Water shapes the planet and all life upon it. Breaking down traditional disciplinary barriers, this accessible, holistic introduction to the role and importance of water in Earth’s physical and biological environments assumes no prior knowledge. It provides the reader with a clear and coherent explanation of the unique properties of water and how these allow it to affect landscapes and underpin all life on Earth. Contemporary issues surrounding water quality – such as the rise of microplastics and climate change – are highlighted, ensuring readers understand current debates. Giving all of the necessary background and up-to-date references, and including numerous examples and illustrations to explain concepts, worked mathematical calculations, and extensive end-of-chapter questions, this is the ideal introductory textbook for students seeking to understand the inextricable links between water and the environment.

This chapter discusses the Fourier series representation for continuous-time signals. This is applicable to signals which are either periodic or have a finite duration. The connections between the continuous-time Fourier transform (CTFT), the discrete-time Fourier transform (DTFT), and Fourier series are also explained. Properties of Fourier series are discussed and many examples presented. For real-valued signals it is shown that the Fourier series can be written as a sum of a cosine series and a sine series; examples include rectified cosines, which have applications in electric power supplies. It is shown that the basis functions used in the Fourier series representation satisfy an orthogonality property. This makes the truncated version of the Fourier representation optimal in a certain sense. The so-called principal component approximation derived from the Fourier series is also discussed. A detailed discussion of the properties of musical signals in the light of Fourier series theory is presented, and leads to a discussion of musical scales, consonance, and dissonance. Also explained is the connection between Fourier series and the function-approximation property of multilayer neural networks, used widely in machine learning. An overview of wavelet representations and the contrast with Fourier series representations is also given.

This chapter defines forward contracts and future contracts, and discusses their advantages as well as their fair market price. Other instruments such as power purchase agreements (PPAs) and contracts for differences (CfDs) are defined. Financial transmission rights (FTRs) are defined and their role in managing risk on networks is discussed. FTR auctions and revenue adequacy are discussed. Call options and callable forward contracts are defined, and their role in enabling demand response is discussed, as well as their pricing. The modeling of risk aversion through risk measures is discussed. Coherent risk measures are defined. Value at risk and conditional value at risk are defined. The worst-case characterization of coherent risk measures through risk-adjusted probability measures is developed. This allows us to quantitatively formalize the back-propagation of prices to forward markets. The representation of risk through utility functions and the specific application of Markowitz risk measures is covered.

Water shapes the planet and all life upon it. Breaking down traditional disciplinary barriers, this accessible, holistic introduction to the role and importance of water in Earth’s physical and biological environments assumes no prior knowledge. It provides the reader with a clear and coherent explanation of the unique properties of water and how these allow it to affect landscapes and underpin all life on Earth. Contemporary issues surrounding water quality – such as the rise of microplastics and climate change – are highlighted, ensuring readers understand current debates. Giving all of the necessary background and up-to-date references, and including numerous examples and illustrations to explain concepts, worked mathematical calculations, and extensive end-of-chapter questions, this is the ideal introductory textbook for students seeking to understand the inextricable links between water and the environment.

This concise and rigorous textbook introduces students to the subject of continuum thermodynamics, providing a complete treatment of the subject with practical applications to material modelling.

• Presents mathematical prerequisites and the foundations of continuum mechanics, taking the student step-by-step through the subject to allow full understanding of the theory.

• Introduces more advanced topics such as theories for the investigation of material models, showing how they relate to real-world practical applications.

• Numerous examples and illustrations, alongside end-of-chapter problems with helpful hints, help describe complex concepts and mathematical derivations.

Water shapes the planet and all life upon it. Breaking down traditional disciplinary barriers, this accessible, holistic introduction to the role and importance of water in Earth’s physical and biological environments assumes no prior knowledge. It provides the reader with a clear and coherent explanation of the unique properties of water and how these allow it to affect landscapes and underpin all life on Earth. Contemporary issues surrounding water quality – such as the rise of microplastics and climate change – are highlighted, ensuring readers understand current debates. Giving all of the necessary background and up-to-date references, and including numerous examples and illustrations to explain concepts, worked mathematical calculations, and extensive end-of-chapter questions, this is the ideal introductory textbook for students seeking to understand the inextricable links between water and the environment.

This chapter explores your role in supporting student digital citizenship and wellbeing. It will consider how digital technologies can be used to support students’ growth as a person and digital citizen, including developing 21st-century skills. It will unpack your responsibilities to help students to develop life skills and behave in a safe and ethical manner at the intersection of the digital and non-digital worlds. The approaches you adopt in supporting students need to be age appropriate and the strategies could vary across year levels and therefore, the early childhood, primary and secondary years will be addressed separately, though, at times, you will note some overlap in the approaches and strategies. A later chapter, Chapter 11, will investigate your personal role and work in the digital world, related to your personal digital identity and how using the affordances of digital technologies can support you in your work, for example, when engaging with and supporting families.

This chapter introduces the unit commitment model. The fixed (startup and min load) and variable cost of a unit are discussed. Initial conditions, transitions, min up/down times, temperature-dependent startups, startup/shutdown profiles, ramp rates, heat rate curves, and reserves are discussed and represented in a mixed integer linear programming model of unit commitment. The extension of the basic model to uncertainty in the stochastic unit commitment model is discussed. The two-settlement system of day-ahead markets is described. Portfolios followed by nominations are compared to unit-based market models. Exchanges are compared to power pools. The possibility of inexistence of a market clearing price in non-convex market clearing models is discussed. Paradoxically rejected orders in European market models are described. Lost opportunity cost as a metric of deviation from equilibrium is introduced, and related notions such as make-whole payments, uplifts, and potential congestion revenue shortfall are introduced. Convex hull pricing is defined and compared to pricing based on linear relaxations and fixing integer variables. The products of the European electricity market (continuous and block orders) are described. The treatment of European pricing rules in the EUPHEMIA algorithm through a branch-and-cut scheme is discussed.

This chapter examines discrete-time LTI systems in detail. It shows that the input–output behavior of an LTI system is characterized by the so-called impulse response. The output is shown to be the so-called convolution of the input with the impulse response. It is then shown that exponentials are eigenfunctions of LTI systems. This property leads to the ideas of transfer functions and frequency responses for LTI systems. It is argued that the frequency response gives a systematic meaning to the term “filtering.” Image filtering is demonstrated with examples. The discrete-time Fourier transform (DTFT) is introduced to describe the frequency domain behavior of LTI systems, and allows one to represent a signal as a superposition of single-frequency signals (the Fourier representation). DTFT is discussed in detail, with many examples. The z-transform, which is of great importance in the study of LTI systems, is also introduced and its connection to the Fourier transform explained. Attention is also given to real signals and real filters, because of their additional properties in the frequency domain. Homogeneous time-invariant (HTI) systems are also introduced. Continuous-time counterparts of these topics are explained. B-splines, which arise as examples in continuous-time convolution, are presented.

This chapter describes the interpretation of figures that show results of meta-analyses. The main types of figure covered include the flow chart or PRISMA diagram for study selection, forest plots of results, and funnel plots used to illustrate any potential publication bias.