This chapter describes techniques related to genetics, at both a molecular and an organismal level. The introduction explains the principles of base pairing and single nucleotide polymorphisms. The molecular techniques and figures explained include transgene construct schematics, Manhattan plots generated from genome-wide association studies, and different analysis methods for studying the microbiome. Organismal-level techniques described include family trees and dendrograms.

This chapter defines the economic dispatch problem and analyzes the KKT conditions that characterize the optimal solution. We then define competitive markets, aggregate variable costs, aggregate marginal costs, aggregate benefit, and aggregate marginal benefit in order to characterize price and quantity adjustment in markets. This allows us to define competitive market equilibrium and competitive price. The equivalence between competitive equilibrium and the optimal solution of the economic dispatch problem is established using KKT conditions. This equivalence is generalized to the context of more general market models with multiple products, and the generalized result is used repeatedly throughout the textbook for establishing the equivalence between market models and centralized optimization problems, which is the cornerstone of the argued efficiency of competitive markets.

This chapter introduces structures and structural interconnections for LTI systems and then considers several examples of digital filters. Examples include moving average filters, difference operators, and ideal lowpass filters. It is then shown how to convert lowpass filters into other types, such as highpass, bandpass, and so on, by use of simple transformations. Phase distortion is explained, and linear-phase digital filters are introduced, which do not create phase distortion. The use of digital filters in noise removal (denoising) is also demonstrated for 1D signals and 2D images. The filtering of an image into low and high-frequency subbands is demonstrated, and the motivation for subband decomposition in audio and image compression is explained. Finally, it is shown that the convolution operation can be represented as a matrix vector multiplication, where the matrix has Toeplitz structure. The matrix representation also shows us how to undo a filtering operation through a process called deconvolution.

This chapter describes the basics of scientific figures. It provides tips for identifying different types of figures, such as experimental protocol figures, data figures, and summary figures. There is a description of ways to compare groups and of different types of variables. A short discussion of statistics is included, describing elements such as central tendency, dispersion, uncertainty, outliers, distributions, and statistical tests to assess differences. Following that is a short overview of a few of the more common graph types, such as bar graphs, boxplots, violin plots, and raincloud plots, describing the advantages that each provides. The end of the chapter is an “Understanding Graphs at a Glance” section which gives the reader a step-by-step outline for interpreting many of the graphs commonly used in neuroscience research, applicable independently of the methodology used to collect those data.

This chapter describes methods for analyzing neuroscience questions at the molecular level. The introduction defines the central dogma of molecular biology and the four levels of protein structure. The chapter then describes techniques including in situ hybridization, RNA-sequencing, immunochemistry and some applications such as Western blot and affinity capture, ribbon diagrams, a variety of genetically encoded fluorescent biosensors, and receptor binding assays.

This chapter introduces different types of signals, and studies the properties of many kinds of systems that are encountered in signal processing. Signals discussed include the exponential signal, the unit step, single-frequency signals, rectangular pulses, Dirac delta signals, and periodic signals. Two-dimensional signals, especially 2D frequencies and sinusoids, are also demonstrated. Many types of systems are discussed, such as homogeneous systems, additive systems, linear systems, stable systems, time-invariant systems, and causal systems. Both continuous and discrete-time cases are discussed. Examples are presented throughout, such as music signals, ECG signals, and so on, to demonstrate the concepts. Subtle differences between discrete-time and continuous-time signals and systems are also pointed out.

The first chapter considers the value of and opportunities with digital technologies, and how they can be used as tools and environments for learning. It talks about the importance of being agentic and using digital tools with purpose. The use of digital tools to develop 21st-century skills in students is discussed and there is an overview of the curriculum and policy mandates for the use of digital technologies, including development of the general capability of digital literacies.

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.