This chapter introduces topics that extend beyond the electricity market, and focuses in particular on oil, natural gas, and biofuels. Short- and long-term equilibriums are analyzed in the context of oil markets. Monopolies, cartels, and the model of the dominant firm are also analyzed in the context of the oil market. The tax incidence problem is formulated as an equivalent optimization problem and analyzed in the context of natural gas markets. One-way substitutability is analyzed in the context of biofuel markets, and the tortilla crisis is illustrated through an optimization model. Hotelling’s rule is stated and proven by considering a dynamic optimization model of a finite nonrenewable resource that is gradually depleted over time while satisfying a price-elastic demand.

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.

This chapter introduces bandlimited signals, sampling theory, and the method of reconstruction from samples. Uniform sampling with a Dirac delta train is considered, and the Fourier transform of the sampled signal is derived. The reconstruction from samples is based on the use of a linear filter called an interpolator. When the sampling rate is not sufficiently large, the sampling process leads to a phenomenon called aliasing. This is discussed in detail and several real-world manifestations of aliasing are also discussed. In practice, the sampled signal is typically processed by a digital signal processing device, before it is converted back into a continuous-time signal. The building blocks in such a digital signal processing system are discussed. Extensions of the lowpass sampling theorem to the bandpass case are also presented. Also proved is the pulse sampling theorem, where the sampling pulse is spread out over a short duration, unlike the Dirac delta train. Bandlimited channels are discussed and it is explained how the data rate that can be transmitted over a channel is limited by channel bandwidth.

This chapter introduces the continuous-time Fourier transform (CTFT) and its properties. Many examples are presented to illustrate the properties. The inverse CTFT is derived. As one example of its application, the impulse response of the ideal lowpass filter is obtained. The derivative properties of the CTFT are used to derive many Fourier transform pairs. One result is that the normalized Gaussian signal is its own Fourier transform, and constitutes an eigenfunction of the Fourier transform operator. Many such eigenfunctions are presented. The relation between the smoothness of a signal in the time domain and its decay rate in the frequency domain is studied. Smooth signals have rapidly decaying Fourier transforms. Spline signals are introduced, which have provable smoothness properties in the time domain. For causal signals it is proved that the real and imaginary parts of the CTFT are related to each other. This is called the Hilbert transform, Poisson’’s transform, or the Kramers–Kronig transform. It is also shown that Mother Nature “computes” a Fourier transform when a plane wave is propagating across an aperture and impinging on a distant screen – a well-known result in optics, crystallography, and quantum physics.

This chapter considers the opportunities for students to explore interests, such as independent learning and personal projects, eSports and interest groups, such as maker spaces and coding clubs. It then looks at the changing roles for students and educators in which you are all co-learning–you as the educator do not need to be the expert.

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.

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.

Incorporating digital technologies in the classroom can be both a daunting and exciting experience for educators of all age groups. Supporting Innovative Pedagogies with Digital Technologies explores intentional teaching approaches for using digital technologies in the classroom as a tool to support rather than replace established strategies. Readers will learn how to innovate their classroom, and vignettes from Early Childhood, Primary and Secondary classrooms will remove the overwhelming pressure of redesigning learning and teaching from scratch.

Over three parts, the text explores understanding learning and teaching with digital technologies; designing and enacting learning with digital technologies; and professional responsibilities for teaching with digital technologies. Each chapter includes vignettes to illustrate key ideas and prompt discussion, reflection activities to encourage critical thinking and inspire educators to use key ideas in their practice, ‘Tips and tricks’ to provide practical hints and expert guidance for future consideration, and review questions to consolidate understanding.

Written by a team of authors, each with over 25 years of experience and expertise in teaching about and with digital technologies, Supporting Innovative Pedagogies with Digital Technologies is a valuable resource for all educators wanting to enhance and transform their classroom learning and teaching strategies for the modern age.

This chapter highlights some of the tools used for imaging features of the nervous system. The introduction defines the concepts of temporal and spatial resolution, the anatomical language used to describe structures in relation to one another, and planes of imaging, all of which are knowledge essential to understanding imaging figures. The chapter then describes both structural and functional imaging techniques and the figures that may accompany these scanning methods, including dissection; CT scans; PET scans; various applications of MRI scanning including arterial spin labeling, functional MRI, and diffusion tensor imaging for tract tracing; SPECT scans; and electroencephalography imaging, including a description of event-related potentials.

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.