A Student's Guide to Laplace Transforms

The Laplace transform is a useful mathematical tool encountered by students of physics, engineering, and applied mathematics, within a wide variety of important applications in mechanics, electronics, thermodynamics and more. However, students often struggle with the rationale behind these transforms, and the physical meaning of the transform results. Using the same approach that has proven highly popular in his other Student's Guides, Professor Fleisch addresses the topics that his students have found most troublesome; providing a detailed and accessible description of Laplace transforms and how they relate to Fourier and Z-transforms. Written in plain language and including numerous, fully worked examples. The book is accompanied by a website containing a rich set of freely available supporting materials, including interactive solutions for every problem in the text, and a series of podcasts in which the author explains the important concepts, equations, and graphs of every section of the book.

THEWEIGHT: A simple and flexible algorithm for simulating non-ideal, age-structured populations

1. The Wright-Fisher model, which directs how matings occur and how genes are transmitted across generations, has long been a lynchpin of evolutionary biology. This model is elegantly simple, analytically tractable, and easy to implement, but it has one serious limitation: essentially no real species satisfies its many assumptions. With growing awareness of the importance of jointly considering both ecology and evolution in eco-evolutionary models, this limitation has become more apparent, causing many researchers to search for more realistic simulation models. 2. A recently described variation retains most of the Wright-Fisher simplicity but provides greater flexibility to accommodate departures from model assumptions. This generalized Wright-Fisher model relaxes the assumption that all individuals have identical expected reproductive success by introducing a vector of parental weights w that specifies relative probabilities different individuals have of producing offspring. With parental weights specified this way, expectations of key demographic parameters are simple functions of w. This allows researchers to quantitatively predict the consequences of non-Wright-Fisher features incorporated into their models. 3. An important limitation of the Wright-Fisher model is that it assumes discrete generations, whereas most real species are age-structured. Here I show how an algorithm (THEWEIGHT) that implements the generalized Wright-Fisher model can be used to model evolution in age-structured populations with overlapping generations. Worked examples illustrate simulation of seasonal and lifetime reproductive success and show how the user can pick vectors of weights expected to produce a desired level of reproductive skew or a desired Ne/N ratio. Alternatively, weights can be associated with heritable traits to provide a simple, quantitative way to model natural selection. Using THEWEIGHT, it is easy to generate positive or negative correlations of individual reproductive success over time, thus allowing explicit modeling of common biological processes like skip breeding and persistent individual differences. 4. R code is provided to implement basic features of THEWEIGHT and applications described here. However, required coding changes to the Wright-Fisher model are modest, so the real value of the new algorithm is to encourage users to adopt its features into their own or others models.

Computational Thinking and Social Studies Teacher Education

Computational thinking is highly applicable to social studies education, particularly decision-focused social studies. To better fit the disciplinary needs of social studies and align with social studies standards, we adapt and group computational thinking skills into a heuristic of data, patterns, rules, and questions (DPR-Q). We then propose a four-step model for social studies teachers to follow when planning lessons that integrate computational thinking within their curricular instruction. Both the DPR-Q heuristic and the instructional planning model are explained with worked examples from social studies classrooms. Successful integration of computational thinking into decision-focused social studies can both enrich the social studies curriculum and provide a curricular home for teaching computational thinking, bearing out Wing's claim that computational thinking is ‘everywhere' and ‘for everyone.'

Astrophysical Magnetic Fields

Magnetic fields permeate space and affect many major astrophysical phenomena, but they are often ignored due to their perceived complexity. This self-contained introduction to astrophysical magnetic fields provides both a comprehensive review of the current state of the subject and a critical discussion of the latest research. It presents our knowledge of magnetic fields from the Early Universe, their evolution in cosmic time through to their roles in present-day galaxies, galaxy clusters and the wider intergalactic medium, with attention given to both theory and observations. This volume also contains an extensive introduction into magnetohydrodynamics, numerous worked examples, observational and mathematical techniques and interpretations of the observations. Its review of our current knowledge, with an emphasis on results that are likely to form the basis for future progress, benefits a broad audience of advanced students and active researchers, including those from fields such as cosmology and general relativity.

Resilience metrics for transport networks: a review and practical examples for bridges

Climate change, diverse geohazards and structural deterioration pose major challenges in planning, maintenance and emergency response for transport infrastructure operators. Hence, to manage these risks and adapt to changing conditions, well-informed resilience assessment and decision-making tools are required. These tools are commonly associated with resilience metrics, which quantify the capacity of transport networks to withstand and absorb damage, recover after a disruption and adapt to future changes. Several resilience metrics have been proposed in the literature, however, there is lack of practical applications and worked examples. This paper attempts to fill this gap and provide engineers and novice researchers with a review of available metrics on the basis of the main properties of resilience, i.e. robustness, redundancy, resourcefulness and rapidity. The main steps of resilience assessment for transport infrastructure such as bridges are discussed and the use of fragility and restoration functions to assess the robustness and rapidity of recovery is demonstrated. Practical examples are provided using a bridge exposed to scour effects as a benchmark. Also, an illustrative example of a systems of assets is provided and different aspects of resilience-based decision making are discussed, aiming to provide a comprehensive, yet straightforward, understanding of resilience.

Geochemical and Biogeochemical Reaction Modeling

An indispensable primer and reference textbook, the third edition of Geochemical and Biogeochemical Reaction Modeling carries the reader from the field's origins and theoretical underpinnings through to a collection of fully worked examples. A clear exposition of the underlying equations and calculation techniques is balanced by real-world example calculations. The book depicts geochemical reaction modeling as a vibrant field of study applicable to a wide spectrum of issues of scientific, practical, and societal concern. The new edition offers a thorough description of surface complexation modeling, including two- and three-layer methods; broader treatment of kinetic rate laws; the effect of stagnant zones on transport; and techniques for determining gas partial pressures. This handbook demystifies and makes broadly accessible an elegant technique for portraying chemical processes in the geosphere. It will again prove to be invaluable for geochemists, environmental scientists and engineers, aqueous and surface chemists, microbiologists, university teachers, and government regulators.

Advanced Topics in Quantum Mechanics

Quantum mechanics is one of the most successful theories in science, and is relevant to nearly all modern topics of scientific research. This textbook moves beyond the introductory and intermediate principles of quantum mechanics frequently covered in undergraduate and graduate courses, presenting in-depth coverage of many more exciting and advanced topics. The author provides a clearly structured text for advanced students, graduates and researchers looking to deepen their knowledge of theoretical quantum mechanics. The book opens with a brief introduction covering key concepts and mathematical tools, followed by a detailed description of the Wentzel–Kramers–Brillouin (WKB) method. Two alternative formulations of quantum mechanics are then presented: Wigner's phase space formulation and Feynman's path integral formulation. The text concludes with a chapter examining metastable states and resonances. Step-by-step derivations, worked examples and physical applications are included throughout.

Coarse Geometry of Topological Groups

This book provides a general framework for doing geometric group theory for many non-locally-compact topological transformation groups that arise in mathematical practice, including homeomorphism and diffeomorphism groups of manifolds, isometry groups of separable metric spaces and automorphism groups of countable structures. Using Roe's framework of coarse structures and spaces, the author defines a natural coarse geometric structure on all topological groups. This structure is accessible to investigation, especially in the case of Polish groups, and often has an explicit description, generalising well-known structures in familiar cases including finitely generated discrete groups, compactly generated locally compact groups and Banach spaces. In most cases, the coarse geometric structure is metrisable and may even be refined to a canonical quasimetric structure on the group. The book contains many worked examples and sufficient introductory material to be accessible to beginning graduate students. An appendix outlines several open problems in this young and rich theory.