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Section 1.1 A reminder of vector calculus
Figure 1.1.1. George Green’s monumental work on electricity and magnetism, making use of many new concepts in vector calculus, 1828. During the first week, we will provide a very brief review of some of the necessities that you may require in terms of vector calculus. Many of you will have taken the MA20223 Vector Calculus and Partial Differential Equations module, and a version of the 2024-25 lecture notes has been updated for easy reference
on Moodle .
We will assume that you are familiar enough with how to interpret many of the vector calculus identities found in Sec. 10 of the University of Bath book of tables, which can be access on Moodle or
via this link .
In general, over the next few weeks, you will want to be familiar with recalling/looking up concepts like:
The use of identities like div curl = 0 and curl grad = 0. Some of these are found on p.24 of the above tables.
The notion of line integrals, surface integrals, and volume integrals.
The divergence theorem and Stokes’ theorem. (p.24)
Conversion of vector operations and integrals into different coordinate systems (p.25)
