Today, Vietnam is much more than a country. It is an evocation, a cause, a slogan. It is a defining chapter in the history of the United States, the label of a global era, an inspiration for the small, the weak, and the oppressed, a model of national liberation. It is, too, a syndrome that cannot be cured, a curse that cannot be exorcised. So much more than a geographical and political entity, it is a veritable incantation for some, a specter for others. Vietnam is a virtual brand name.Why is this all the case? Why do we keep evoking Vietnam? How did a small, impoverished country the size of a postage stamp on a large map of the world become the object of the second longest war in US history? And how did that war come to mean so much to Americans? What accounts for the enduring preoccupation with it in US political, military, and academic circles? Why, after more than five decades, does Vietnam still matter? This introduction answers these and related questions with a view to underscoring the Vietnam’s War’s enduring relevance.

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.