Vector Calculus & Electromagnetics

Resources for Vector Calculus & Electromagnetics聽- for more information about the courses, please see聽course outlines.

MLC Drop-In Centre

Students from Vector Calc & Electromag聽can use the drop-in centre, but we will give priority to first year students. If you see every other table has students, then we would appreciate it if you found another place to sit so that there is room for new students.

Please note that not every staff member in the MLC knows all of the content in Vector Calc & Electromag, there will be times when we can only give general study advice for this course.

Assumed knowledge

Resources that you can use to help you revise assumed knowledge for Vector Calc & Electromag. The various topics in the course are taught assuming you know this information.

  • Techniques of integration

    A very large part of MCC concerns integration. You need to be really comfortable with performing definite integrals. These resources from Maths IA should help you revise.

    These three PDF handouts are useful for doing different types of integration:

    This PDF document contains many written worked examples of various techniques of integration.

    This seminar was given in Sem 1 2021 and covered the techniques of integration (substitution, by parts, trig substitution, partial fractions and upper and lower sums).

    This seminar was given in Sem 1 2014 and covered the entire of the techniques of integration topic. (Note that the seminar also includes reduction formulas and numerical integration,聽which are no longer in Maths 1A.)

  • Complex numbers

    The end of MCC concerns the calculus of complex numbers, which requires you to know about complex numbers first!

    In Semester 1 2017, the MLC gave a revision seminar on Complex Numbers to Maths 1M students. In this seminar, David covered where the complex numbers fit in the families of number, and how the various operations relate to the three main representations of complex numbers.聽

  • Vector algebra

    In MCC, it's important to be able to represent objects like curves, lines and planes with vectors and parameters. It's also important to know how to do vector calculations like the dot and cross product.聽These resources made for Maths 1M will help to revise and prepare.

    This seminar in聽Semester 1 2015 was聽on vectors. The seminar covered the major things you can calculate with vectors (such as dot and cross product, projections and angles), and doing geometry proofs with vectors, and also briefly discussed equations of lines and planes. Note I mentioned a list of versions of the right hand rule, which is linked below.

    This seminar in Semester 1 2016 was on curves. David discussed what a curve is, converting between parametric and Cartesian form, and finding tangents to curves.

    This seminar in Semester 2 2020 started with a section on dot and cross products of vectors in 3D.

  • Multivariable calculus

    MCC II picks up roughly where Maths 1B calculus left off, so it might help to revise the multivariable calculus content in Maths IB.

    In this seminar from Summer Semester 2019,聽David spent a lot of time talking about different ways to imagine multivariable functions and their derivatives.

    This seminar from 2012 covers domains, ranges, partial derivatives, maxima and minima in multivariable calculus..

    This seminar from 2013 covered directional derivatives and tangent planes in multivariable (3D) calculus.

Vector Calculus

The course Vector Calculus & Electromagnetics was new in 2020, and so there are no revision seminars聽designed specially for this course. However, the old course Engineering Mathematics IIB, and the course for Maths/Physics students Multivariable & Complex Calculus II have similar content, so the revision seminars聽made for those courses should be helpful.

In Semester 1 2019, David did聽a revision seminar on integrals for students in MCC II. He talked about each of the nine kinds of integrals in the course, comparing their features and finding where the various integral theorems connect them together. He finished off with a couple of examples of using the theorems to make some integrals easier. (David thinks this is one of his best revision seminars for any course ever.) He also turned his paper-and-play-dough diagram from the seminar into a handout, which is linked below.

In Semester 1 2021. David gave a revision seminar for MCC II where he discussed setting up and doing integrals in order to calculate volumes.

In Semester 1 2018,聽David did a revision seminar for MCC II where he聽talked about path, surface and volume integrals, working through an exam question involving all of them. He then finished off with a description of parameterisations of various curves and surfaces (starting at 1h40m30s).

In Semester 1 2017, David did a revision seminar for MCC II which聽contained examples of doing the path, surface and volume integrals that are mentioned in Stokes' Theorem and Gauss' Divergence Theorem.

In Semester 2, 2013,聽David gave a revision seminar on Vector Calculus including different types of derivatives and integrals (and some aspects of Complex Calculus) to Engineering Maths IIB students.聽

In Semester 2 2018, David did a revision seminar for Engineering Maths IIB students, whose middle section (starting at 25m46s)聽consisted of several examples of exam-style questions on multivariable integrals.

In Semester 2, 2019, David gave a revision seminar for Engineering Maths IIB where the last section (starting at 1h17m45s) was about line and flux integrals.

In 2017, David did a fully worked example for an engineering course about calculating the integrals involved to verify Green's Theorem in the plane. (Note this version of Green's Theorem might be slightly different to the one presented in your course, but the integral techniques are the same.)聽