# Mathematics and Physics - 2nd Year

The core modules in the second year complete the foundations of analysis and differential equations. It also introduce some of the most fundamental ideas in physics. The implications of some of these ideas will be explored in the third and fourth years.

You will have to choose at least 30% from lists of options. There is a lot on offer particularly in mathematics and it is unlikely that you could cope with everything even if you wanted to. As a result, you will need to think carefully about your choice of options. The mathematics options allow you to continue with algebra and geometry and to study some advanced analysis. The picture with regard to physics options is slightly different. The large part of physics which you leave out, namely laboratory work, is not available. As a result you have room to cover most of the mainstream areas of physics.

#### Aims

- To continue the training in Real Analysis required by future mathe0matics courses
- To teach mathematical techniques and their applications in applied mathematics and physics including: Vector Calculus, Fourier methods, Separation of Variables and Complex Variable Theory
- To teach concepts in the three areas of fundamental physics: Electromagnetism, Quantum Mechanics and Statistical Mechanics
- To help students identify their talents and interests and guide each student towards an appropriate combination of modules
- To encourage initiative, self-reliance and the development of transferable skills in communication, problem-solving and computing

#### Learning Outcomes

At the end of the second year, you should

- Be familiar with some important theorems on integration, convergence of sequences of functions.
- Know how to use Fourier methods, separation of variables, results from vector analysis (divergence and Stokes' theorem in particular) and complex analysis
- Have a good working understanding of the principles of quantum mechanics, statistical mechanics and electromagnetism
- Have studied further topics in mathematics and physics including fluid mechanics