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.

This chapter discusses many interesting properties of bandlimited signals. The subspace of bandlimited signals is introduced. It is shown that uniformly shifted versions of an appropriately chosen sinc function constitute an orthogonal basis for this subspace. It is also shown that the integral and the energy of a bandlimited signal can be obtained exactly from samples if the sampling rate is high enough. For non-bandlimited functions, such a result is only approximately true, with the approximation getting better as the sampling rate increases. A number of less obvious consequences of these results are also presented. Thus, well-known mathematical identities are derived using sampling theory. For example, the Madhava–Leibniz formula for the approximation of π can be derived like this. When samples of a bandlimited signal are contaminated with noise, the reconstructed signal is also noisy. This noise depends on the reconstruction filter, which in general is not unique. Excess bandwidth in this filter increases the noise, and this is quantitatively analyzed. An interesting connection between bandlimited signals and analytic functions (entire functions) is then presented. This has many implications, one being that bandlimited signals are infinitely smooth.

This chapter presents the generation capacity expansion planning problem and provides an economic analysis of the model. Scarcity rents in energy-only markets are defined, and the equivalence of the centralized expansion planning problem to a decentralized long-term economic equilibrium is established. The missing money problem is discussed, and various approaches for overcoming it are analyzed through models. The value of lost load pricing mechanism remunerates units when the system is scarce at the estimated value of lost load. Capacity mechanisms introduce a separate revenue stream for paying investors to build or maintain capacity. The cost of new entry is defined, and is related to the loss of load expectation. A model for capacity auctions is introduced and the shape of the capacity auction demand curve and role of capacity credit is discussed. The role of reliability options in capacity auctions is discussed. Alternative mechanisms such as installed capacity obligations, capacity payments, decentralized capacity mechanisms, and strategic reserves are discussed. The operating reserve demand curve mechanism remunerates units for offering flexible capacity in the form of reserve. The ORDC model of chapter 6 is revisited in the context of a long-term equilibrium.

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 introduces the discrete Fourier transform (DFT), which is different from the discrete-time Fourier transform (DTFT) introduced earlier. The DFT transforms an N-point sequence x[n] in the time domain to an N-point sequence X[k] in the frequency domain by sampling the DTFT of x[n]. A matrix representation for this transformation is introduced, and the properties of the DFT matrix are studied. The fast Fourier transform (FFT), which is a fast algorithm to compute the DFT, is also introduced. The FFT makes the computation of the Fourier transforms of large sets of data practical. The digital signal processing revolution of the 1960s was possible because of the FFT. This chapter introduces the simplest form of FFT, called the radix-2 FFT, and a number of its properties. The chapter also introduces circular or cyclic convolution, which has a special place in DFT theory, and explains the connection to ordinary convolution. Circular convolution paves the way for fast algorithms for ordinary convolution, using the FFT. The chapter also summarizes the relationships between the four types of Fourier transform studied in this book: CTFT, DTFT, DFT, and Fourier series.

Chapter 4 relates the impact of the Americanization of the Fourth Civil War for Vietnam. Despite public claims to the contrary, Hanoi at that time had no desire to negotiate an end to the conflict; it was committed to “complete victory.” Nothing short of the surrender of its enemies was going to satisfy it. To meet that end, Le Duan’s regime relied heavily on political and material support from the Soviet Union and China, which was not always easy to obtain in light of the growing ideological dispute between the two. Mounting frustration with the course of the war eventually prompted Le Duan to order a major, months-long military campaign to break the stalemate and expedite victory: the Tet Offensive of 1968. Although it dealt the United States a major psychological blow, the three-staged offensive fell far short of meeting Le Duan’s own expectations. In fact, it energized the regime in Saigon and rallied the Southern population behind it to an unprecedented degree.