Multivariable Calculus is one of the most powerful and useful areas of Mathematics. The primary goal of the course is to extend the concepts of differentiation and integration from Single Variable Calculus to 2,3, and n dimensions. We will discover that this leads to a rich and comprehensive theory with many new ideas that only reveal themselves in the higher dimensional setting. The objects of study will involve curves, surfaces, and vector fields. As a unifying theme, we will see how many of the biggest theorems of multivariable and vector calculus going all the way up to Stokes’ Theorem and the Divergence Theorem build on the same basic idea behind the Fundamental Theorems of Calculus.
Multivariable Calculus Masterclass with Dr Trefor
Please note these courses are advertised in UK Time and students will need to consider their own local time zones for Live Webinars before enrolling.
Overview
This course combines online study with a weekly 45 minutes live webinar led by your tutor. Find out more about how our short online courses are taught.
Programme details
Week 1: Curves including Tangents, Arclength, and Curvature
Week 2: Limits, Continuity, Partial Derivatives, and Differentiation of Multivariable Functions
Week 3: Differentiation Tools including Chain Rule, Directional Derivatives, Tangent Planes, and Extreme Values
Week 4: Multivariable Integration including Cartesian, Cylindrical, Spherical, and Jacobians
Week 5: Reading Week (no work set and no live class)
Week 6: Line Integrals and Vector Fields
Week 7: Fundamental Theorem of Line Integrals and Green’s Theorem
Week 8: Surface Integrals
Week 9: Stokes Theorem, Divergence Theorem, and a unified view of Vector Calculus
Recommended reading
All course material including video lectures will be included within the online course.
Fees
| Description | Costs |
|---|---|
| Course Fee | £495.00 |
Tutor
Trefor Bazett
Trefor is an award winning teaching professor in mathematics at the University of Victoria, in Canada. Trefor also runs math-focused ‘Dr. Trefor’ YouTube channel with over a half million subscribers. Trefor received his PhD from the University of Toronto in the field of algebraic topology.
Course aims
To provide a mathematically rigorous treatment to the subject of Multivariable and Vector Calculus.
Teaching methods
This course takes place over 9 weeks (with an additional one week “reading break” in the middle), 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. Working through these materials over the course of the week will prepare students for a weekly 45 minute live webinar you will share with your expert tutor and fellow students. All courses are structured to amount to 80 study hours, so that on average, you should set aside 10 hours a week for study. Although the course finishes after 8 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 (maximum 12) 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 the course students will be expected to:
- Apply techniques of differentiation and integration in the context of curves, surfaces, and vector fields.
- Interpret and compute geometric quantities related to multivariable and vector calculus
- Explain and apply the major theorems of Vector Calculus such as the Fundamental Theorem for Line Integrals, Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem, highlighting their unifying themes.
Assessment methods
Students must attend at least 75% of live classes to be eligible for a digital badge.
Application
Please use the 'Book now' button on this page. Alternatively, please complete an enrolment form.
Level and demands
Familiarity with Single Variable Calculus is presumed. Students should be able to understand the core ideas behind derivatives and integrals. In this course we will build on those Single Variable concepts in higher dimensional settings.
You will be expected to engage in independent study in preparation for your assignments and for the weekly webinar. This may take the form, for instance, of reading and analysing set texts, responding to questions or tasks, or preparing work to present in class. Our 8-week Short Online Courses come with an expected total commitment of 80 study hours, including those spent in live webinars.
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.