We will explore the EU’s relationship to values in three main steps. First we look at the content of the values: where do these values come from, which fundamental rights exist, and who do they protect? The chapter also assesses how values inform and influence EU law and governance. What are the main mechanisms by which norms like human rights shape the way EU institutions and policies develop? Finally, we will consider the limits of EU values, both in terms of their application vis-à-vis national understandings of fundamental rights and in vis-à-vis other objectives of the EU, paying particular attention to the rule of law crisis of the 2020s.

The creation of an internal market that transcends all Member States has without doubt been the EU’s priority in the last sixty years. Conceptualising Europe as a market, however, requires a careful appreciation of how its economic objectives and its political objectives intersect. This chapter will focus on exactly this. We analyse what the different available methods of market integration, and their subsequent implications, tell us about the nature of the EU’s market. Which institutions have power, and why? What is the balance between economic interests and other values, and is that balance appropriate? In this chapter, we analyse the many parts to the puzzle that is the internal market. We will then focus on the two main regulatory techniques of the internal market: positive integration, through which the EU re-regulates the European market by the creation of new legislation and negative integration, which takes place where national rules governing the market are declared inapplicable as they impede the functioning of the internal market. Each of these regulatory techniques, as we will see, comes with its own assumptions, problems and implications.

We review the difference between real-world and risk-neutral processes. We illustrate asset processes using two years of daily returns from the S\&P 500 stock index, and with 30 years of monthly data from the S\&P/TSX (Toronto Stock Exchange) stock index. We describe three models for modelling asset prices in discrete time: the independent lognormal model, the GARCH model, and the regime-switching lognormal model. We describe how the models are fitted to data, and briefly discuss how to choose between models.

EU law has increasingly become entangled in difficult and sensitive political questions, which means that studying EU law without appreciating the political context within which it operates risks missing the point. The message of this book, then, is that in studying EU law, the law itself matters as much as context; and context also matters as much as law. This first chapter tackles a question that is at the core of this book: what is the EU for? We will look at four theories that have different answers to the question what the ‘point’ of the EU is: intergovernmentalism, neo-functionalism, supranationalism and post-functionalism. These four theories offer heuristic models to think about the nature of the EU and the choices that are implicit in EU law. As we will see, the tensions, problems and questions discussed in this chapter will resurface throughout the book.

Emmy Noether is recognized as one of the greatest mathematicians of the twentieth century. She was born in Germany in 1882 to an intellectual Jewish family and died in the United States in 1935. Emmy trained as a language teacher, but after passing the qualifying exams to teach, she decided to study mathematics at the University of Erlangen. At that time in Germany a university education was limited to men, although women were allowed to attend classes if given permission by the professor. (She was half of the total female student body at that university.) She spent a semester at the University of Gottingen, at that time a world leader in mathematics and physics. There she attended lectures from a number of leading mathematicians, including Hermann Minkowski (who you will run into in Chapter 20) and Karl Schwarzschild (whose theory of black holes you will encounter in Chapter 9).

This chapter and the next are a study of the general motion of a rigid body. This is a fairly complicated topic which involves mathematical concepts that you may not have encountered before.

I denoted this chapter as “optional” because it contains essentially no new physics. However, it does introduce some useful mathematical concepts and techniques. The methods introduced here are applied in several areas of physics including quantum mechanics and solid-state physics.

This book has concentrated on “integrable” problems, that is, problems whose equations of motion can be integrated yielding closed-form solutions.

As you will soon appreciate, the physics of a pendulum is much more complex than you might imagine.

In this chapter we consider the basic concepts of the statics and dynamics of fluids. As the name indicates, a fluid is any substance that flows, such as liquids and gases. The general categories of our study are fluid statics or hydrostatics concerning the behavior of fluids at rest, and fluid dynamics which is a study of the motion of fluids and of objects moving with respect to fluids. This is further subdivided into studies of the dynamics of liquids and gases or hydrodynamics and gas dynamics.

Classical field theory is primarily a study of electromagnetic and gravitational fields. This chapter is an introduction to field theory and is limited to a few aspects of the gravitational field.

This chapter treats several advanced concepts in statics, well beyond the brief summary of statics in Section 1.6. We will begin with a few definitions and two simple theorems concerning systems of forces acting on rigid bodies, then go on to analyze the statics of freely deformable bodies such as a string or cable hanging from stationary supports. This is followed by definitions of stress and strain and a generalization of Hooke’s law. The last topic is d’Alembert’s principle and the concept of virtual work. You will see how this principle can be used to derive Lagrange’s equations. An important application is an investigation of the properties of a fluid in equilibrium (hydrostatics), but we will leave that for Chapter 19 where we consider fluids in general.

The orbital motion of a planet around the Sun was one of the first important problems to be analyzed in terms of Newton’s laws of motion. The gravitational force attracting a planet to the Sun is a central force, that is, a force directed towards a fixed point. The motion of a planet is a prime example of the more general problem of the behavior of a particle acted upon by a central force.