CHRIS HALCROW

Teaching

I have taught courses from part IB and part III of the maths tripos at Cambridge. Below, you'll find some resources for each course. If you have any questions about the material, or about maths at Cambridge more generally, please feel free to get in touch. My e-mail is cjh95@cam.ac.uk.

Part IB

Methods

This course teaches some key methods for solving differential equations and starts looking at some deeper issues such as: when can you actually solve a problem? How do boundary conditions change things? And, can we classify equations?

Variational Principles

What surface minimises area, given certain constraints? What route does light take through a medium? What shape is a soap film and why? These questions can be answered using the variational method which we'll learn in this course. It turns out that pretty much all physics problems can be formulated variationally so it's a good things to know about!

Electromagnetism

In this course we'll learn about electromagnetism by studying Maxwell's equations. Although you can write them all down in a couple of lines they contain an awful lot of physics. This is also the first time we really get to study a field theory which are the theories that underpin all of modern physics.

Complex Methods

Certain line integrals in the complex plane are easy thanks to some amazing theorems which we'll learn in this course. We'll then try and see what we can do with our newly found integration powers. Namely, we'll discover lots of solutions to Laplace's equation, do some hard looking real-valued integrals, solve some new differential equations and find the value to some cute infinte sums.

There is also a course in Lent Term called Complex Analysis. Here, you'll do things a little slower and learn the proofs of the main theorems but apply your knowledge to fewer problems. So you have to decide whether you'd prefer more proofs or more examples. Don't worry too much, you'll have no trouble learning the stuff you miss out on by reading the book I mention below.