If your students struggle with standard deviation, statistical tests and logarithmic functions, this is the book for them. This textbook companion will help improve their essential maths skills for biology, whichever awarding body specification you're following. You can use it throughout the course, whenever you feel they need some extra help. - Develop understanding of both maths and biology with all worked examples and questions within a biology context - Improve confidence with a step-by-step approach to every maths skill - Measure progress with guided and non-guided questions - Understand misconceptions with full worked solutions to every question - Feel confident in expert guidance from experienced teacher and former Senior Examiner Dan Foulder

Montgomery, Runger, and Hubele provide modern coverage of engineering statistics, focusing on how statistical tools are integrated into the engineering problem-solving process. All major aspects of engineering statistics are covered, including descriptive statistics, probability and probability distributions, statistical test and confidence intervals for one and two samples, building regression models, designing and analyzing engineering experiments, and statistical process control. Developed with sponsorship from the National Science Foundation, this revision incorporates many insights from the authors teaching experience along with feedback from numerous adopters of previous editions.

First published in 1978. Routledge is an imprint of Taylor & Francis, an informa company.

This book helps the reader make use of the mathematical models of biological phenomena starting from the basics of programming and computer simulation. Computer simulations based on a mathematical model enable us to find a novel biological mechanism and predict an unknown biological phenomenon. Mathematical biology could further expand the progress of modern life sciences. Although many biologists are interested in mathematical biology, they do not have experience in mathematics and computer science. An educational course that combines biology, mathematics, and computer science is very rare to date. Published books for mathematical biology usually explain the theories of established mathematical models, but they do not provide a practical explanation for how to solve the differential equations included in the models, or to establish such a model that fits with a phenomenon of interest. MATLAB is an ideal programming platform for the beginners of computer science. This book starts from the very basics about how to write a programming code for MATLAB (or Octave), explains how to solve ordinary and partial differential equations, and how to apply mathematical models to various biological phenomena such as diabetes, infectious diseases, and heartbeats. Some of them are original models, newly developed for this book. Because MATLAB codes are embedded and explained throughout the book, it will be easy to catch up with the text. In the final chapter, the book focuses on the mathematical model of the proneural wave, a phenomenon that guarantees the sequential differentiation of neurons in the brain. This model was published as a paper from the author's lab (Sato et al., PNAS 113, E5153, 2016), and was intensively explained in the book chapter "Notch Signaling in Embryology and Cancer", published by Springer in 2020. This book provides the reader who has a biological background with invaluable opportunities to learn and practice mathematical biology.

Modeling and Computation in Engineering II (CMCE 2013, Hong Kong, 22-23 June 2013) includes 50 contributions on modeling and simulation technology, which were presented at the 2nd SREE Conference on Modeling and Computation in Engineering (CMCE 2013) and the 3rd SREE Workshop on Applied Mechanics and Civil Engineering (AMCE 2013), both held in Hong Kong, 22-23 June 2013 . The topics covered include:

- Modeling technology

- Simulation technology and tools

- Computation methods and their engineering applications

- Mechanics in engineering

Modeling and Computation in Engineering II reviews recent advances in multiple areas, including applied mechanics & civil engineering, modeling & simulation in engineering, design theories, construction science and advanced material applications in building structures, underground structures, bridge structures, hydraulic engineering, municipal engineering, port and coastal engineering, road and transportation engineering, and will be invaluable to academics and professional interested in civil, hydraulic and mechanical engineering.

With its fresh reader-friendly design, MATHEMATICS FOR ELECTRICITY AND ELECTRONICS, 4E equips learners with a thorough understanding of essential algebra and trigonometry for electricity and electronics technology. Well-illustrated information sharpens the reader's ability to think quantitatively, predict results, and troubleshoot effectively, while problem sets for drill and practice reinforce comprehension. To ensure mastery of the latest ideas and technology, the book thoroughly explains all mathematical concepts, symbols, and formulas required by future technicians and technologists.

This primer discusses a numerical formulation of the theory of an elastic rod, known as a discrete elastic rod, that was recently developed in a series of papers by Miklos Bergou et al. Their novel formulation of discrete elastic rods represents an exciting new method to simulate and analyze the behavior of slender bodies that can be modeled using an elastic rod. The formulation has been extensively employed in computer graphics and is highly cited. In the primer, we provide relevant background from both discrete and classical differential geometry so a reader familiar with classic rod theories can appreciate, comprehend, and use Bergou et al.'s computational efficient formulation of a nonlinear rod theory. The level of coverage is suitable for graduate students in mechanics and engineering sciences.

This book explains the principles of biosignal processing and its practical applications using MATLAB. Topics include the emergence of biosignals, electrophysiology, analog and digital biosignal processing, signal discretization, electrodes, time and frequency analysis, analog and digital filters, Fourier-transformation, z-transformation, pattern recognition, statistical data analysis, physiological modelling and applications of EEG, ECG, EMG, PCG and PPG signals. Additional scientifi c contributions on motion analysis by guest authors Prof. Dr. J. Subke and B. Schneider as well as classification of PPG signals by Dr. U. Hackstein.

Recognized as a powerful tool for dealing with uncertainty, Markov modeling can enhance your ability to analyze complex production and service systems. However, most books on Markov chains or decision processes are often either highly theoretical, with few examples, or highly prescriptive, with little justification for the steps of the algorithms used to solve Markov models. Providing a unified treatment of Markov chains and Markov decision processes in a single volume, Markov Chains and Decision Processes for Engineers and Managers supplies a highly detailed description of the construction and solution of Markov models that facilitates their application to diverse processes.

Organized around Markov chain structure, the book begins with descriptions of Markov chain states, transitions, structure, and models, and then discusses steady state distributions and passage to a target state in a regular Markov chain. The author treats canonical forms and passage to target states or to classes of target states for reducible Markov chains. He adds an economic dimension by associating rewards with states, thereby linking a Markov chain to a Markov decision process, and then adds decisions to create a Markov decision process, enabling an analyst to choose among alternative Markov chains with rewards so as to maximize expected rewards. An introduction to state reduction and hidden Markov chains rounds out the coverage.

In a presentation that balances algorithms and applications, the author provides explanations of the logical relationships that underpin the formulas or algorithms through informal derivations, and devotes considerable attention to the construction of Markov models. He constructs simplified Markov models for a wide assortment of processes such as the weather, gambling, diffusion of gases, a waiting line, inventory, component replacement, machine maintenance, selling a stock, a charge account, a career path, patient flow in a hospital, marketing, and a production line. This treatment helps you harness the power of Markov modeling and apply it to your organization s processes.

Nonlinear Partial Differential Equations (PDEs) have become increasingly important in the description of physical phenomena. Unlike Ordinary Differential Equations, PDEs can be used to effectively model multidimensional systems. The methods put forward in Discrete Variational Derivative Method concentrate on a new class of "structure-preserving numerical equations" which improves the qualitative behaviour of the PDE solutions and allows for stable computing. The authors have also taken care to present their methods in an accessible manner, which means that the book will be useful to engineers and physicists with a basic knowledge of numerical analysis. Topics discussed include: * "Conservative" equations such as the Korteweg-de Vries equation (shallow water waves) and the nonlinear Schr dinger equation (optical waves) * "Dissipative" equations such as the Cahn-Hilliard equation (some phase separation phenomena) and the Newell-Whitehead equation (two-dimensional B nard convection flow) * Design of spatially and temporally high-order schemas * Design of linearly-implicit schemas * Solving systems of nonlinear equations using numerical Newton method libraries

This contributed volume presents some of the latest research related to model order reduction of complex dynamical systems with a focus on time-dependent problems. Chapters are written by leading researchers and users of model order reduction techniques and are based on presentations given at the 2019 edition of the workshop series Model Reduction of Complex Dynamical Systems - MODRED, held at the University of Graz in Austria. The topics considered can be divided into five categories: system-theoretic methods, such as balanced truncation, Hankel norm approximation, and reduced-basis methods; data-driven methods, including Loewner matrix and pencil-based approaches, dynamic mode decomposition, and kernel-based methods; surrogate modeling for design and optimization, with special emphasis on control and data assimilation; model reduction methods in applications, such as control and network systems, computational electromagnetics, structural mechanics, and fluid dynamics; and model order reduction software packages and benchmarks. This volume will be an ideal resource for graduate students and researchers in all areas of model reduction, as well as those working in applied mathematics and theoretical informatics.

This book constitutes an up-to-date account of principles, methods, and tools for mathematical and statistical modelling in a wide range of research fields, including medicine, health sciences, biology, environmental science, engineering, physics, chemistry, computation, finance, economics, and social sciences. It presents original solutions to real-world problems, emphasizes the coordinated development of theories and applications, and promotes interdisciplinary collaboration among mathematicians, statisticians, and researchers in other disciplines. Based on a highly successful meeting, the International Conference on Applied Mathematics, Modeling and Computational Science, AMMCS 2019, held from August 18 to 23, 2019, on the main campus of Wilfrid Laurier University, Waterloo, Canada, the contributions are the results of submissions from the conference participants. They provide readers with a broader view of the methods, ideas and tools used in mathematical, statistical and computational sciences.

Generating a quality finite element mesh is difficult and often very time-consuming. Mesh-free methods operations can also be complicated and quite costly in terms of computational effort and resources. Developed by the authors and their colleagues, the smoothed finite element method (S-FEM) only requires a triangular/tetrahedral mesh to achieve more accurate results, a generally higher convergence rate in energy without increasing computational cost, and easier auto-meshing of the problem domain. Drawing on the authors extensive research results, Smoothed Finite Element Methods presents the theoretical framework and development of various S-FEM models.

After introducing background material, basic equations, and an abstracted version of the FEM, the book discusses the overall modeling procedure, fundamental theories, error assessment matters, and necessary building blocks to construct useful S-FEM models. It then focuses on several specific S-FEM models, including cell-based (CS-FEM), node-based (NS-FEM), edge-based (ES-FEM), face-based (FS-FEM), and a combination of FEM and NS-FEM (?FEM). These models are then applied to a wide range of physical problems in solid mechanics, fracture mechanics, viscoelastoplasticity, plates, piezoelectric structures, heat transfer, and structural acoustics.

Requiring no previous knowledge of FEM, this book shows how computational methods and numerical techniques like the S-FEM help in the design and analysis of advanced engineering systems in rapid and cost-effective ways since the modeling and simulation can be performed automatically in a virtual environment without physically building the system. Readers can easily apply the methods presented in the text to their own engineering problems for reliable and certified solutions.

Is anything truly random? Does infinity actually exist? Could we ever see into other dimensions?

In this delightful journey of discovery, David Darling and extraordinary child prodigy Agnijo Banerjee draw connections between the cutting edge of modern maths and life as we understand it, delving into the strange would we like alien music? and venturing out on quests to consider the existence of free will and the fantastical future of quantum computers. Packed with puzzles and paradoxes, mind-bending concepts and surprising solutions, this is for anyone who wants life s questions answered even those you never thought to ask.

This volume explores the connections between mathematical modeling, computational methods, and high performance computing, and how recent developments in these areas can help to solve complex problems in the natural sciences and engineering. The content of the book is based on talks and papers presented at the conference Modern Mathematical Methods and High Performance Computing in Science & Technology (M3HPCST), held at Inderprastha Engineering College in Ghaziabad, India in January 2020. A wide range of both theoretical and applied topics are covered in detail, including the conceptualization of infinity, efficient domain decomposition, high capacity wireless communication, infectious disease modeling, and more. These chapters are organized around the following areas: Partial and ordinary differential equations Optimization and optimal control High performance and scientific computing Stochastic models and statistics Recent Trends in Mathematical Modeling and High Performance Computing will be of interest to researchers in both mathematics and engineering, as well as to practitioners who face complex models and extensive computations.

This book speaks about physics discoveries that intertwine mathematical reasoning, modeling, and scientific inquiry. It offers ways of bringing together the structural domain of mathematics and the content of physics in one coherent inquiry. Teaching and learning physics is challenging because students lack the skills to merge these learning paradigms. The purpose of this book is not only to improve access to the understanding of natural phenomena but also to inspire new ways of delivering and understanding the complex concepts of physics. To sustain physics education in college classrooms, authentic training that would help develop high school students' skills of transcending function modeling techniques to reason scientifically is needed and this book aspires to offer such training The book draws on current research in developing students' mathematical reasoning. It identifies areas for advancements and proposes a conceptual framework that is tested in several case studies designed using that framework. Modeling Newton's laws using limited case analysis, Modeling projectile motion using parametric equations and Enabling covariational reasoning in Einstein formula for the photoelectric effect represent some of these case studies. A wealth of conclusions that accompany these case studies, drawn from the realities of classroom teaching, is to help physics teachers and researchers adopt these ideas in practice.

Updating the original, Transforms and Applications Handbook, Third Edition solidifies its place as the complete resource on those mathematical transforms most frequently used by engineers, scientists, and mathematicians. Highlighting the use of transforms and their properties, this latest edition of the bestseller begins with a solid introduction to signals and systems, including properties of the delta function and some classical orthogonal functions. It then goes on to detail different transforms, including lapped, Mellin, wavelet, and Hartley varieties. Written by top experts, each chapter provides numerous examples and applications that clearly demonstrate the unique purpose and properties of each type. The material is presented in a way that makes it easy for readers from different backgrounds to familiarize themselves with the wide range of transform applications. Revisiting transforms previously covered, this book adds information on other important ones, including: Finite Hankel, Legendre, Jacobi, Gengenbauer, Laguerre, and Hermite Fraction Fourier Zak Continuous and discrete Chirp-Fourier Multidimensional discrete unitary Hilbert-Huang Most comparable books cover only a few of the transforms addressed here, making this text by far the most useful for anyone involved in signal processing-including electrical and communication engineers, mathematicians, and any other scientist working in this field.

Exploring the relationship between mathematics and ecology, Spatial Ecology focuses on some important emerging challenges in the field. These challenges consist of understanding the impact of space on community structure, incorporating the scale and structure of landscapes into mathematical models, and developing connections between spatial ecology and evolutionary theory, epidemiology, and economics. The book begins with essays on how spatial effects influence the dynamics of populations and the structure of communities. It then discusses how spatial scale and structure and dispersal behavior connect to phenomena in population dynamics, evolution, epidemiology, and economics. Subsequent chapters focus on the interplay of ecology with evolution, epidemiology, and economics. The chapters on ecology and evolutionary theory provide a guided tour through a number of scenarios and modeling approaches that represent active areas of current research and suggest some paths toward conceptual unification. The book then illustrates how problems in epidemiology and ecology can be profitably addressed by similar modeling regimes. It concludes with essays that describe how ideas from economics, ecology, and quality control theory may be combined to address issues in natural resource management. With contributions from some of the best in the field, this volume promotes the advancement of ecology as a truly quantitative science, particularly as it touches on the role of space. The book will inspire readers to open up new areas of research in the mathematical theory of spatial ecology and its connections with evolutionary theory, epidemiology, and economics.

This book presents a systematic exposition of the main ideas and methods in treating inverse problems for PDEs arising in basic mathematical models, though it makes no claim to being exhaustive. Mathematical models of most physical phenomena are governed by initial and boundary value problems for PDEs, and inverse problems governed by these equations arise naturally in nearly all branches of science and engineering. The book's content, especially in the Introduction and Part I, is self-contained and is intended to also be accessible for beginning graduate students, whose mathematical background includes only basic courses in advanced calculus, PDEs and functional analysis. Further, the book can be used as the backbone for a lecture course on inverse and ill-posed problems for partial differential equations. In turn, the second part of the book consists of six nearly-independent chapters. The choice of these chapters was motivated by the fact that the inverse coefficient and source problems considered here are based on the basic and commonly used mathematical models governed by PDEs. These chapters describe not only these inverse problems, but also main inversion methods and techniques. Since the most distinctive features of any inverse problems related to PDEs are hidden in the properties of the corresponding solutions to direct problems, special attention is paid to the investigation of these properties. For the second edition, the authors have added two new chapters focusing on real-world applications of inverse problems arising in wave and vibration phenomena. They have also revised the whole text of the first edition.

This volume gathers together selected, peer-reviewed papers presented at the BIOMAT 2020 International Symposium, which was virtually held on November 1-6, 2020, with an organization staff based in Rio de Janeiro, Brazil. Topics covered in this volume include infection modeling, with an emphasis on different aspects of the COVID-19 and novel Coronavirus spread; a description of the effectiveness of quarantine measures via dynamic analysis of SLIR model; hemodynamic simulations in time-dependent domains; an optimal control model for the Ebola disease; and the co-existence of chaos and control in the context of biological models. Texts in agroforestry, economic development, and wastewater treatment processes complete this volume. Held every year since 2001, the BIOMAT International Symposium gathers together, in a single conference, researchers from Mathematics, Physics, Biology, and affine fields to promote the interdisciplinary exchange of results, ideas and techniques, promoting truly international cooperation for problem discussion. The 20th edition of the BIOMAT International Symposium has received contributions by authors from 18 countries: Algeria, Brazil, Cameroon, Canada, Chile, China (Hong Kong), Colombia, Germany, Hungary, India, Italy, Morocco, Nigeria, Russia, Senegal, South Africa, USA, and Uzbekistan. Previous BIOMAT volumes with selected works from 2017, 2018, and 2019 were also published by Springer.

Just the math skills you need to excel in the study or practice of engineering

Good math skills are indispensable for all engineers regardless of their specialty, yet only a relatively small portion of the math that engineering students study in college mathematics courses is used on a frequent basis in the study or practice of engineering. That's why "Essential Math Skills for Engineers" focuses on only these few critically essential math skills that students need in order to advance in their engineering studies and excel in engineering practice.

"Essential Math Skills for Engineers" features concise, easy-to-follow explanations that quickly bring readers up to speed on all the essential core math skills used in the daily study and practice of engineering. These fundamental and essential skills are logically grouped into categories that make them easy to learn while also promoting their long-term retention. Among the key areas covered are:

Algebra, geometry, trigonometry, complex arithmetic, and differential and integral calculus

Simultaneous, linear, algebraic equations

Linear, constant-coefficient, ordinary differential equations

Linear, constant-coefficient, difference equations

Linear, constant-coefficient, partial differential equations

Fourier series and Fourier transform

Laplace transform

Mathematics of vectors

With the thorough understanding of essential math skills gained from this text, readers will have mastered a key component of the knowledge needed to become successful students of engineering. In addition, this text is highly recommended for practicing engineers who want to refresh their math skills in order to tackle problems in engineering with confidence.

This revised textbook motivates and illustrates the techniques of applied probability by applications in electrical engineering and computer science (EECS). The author presents information processing and communication systems that use algorithms based on probabilistic models and techniques, including web searches, digital links, speech recognition, GPS, route planning, recommendation systems, classification, and estimation. He then explains how these applications work and, along the way, provides the readers with the understanding of the key concepts and methods of applied probability. Python labs enable the readers to experiment and consolidate their understanding. The book includes homework, solutions, and Jupyter notebooks. This edition includes new topics such as Boosting, Multi-armed bandits, statistical tests, social networks, queuing networks, and neural networks. For ancillaries related to this book, including examples of Python demos and also Python labs used in Berkeley, please email Mary James at [email protected]. This is an open access book.

This book is a collection of papers devoted to the emergence and development in Bulgarian Academy of Sciences of some of the areas of informatics, including artificial intelligence. The papers are prepared by specialists from the Academy, some of whom are among the founders of these scientific and application areas in Bulgaria and in some cases - in the world. The book is interesting for specialists in informatics and computer science and researchers in history of sciences.

The intention of this collection agrees with the purposes of the homonymous mini-symposium (MS) at ICIAM-2019, which were to overview the essentials of geometric calculus (GC) formalism, to report on state-of-the-art applications showcasing its advantages and to explore the bearing of GC in novel approaches to deep learning. The first three contributions, which correspond to lectures at the MS, offer perspectives on recent advances in the application GC in the areas of robotics, molecular geometry, and medical imaging. The next three, especially invited, hone the expressiveness of GC in orientation measurements under different metrics, the treatment of contact elements, and the investigation of efficient computational methodologies. The last two, which also correspond to lectures at the MS, deal with two aspects of deep learning: a presentation of a concrete quaternionic convolutional neural network layer for image classification that features contrast invariance and a general overview of automatic learning aimed at steering the development of neural networks whose units process elements of a suitable algebra, such as a geometric algebra. The book fits, broadly speaking, within the realm of mathematical engineering, and consequently, it is intended for a wide spectrum of research profiles. In particular, it should bring inspiration and guidance to those looking for materials and problems that bridge GC with applications of great current interest, including the auspicious field of GC-based deep neural networks.

"Emphasizes the Basic Principles of Computational Arithmetic and Computational Structure Design"

Taking an interdisciplinary approach to the nanoscale generation of computer devices and systems, Computer Arithmetics for Nanoelectronics develops a consensus between computational properties provided by data structures and phenomenological properties of nano and molecular technology.

"Covers All Stages of the Design Cycle, from Task Formulation to Molecular-Based Implementation"

The book introduces the theoretical base and properties of various data structures, along with techniques for their manipulation, optimization, and implementation. It also assigns the computational properties of logic design data structures to 3D structures, furnishes information-theoretical measures and design aspects, and discusses the testability problem. The last chapter presents a nanoscale prospect for natural computing based on assorted computing paradigms from nature.

"Balanced Coverage of State-of-the-Art Concepts, Techniques, and Practices"

Up-to-date, comprehensive, and pragmatic in its approach, this text provides a unified overview of the relationship between the fundamentals of digital system design, computer architectures, and micro- and nanoelectronics.