quantum Field Theories and has been teaching for the Department of Mathematics at LSE since 2016.
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.
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.
This course is offered at FHEQ level 4 (first year undergraduate level), and you will be expected to engage in independent study in preparation for your assignments. Our 10-week Short Online Courses come with an expected total commitment of 100 study hours.
English Language Requirements
We do not insist that applicants hold an English language certification, but we 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 see here.
Fees
| Description | Costs |
|---|---|
| Course Fee | £430.00 |
Module code: O26P767MAZ
Please use the ‘Book now’ button on this page. Alternatively, please complete an enrolment form.