This is a detailed chapter on digital filter design. Specific digital filters such as notch and antinotch filters, and sharp-cutoff lowpass filters such as Butterworth filters are discussed in detail. Also discussed are allpass filters and some of their applications, including the implementation of notch and antinotch filters. Computational graphs (structures) for allpass filters are presented. It is explained how continuous-time filters can be transformed into discrete time by using the bilinear transformation. A simple method for the design of linear-phase FIR filters, called the window-based method, is also presented. Examples include the Kaiser window and the Hamming window. A comparative discussion of FIR and IIR filters is given. It is demonstrated how nonlinear-phase filters can create visible phase distortion in images. Towards the end, a detailed discussion of steady-state and transient components of filter outputs is given. The dependence of transient duration on pole position is explained. The chapter concludes with a discussion of spectral factorization.

This chapter introduces some basic mathematical notions that are used throughout the book. Convex sets and functions, optimization problems, feasible solutions, and optimal solutions are first defined. The chapter then covers duality theory, including the definition of the Lagrangian function and the dual function, which are used to derive the duals of linear programs. Weak and strong duality are then defined and related to certain classes of optimization problems. The Karush–Kuhn–Tucker (KKT) conditions are defined, and their relation to the optimal solution of mathematical programs is discussed. KKT conditions are a fundamental concept used extensively in the book in order to understand the properties and economic interpretations of the various economic models encountered. Subgradients are subsequently defined in order to establish the relation between Lagrange multipliers and the sensitivity of an optimization model with respect to changes in the right-hand side parameters of its constraints. These sensitivity results are also used repeatedly in the book, for instance in order to derive locational marginal prices in chapter 5.

This chapter provides an overview of matrices. Basic matrix operations are introduced first, such as addition, multiplication, transposition, and so on. Determinants and matrix inverses are then defined. The rank and Kruskal rank of matrices are defined and explained. The connection between rank, determinant, and invertibility is elaborated. Eigenvalues and eigenvectors are then reviewed. Many equivalent meanings of singularity (non-invertibility) of matrices are summarized. Unitary matrices are reviewed. Finally, linear equations are discussed. The conditions under which a solution exists and the condition for the solution to be unique are also explained and demonstrated with examples.

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.

In addition to knowledge of information (details and organising ideas), students also need to develop the skills and processes needed to complete mental tasks, for example, how to do long division, how to read a map and how to write in a specific genre. This domain of knowledge is called mental procedures. Mental procedures are learned through practice and are executed when needed to complete a task. Mental procedures occur inside a person’s brain. Educators use pedagogies to help students to learn these procedures and, once learned, to activate and facilitate this mode of thinking. This chapter will focus on how digital technologies can be used to support these pedagogies while also exploring some new opportunities.

This chapter begins by explaining mental procedures domain of knowledge. After using the TPACK model (see Chapter 3) to highlight the importance of intentionally using digital technologies, it then explores how they can be used to develop mental procedures and to guide student’s when using mental procedures.

This chapter describes some commonly used nonhuman paradigms for assessing animal behavior and the figures that are used to present those data. The chapter opens with an overview of some animal species used in neuroscience research, a discussion about nonhuman housing, and a description of types of validity that behavioral neuroscientists concern themselves with. The behavioral tests described here are divided into five major categories: motor behaviors; pain; learning and memory; mental disorders such as anxiety, depression, and substance use disorder; and social behaviors. Included is a description of a survival analysis and an explanation of interpreting Kaplan–Meier curves.

The epilogue explains that the resilience and stubbornness of Le Duan and other communist leaders hindered the country’s reconstruction and development after the Vietnamese Civil War finally ended. In the decade of life and leadership left for Le Duan, few positive changes took place in Vietnam. The 1978–9 incursion into Cambodia eliminated the Khmer Rouge threat, but the decade-long occupation of that country by Vietnamese forces that followed brought worldwide condemnation. Vietnam contained the Chinese incursion into its own territory in 1979, but anti-Chinese campaigns domestically prompted an exodus of tens of thousands of productive members of society. Through all this, Le Duan’s unwavering adherence to Stalinist principles of economic transformation hampered economic growth. His death in 1986 paved the way for Đổi mới, the “renovation” policy that introduced market reforms. It also set the stage for the normalization of diplomatic relations with the United States – and of life itself for average Vietnamese. Although Vietnam’s American War and Fourth Civil War have been over for nearly fifty years, the struggle for their memory continues.

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.

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.

Learning is a process. It takes time and often involves a degree of challenge. But how do students know that their learning is progressing? How do they identify ways to improve their learning? How do educators know whether the strategies and activities that they are using are helping students? This is the role of assessment – it helps students and educators to gauge progress and identify opportunities for improvement.

In Chapters 5, 6 and 7 we explored how to use digital technologies in the learning and teaching of the three domains of knowledge. In this chapter, we will close the loop by focusing on assessment and how digital technologies can help. We will start by considering the important role of assessment in learning and teaching. Following this, we will explore how to capture evidence of learning, assess learning and provide feedback using digital technologies. The chapter will conclude by exploring how to store and analyse assessment data using digital technologies.