### Week 2: Extracurricular Class “Calculus of Variations in the smallest possible nutshell”

The calculus of variations appears in innumerable applications in physics – mechanics, quantum mechanics, relativity, electromagnetism, and elsewhere – and has beautiful applications in statistics, theoretical neuroscience, and mathematical biology. In the first hour of this class, we will think about the idea of functionals and study the key ways of minimizing them in practice. We will then apply the methods of the calculus of variations to a number of scientific problems in different fields. The aim is to treat the topic in a direct, applicable, and interactive way.

Mark Chonofsky is a DPhil student with the Systems Biology DTC and a former mathematics teacher.

**When: Friday 27th January 2017, 4pm – 6pm**

**Where: Lindermann Lecture Theatre, Clarendon Laboratory**

### Week 3: “Differential Forms in R^n”, Extracurricular Class by Andre Lukas, Part I

Differential forms have long been a standard tool of modern theoretical physics, with applications in many areas of basic physics, such as Classical Mechanics and Electrodynamics, as well as in areas of contemporary research. Prof Andre Lukas will give a basic introduction to differential forms on R^n and sub-manifolds of R^n and explore their relation to traditional vector calculus. As an application to physics, he will discuss the formulation of Electrodynamics in terms of differential forms.

**When: Friday of 3rd week (3rd February), 4pm-6pm
**

**Where: Lindemann Lecture Theatre**

### Week 4: “Differential Forms in R^n”, Extracurricular Class by Andre Lukas, Part II

Differential forms have long been a standard tool of modern theoretical physics, with applications in many areas of basic physics, such as Classical Mechanics and Electrodynamics, as well as in areas of contemporary research. Prof Andre Lukas will give a basic introduction to differential forms on R^n and sub-manifolds of R^n and explore their relation to traditional vector calculus. As an application to physics, he will discuss the formulation of Electrodynamics in terms of differential forms.

**When: Friday of 4th week (10th February), 4pm-6pm
**

**Where: Lindemann Lecture Theatre**

### Week 6: “Differential Forms in R^n”, Extracurricular Class by Andre Lukas, Part III

In the first two lectures Prof Andre Lukas has introduced differential forms in R^n at a basic level. We have seen that the calculus of differential forms in R^3 contains the standard vector calculus and we have discussed symplectic manifolds as a mathematical formulation of Classical Mechanics. In the last lecture, he will introduce the formulation of Electromagnetism and General Relativity in terms of differential forms.

**When: Friday of 6th week (24th February), 4pm-6pm
**

**Where: Lindemann Lecture Theatre**

### Week 7: “Spherical Astronomy”, Extracurricular Class by Sandor Kruk

How long does it take to fly from London to New York? At what time will the Sun rise tomorrow? Come along to the OUPS extracurricular class and discover one of the oldest branches of astronomy! We will cover concepts in spherical trigonometry and positional astronomy which are frequently used by astronomers, but are not taught in school. We will also solve some interesting questions from the International Astronomy Olympiads on these topics, so make sure you bring your calculators!

**When: Friday of 7th week (3rd March), 4pm-6pm
**

**Where: Lindemann Lecture Theatre**