Applied mathematics Books

Book SynopsisThis book is an extensive guide to the IB Mathematics Analysis and Approaches Internal Assessment component. It provides IB Diploma students with tips, resources, and ideas to help them maximize their marks on their IA. Our guide makes frequent reference to the grading matrix and the format that your IA should follow, as well as highlighting details which you must bear in mind when carrying out your investigation. There is a 50-page introductory section which includes step-by-step advice on: - Structure: how to plan your Math IA the ideal way- Ideas: an exhaustive list of excellent sources and inspirational websites- Assessment: maximizing your marks with one eye on the grading criterion- Technology: which tools can be used to improve your IA Alongside the extensive guide, we have included SEVEN excellent student IA which have scored near-perfect marks after being moderated, including several 20/20 explorations.  

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Book SynopsisThis textbook invites the reader to develop a holistic grounding in mathematical finance, where concepts and intuition play as important a role as powerful mathematical tools. Financial interactions are characterized by a vast amount of data and uncertainty; navigating the inherent dangers and hidden opportunities requires a keen understanding of what techniques to apply and when. By exploring the conceptual foundations of options pricing, the author equips readers to choose their tools with a critical eye and adapt to emerging challenges. Introducing the basics of gambles through realistic scenarios, the text goes on to build the core financial techniques of Puts, Calls, hedging, and arbitrage. Chapters on modeling and probability lead into the centerpiece: the Black–Scholes equation. Omitting the mechanics of solving Black–Scholes itself, the presentation instead focuses on an in-depth analysis of its derivation and solutions. Advanced topics that follow include the Greeks, American options, and embellishments. Throughout, the author presents topics in an engaging conversational style. “Intuition breaks” frequently prompt students to set aside mathematical details and think critically about the relevance of tools in context. Mathematics of Finance is ideal for undergraduates from a variety of backgrounds, including mathematics, economics, statistics, data science, and computer science. Students should have experience with the standard calculus sequence, as well as a familiarity with differential equations and probability. No financial expertise is assumed of student or instructor; in fact, the text’s deep connection to mathematical ideas makes it suitable for a math capstone course. A complete set of the author’s lecture videos is available on YouTube, providing a comprehensive supplementary resource for a course or independent study.Trade Review“This textbook provides excellent tools for a holistic understanding of mathematical finance, which combine intuitive common sense with financial and mathematical concepts. The book appeared as notes for undergraduates from a variety of backgrounds, from mathematics and computer science to economics and finance.” (Nikita Y. Ratanov, Mathematical Reviews, August, 2020)Table of Contents1. Preliminaries via Gambles.- 2. Options.- 3. Modeling.- 4. Some Probability.- 5. The Black–Scholes Equation.- 6. Solutions of Black–Scholes.- 7. Partial information: the Greeks.- 8. Sketching and the American Options.- 9. Embellishments.

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This book gives a concise presentation of the mathematical foundations of Game Theory, with an emphasis on strategic analysis linked to information and dynamics. It is largely self-contained, with all of the key tools and concepts defined in the text.Combining the basics of Game Theory, such as value existence theorems in zero-sum games and equilibrium existence theorems for non-zero-sum games, with a selection of important and more recent topics such as the equilibrium manifold and learning dynamics, the book quickly takes the reader close to the state of the art. Applications to economics, biology, and learning are included, and the exercises, which often contain noteworthy results, provide an important complement to the text.Based on lectures given in Paris over several years, this textbook will be useful for rigorous, up-to-date courses on the subject. Apart from an interest in strategic thinking and a taste for mathematical formalism, the only prerequisite for reading the book is a solid knowledge of mathematics at the undergraduate level, including basic analysis, linear algebra, and probability.

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Book SynopsisThis book provides a broad overview of state-of-the-art research at the intersection of the Koopman operator theory and control theory. It also reviews novel theoretical results obtained and efficient numerical methods developed within the framework of Koopman operator theory.The contributions discuss the latest findings and techniques in several areas of control theory, including model predictive control, optimal control, observer design, systems identification and structural analysis of controlled systems, addressing both theoretical and numerical aspects and presenting open research directions, as well as detailed numerical schemes and data-driven methods. Each contribution addresses a specific problem. After a brief introduction of the Koopman operator framework, including basic notions and definitions, the book explores numerical methods, such as the dynamic mode decomposition (DMD) algorithm and Arnoldi-based methods, which are used to represent the operator in a finite-dimensional basis and to compute its spectral properties from data. The main body of the book is divided into three parts: theoretical results and numerical techniques for observer design, synthesis analysis, stability analysis, parameter estimation, and identification; data-driven techniques based on DMD, which extract the spectral properties of the Koopman operator from data for the structural analysis of controlled systems; and Koopman operator techniques with specific applications in systems and control, which range from heat transfer analysis to robot control. A useful reference resource on the Koopman operator theory for control theorists and practitioners, the book is also of interest to graduate students, researchers, and engineers looking for an introduction to a novel and comprehensive approach to systems and control, from pure theory to data-driven methods.Table of ContentsPart I: Control Design, Observation, and Identification.- Linear Observer Synthesis for Nonlinear Systems.- Linear Predictors for Nonlinear Dynamical Systems.- Global Stability Analysis.- Pulse-based Optimal Control.- Parameter Estimation and Identification of Nonlinear Systems.- Koopman Spectrum and Stability of Cascaded Dynamical Systems.- Open and Closed Loop Control of PDEs via Switched Systems and Koopman operator based reduced order models.- Part II: Data-Driven Analysis.- Data-driven Approximations of Dynamical Systems Operators for Control.- Operator Theoretic-based Data-driven Approach for Optimal Stabilization of Nonlinear System.- Manifold Learning for Data-Driven Dynamical Systems Analysis.- Use of Data-Driven Koopman Spectrum Computation and Delay Embedding.- Part III: Applications.- Modeling of Advective Heat Transfer in a Practical Building Atrium via Koopman Mode Decomposition.- Phase-amplitude Reduction of Limit-cycling Systems.- Exploiting Effects of Network Topology on Performance in Nonlinear Consensus Networks.- Koopman Operators in Embedded Control.

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Book SynopsisThis Festschrift is in honor of Ker-I Ko, Professor in the Stony Brook University, USA. Ker-I Ko was one of the founding fathers of computational complexity over real numbers and analysis. He and Harvey Friedman devised a theoretical model for real number computations by extending the computation of Turing machines. He contributed significantly to advancing the theory of structural complexity, especially on polynomial-time isomorphism, instance complexity, and relativization of polynomial-time hierarchy. Ker-I also made many contributions to approximation algorithm theory of combinatorial optimization problems. This volume contains 17 contributions in the area of complexity and approximation. Those articles are authored by researchers over the world, including North America, Europe and Asia. Most of them are co-authors, colleagues, friends, and students of Ker-I Ko.Table of ContentsIn Memoriam: Ker-I Ko (1950-2018).- Ker-I Ko and the Study of Resource-Bounded Kolmogorov Complexity.- The Power of Self-Reducibility Selectivity, Information, and Approximation.- Who Asked Us - How the Theory of Computing Answers, QuestionsAbout Analysis.- Promise Problems on Probability Distributions.- On Nonadaptive Reductions to the Set of Random Strings and its Dense Subsets.- Computability of the Solutions to Navier-Stokes Equations via Recursive Approximation.- Automatic Generation of Structured Overviews over a Very Large Corpus of Documents.- Better Upper Bounds for Searching on a Line with Byzantine Robots.- A Survey on Double Greedy Algorithms for Maximizing Non-monotone Submodular Functions.- Sequential Location Game on Continuous Directional Star Networks.- Core Decomposition, Maintenance and Applications.- Active and Busy Time Scheduling Problem: a Survey.- A Note on the Position Value for Hypergraph Communication Situations.- An Efficient Approximation Algorithm for the Steiner Tree Problem.- A Review for Submodular Optimization on Machine Scheduling Problems.- Edge Computing Integrated with Blockchain Technologies.

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Book SynopsisThis brief addresses the estimation of quantile regression models from a practical perspective, which will support researchers who need to use conditional quantile regression to measure economic relationships among a set of variables. It will also benefit students using the methodology for the first time, and practitioners at private or public organizations who are interested in modeling different fragments of the conditional distribution of a given variable. The book pursues a practical approach with reference to energy markets, helping readers learn the main features of the technique more quickly. Emphasis is placed on the implementation details and the correct interpretation of the quantile regression coefficients rather than on the technicalities of the method, unlike the approach used in the majority of the literature. All applications are illustrated with R. Table of ContentsWhy and When Should Quantile Regression Be Used?- A Case of Study: Modelling Energy Markets by the Means of Quantile Regression.- Quantile Regression: A Methodological Overview.- Cross-Sectional Quantile Regression.- Time Series Quantile Regression.- Goodness of Fit in Quantile Regression Models.- Novel Approaches in Quantile Regression.- What Have We Learned from Quantile Regression? Implications for Economics and Finance.- Appendix: Programs for Quantile Regression and Implementation in R.

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Book SynopsisThe field of elliptic functions, apart from its own mathematical beauty, has many applications in physics in a variety of topics, such as string theory or integrable systems. This book, which focuses on the Weierstrass theory of elliptic functions, aims at senior undergraduate and junior graduate students in physics or applied mathematics. Supplemented by problems and solutions, it provides a fast, but thorough introduction to the mathematical theory and presents some important applications in classical and quantum mechanics. Elementary applications, such as the simple pendulum, help the readers develop physical intuition on the behavior of the Weierstrass elliptic and related functions, whereas more Interesting and advanced examples, like the n=1 Lamé problem-a periodic potential with an exactly solvable band structure, are also presented.Table of ContentsWeierstrass Elliptic Function.- Weierstrass Quasi-periodic Functions.- Real Solutions of Weierstrass Equation.- Applications in Classical Mechanics.- Applications in Quantum Mechanics.- Epilogue and Projects for the Advanced Reader.

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Book SynopsisThis open access volume presents a novel computational framework for understanding how collections of excitable cells work. The key approach in the text is to model excitable tissue by representing the individual cells constituting the tissue. This is in stark contrast to the common approach where homogenization is used to develop models where the cells are not explicitly present. The approach allows for very detailed analysis of small collections of excitable cells, but computational challenges limit the applicability in the presence of large collections of cells.Table of ContentsDerivation of a cell-based mathematical model of excitable cells.- A cell-based model for ionic electrodiffusion in excitable tissue.- Modeling cardiac mechanics on a subcellular scale.- Operator splitting and finite difference schemes for solving the EMI model.- Solving the EMI equations using finite element methods.- Iterative solvers for EMI models.- Improving neural simulations with the EMI model.- Index.

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Book SynopsisThis book introduces physics students to concepts and methods of finance. Despite being perceived as quite distant from physics, finance shares a number of common methods and ideas, usually related to noise and uncertainties. Juxtaposing the key methods to applications in both physics and finance articulates both differences and common features, this gives students a deeper understanding of the underlying ideas. Moreover, they acquire a number of useful mathematical and computational tools, such as stochastic differential equations, path integrals, Monte-Carlo methods, and basic cryptology. Each chapter ends with a set of carefully designed exercises enabling readers to test their comprehension.Table of ContentsChapter 1 - Introduction Chapter 2 - Concepts of finance Chapter 3 - Portfolio theory and CAPM Chapter 4 - Stochastic processes Chapter 5 - Black-Scholes differential equation Chapter 6 - The Greeks and risk management Chapter 7 - Regression models and hypothesis testing Chapter 8 - Time series Chapter 9 - Bubbles, crashes, fat tails and Levy-stable distributions Chapter 10 - Quantum finance and path integrals Chapter 11 - Optimal control theory.

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Book SynopsisThis book explores the fascinating and intimate relationship between music and physics. Over millennia, the playing of, and listening to music have stimulated creativity and curiosity in people all around the globe. Beginning with the basics, the authors first address the tonal systems of European-type music, comparing them with those of other, distant cultures. They analyze the physical principles of common musical instruments with emphasis on sound creation and particularly charisma. Modern research on the psychology of musical perception – the field known as psychoacoustics – is also described. The sound of orchestras in concert halls is discussed, and its psychoacoustic effects are explained. Finally, the authors touch upon the role of music for our mind and society. Throughout the book, interesting stories and anecdotes give insights into the musical activities of physicists and their interaction with composers and musicians.Table of Contents

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Book SynopsisAsset pricing theory yields deep insights into crucial market phenomena such as stock market bubbles. Now in a newly revised and updated edition, this textbook guides the reader through this theory and its applications to markets. The new edition features ​new results on state dependent preferences, a characterization of market efficiency and a more general presentation of multiple-factor models using only the assumptions of no arbitrage and no dominance. Taking an innovative approach based on martingales, the book presents advanced techniques of mathematical finance in a business and economics context, covering a range of relevant topics such as derivatives pricing and hedging, systematic risk, portfolio optimization, market efficiency, and equilibrium pricing models. For applications to high dimensional statistics and machine learning, new multi-factor models are given. This new edition integrates suicide trading strategies into the understanding of asset price bubbles, greatly enriching the overall presentation and further strengthening the book’s underlying theme of economic bubbles. Written by a leading expert in risk management, Continuous-Time Asset Pricing Theory is the first textbook on asset pricing theory with a martingale approach. Based on the author’s extensive teaching and research experience on the topic, it is particularly well suited for graduate students in business and economics with a strong mathematical background. Table of Contents

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Book SynopsisThis text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.Trade Review“This book has a large amount of new exercise problems that are uniformly distributed across the text. … this book is a very nice text which will serve well for the undergraduate as well as graduate students and will also become a ready reference for scholars.” (Murli M. Gupta, Mathematical Reviews, April, 2023)“Many of the SIAM Review readership will be interested in NMEPPDE from the standpoint of self-study or classroom education. … NMEPPDE offers the applied mathematics reader nearly a single point of entry to our broad and challenging area. … a bit of open space on the bookshelf could profitably be well filled with a copy of NMEPPDE.” (Robert C. Kirby, SIAM Review, Vol. 65 (1), March, 2023)Table of ContentsFor Example: Modelling Processes in Porous Media with Differential Equations.- For the Beginning: The Finite Difference Method for the Poisson Equation.- The Finite Element Method for the Poisson Equation.- The Finite Element Method for Linear Elliptic Boundary Value Problems of Second Order.- Grid Generation and A Posteriori Error Estimation.- Iterative Methods for Systems of Linear Equations.- Beyond Coercivity, Consistency and Conformity.- Mixed and Nonconforming Discretization Methods.- The Finite Volume Method.- Discretization Methods for Parabolic Initial Boundary Value Problems.- Discretization Methods for Convection-Dominated Problems.- An Outlook to Nonlinear Partial Differential Equations.- Appendices.

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Book SynopsisThis book is intended to serve as a basic introduction to scientific computing by treating problems from various areas of physics - mechanics, optics, acoustics, and statistical reasoning in the context of the evaluation of measurements. After working through these examples, students are able to independently work on physical problems that they encounter during their studies. For every exercise, the author introduces the physical problem together with a data structure that serves as an interface to programming in Excel and Python. When a solution is achieved in one application, it can easily be translated into the other one and presumably any other platform for scientific computing. This is possible because the basic techniques of vector and matrix calculation and array broadcasting are also achieved with spreadsheet techniques, and logical queries and for-loops operate on spreadsheets from simple Visual Basic macros. So, starting to learn scientific calculation with Excel, e.g., at High School, is a targeted road to scientific computing. The primary target groups of this book are students with a major or minor subject in physics, who have interest in computational techniques and at the same time want to deepen their knowledge of physics. Math, physics and computer science teachers and Teacher Education students will also find a companion in this book to help them integrate computer techniques into their lessons. Even professional physicists who want to venture into Scientific Computing may appreciate this book.Table of Contents

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Book Synopsis1.Un dittatore deve sempre esistere.- 2.Il teorema di Arrow è un potente strumento per comprendere molti fenomeni sociali.- 3.Caterina la Grande e Gengis Khan: Il potere non ha genere.- 4.Alcuni problemi aperti per una teoria matematica generale delle strutture sociali.- 5.Fenomenologia della leadership.- 6.Fenomenologia della dittatura.

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Book SynopsisChapter 1: Making Up Our Minds: Imaginative Deconstruction in MathArt, 1920 Present .- Chapter 2: What is a Mathematical Ode? .- Chapter 3: Venice, Glass, and Math .- Chapter 4: A Topological Journal of the Plague Year .- Chapter 5: Artistic Mediation in Mathematized Phenomenology.- Chapter 6: History.- Chapter 7: The Making of a Mathematician: Personal and Professional Growth Through Writing.- Chapter 8: MathLIKE: Coining a New Word, Using It in Teaching, and in Interpreting Some of My Own Math-Poetry.- Chapter 9: A Meaningful Intersection: Mathematics, Computer Programming, and Art.- Chapter 10: Twas the Functorial Night.- Chapter 11: Sonnets.- Chapter 12: Categorical Colors in Diamonds: Sight as Site: Categorical Ozma and Cinderella.- Chapter 13: Old Math.- Chapter 14: Design of Strips with Geometry Shapes and Mathematical Analysis.- Chapter 15: Imagination as Mathematics.- Chapter 16: The Long Fraction line: Mathematical Concepts Rhymers.- Chapter 17: Solving with Sherlock.- Chapter 18: Qurio: Meta-Learning Curiosity Algorithms and Agentive AI Tutors.- Chapter 19: Marvels.- Chapter 20: Decembris: My Emerald Winter Color Walk.

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Book SynopsisA Neurophysiology Primer for Mathematicians.- A Discrete Time Stochastic Neural Network Model.- Mean Field Limits for Discrete Time Stochastic Neural Network Models.- But Time is Continuous!.- Models without Reset: Hawkes Processes.- What is a Stationary State in a Potentially Infinite System?.- Statistical Estimation of the Interaction Graph.- Mean Field Limits and Short-Term Synaptic Facilitation in Continuous Time Models.- A Non-Exhaustive List of Some Open Questions.- Appendix A.- Appendix B.- Appendix C.- Appendix D.- Appendix E.- Appendix F.- References.- Index.

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Book SynopsisGenerative Modelling of Stochastic Rotating Shallow Water Noise.- Collisions of Burgers Bores with Nonlinear Waves.- Average dissipation for stochastic transport equations with Lévy noise.- General Solution Theory for the Stochastic Navier-Stokes Equations.- Geometric theory of perturbation dynamics around non-equilibrium fluid flows.- On forward-backward SDE approaches to conditional estimation.- Data Assimilation for the  Stochastic Camassa-Holm Equation Using  Particle Filtering: A Numerical Investigation.- Some properties of a non-hydrostatic stochastic oceanic primitive equations model.- Derivation of stochastic models for coastal waves.- The Effects of Unresolved Scales on Analogue Forecasting Ensembles.- Particle-based algorithm for stochastic optimal control.- Maximum likelihood estimation of subgrid flows from tracer image sequences.- Transport noise defined from wavelet transform for model-based stochastic ocean models.- Stochastic fluids with transport noise: Approximating diffusion from data using SVD and ensemble forecast back-propagation.

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Book SynopsisWhat is Vagueness.- Sets and their Properties.- Fuzzy Sets and their Properties.- Extensions of Fuzzy Sets.- Fuzzy Numbers.- Other Fuzzy Constructs.

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Book Synopsis- 1. Models.- 2. Limit Passages.- 3. Central Limit-type Theorems.- 4. Selected Superprocesses.- 5. Phenotype Models.- 6. Modelling of Phytoplankton Dynamics.- 7. Chemotaxis Models.

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Book Synopsis- 1. Introduction.- 2. Cauchy Problem, Steady States, and Diffusive Behaviour.- 3. Travelling Waves.- 4. Sharp Fisher-KPP Spreading.- 5. Sharp ZFK Spreading.- 6. Spreading in Several Space Dimensions.- 7. Final Remarks.

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Book Synopsis- 1. Mike and Me Since 1973: A Review of a Long Friendship and Research Relationship.- 2. Michael Mackey and Data-Driven Models of Chemotherapy-Induced Neutropenia.- 3. Biological rhythms: Mechanisms, functions, and associated disorders.- 4. Mathematical Modeling of Heterogeneous Stem Cell Regeneration: From Cell Division to Waddington's Epigenetic Landscape.- 5. A Mathematical Model to Describe the Formation of Perinuclear ATM Crown and the Effect of Irradiation and Antioxidants in Cells Affected by Alzheimer's Disease.- 6. Ergodic and Chaotic Properties of Some Biological Models.- 7. Quantitative Insights into Glucose Regulation: A Review of Mathematical Modeling Efforts.- 8. Why does a Stick Balanced on the Fingertip fall?.

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Book SynopsisTopics of Linear Algebra.- Introduction to Functions of Several Real Variables.- Introduction to Convex Analysis.- Static Optimization.- Linear Programming.- Continuous Dynamical Systems.- Discrete Dynamical Systems.- Introduction to Dynamic Optimization.

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Book SynopsisIntroduction.- Asymptotics in Digital Humanities.- Function Diagrams in Digital Humanities.- History of War.- History Through Clocks.- Networks and Macrohistory.- Networks Microhistory.- What Is a Computational Model for History.- History through the Core.- History after the Death of the Witnesses.- History while the Witnesses are Still Alive.- Propaganda in History.- Stochastic terrorism.- Historian Machine.- Information and History.- Machine Learning and History.- Representing Historical Information.- Fake History.

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Book SynopsisCancer genomics.- Novel Driver Mutations in GCB Lymphoma Patients That Affect Transcription Factors Binding..- Inferring Phylogenetic Trees of Cancer Evolution from Longitudinal Single-Cell Copy Number Profiles.Homology and Reconciliation.- Tree decomposition for reconstructing ancestral RNA sequences of multiple families..- Whole-genome duplication detection with phylogenomics reconciliation: a scalable approach..- A Sankoff-Rousseau-like Algorithm for Minimizing Lateral Gene Transfers and Losses on Single Origin Characters..- tMHG-Finder: Tree-guided Maximal Homologous Group Finder for Bacterial Genomes.Phylogenetics.- Phylogenetic Network Diversity Parameterized by Reticulation Number and Beyond..- On the robustness to gene tree rooting (or lack thereof) of triplet-based species tree estimation methods..- Exact Counts of Binary Phylogenetic Networks with Two and Three Reticulation Events..- Ancestral pangenomes and their phylogenetic reconstruction..- QT-WEAVER: Correcting quartet distribution improves phylogenomic analyses despite gene tree estimation error..- Fast calculation of cherry distance on level-1 orchard networks: optimization, heuristic and implementation.Sequence analysis.- Detecting and Mapping Local Model Violations During Biomolecular Sequence Analysis: a RE sampling and Visual EvALuation Approach..- A simple way to find related sequences with position-specific probabilities..- Position Specific Scoring Is All You Need? Revisiting Protein Sequence Classification Tasks.Epidemiology.- Residual immunity and seasonality of an epidemic..- Adapting the cov2clusters tool for clustering MPOXV whole genome sequences.Genome evolution.- Probability-based sequence comparison finds the oldest ever nuclear mitochondrial DNA segments in mammalian genomes..- Unraveling Insect Immunity: A Cross-Order Comparative Genomic Analysis of Key Immune Proteins..- Analyzing Sequence Similarity Distributions in Salmonidae: A Branching Process Approach..- Evolutionary Reconstruction of Hormone-bHLH Regulatory Networks in Solanaceae: Phylogenomic Insights from PSTVd-Tomato Interactions.

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Book SynopsisThe dynamics of sensorimotor integration.- Unveiling the intrinsic dynamics of biological and artificial neural networks: from criticality to optimal representations.- Emergent complex dynamics in neuronal cultures and its relation to neuroengineering and medicine.- Modeling and analyzing biological systems using branching processes.- Stochastic reaction-diffusion systems in biophysics: towards a toolbox for quantitative model evaluation.- Networks: the visual language of complexity.- Modelling the formation of the granuloma inside secondary lobule of the lungs.- Mathematical model for sustainable biodegradation process.

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Book SynopsisThis book discusses questions of numerical solutions of applied problems on parallel computing systems. Nowadays, engineering and scientific computations are carried out on parallel computing systems, which provide parallel data processing on a few computing nodes. In the development of up-to-date applied software, this feature of computers must be taken into account for the maximum efficient usage of their resources. In constructing computational algorithms, we should separate relatively independent subproblems in order to solve them on a single computing node.

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Book SynopsisA comprehensive and easy to understand introduction to a wide range of tools to help designers to optimize their projects. The authors are engineers and therefore many of the examples are on engineering applications, but the techniques presented are common to various areas of knowledge and pervade disciplinary divisions. The book describes the fundamental ideas, mathematical and graphic methods and shows how to use Matlab and EXCEL for optimization.

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Book SynopsisThis book starts with the description of polarization in classical optics, including also a chapter on crystal optics, which is necessary to understand the use of nonlinear crystals. In addition, spatially non-uniform polarization states are introduced and described. Further, the role of polarization in nonlinear optics is discussed. The final chapters are devoted to the description and applications of polarization in quantum optics and quantum technologies.

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Book SynopsisMany nonlinear systems around us can generate a very complex and counter-intuitive dynamics that contrasts with their simplicity, but their understanding requires concepts that are outside the basic training of most science students. This textbook, which is the fruit of graduate courses that the authors have taught at their respective universities, provides a richly illustrated introduction to nonlinear dynamical systems and chaos and a solid foundation for this fascinating subject. It will satisfy those who want discover this field, including at the undergraduate level, but also those who need a compact and consistent overview, gathering the concepts essential to nonlinear scientists.The first and second chapters describe the essential concepts needed to describe nonlinear dynamical systems as well as their stability. The third chapter introduces the concept of bifurcation, where the qualitative dynamical behavior of a system changes. The fourth chapter deals with oscillations, from their birth to their destabilization, and how they respond to external driving. The fifth and sixth chapters discuss complex behaviors that only occur in state spaces of dimension three and higher: quasi-periodicity and chaos, from their general properties to quantitative methods of characterization. All chapters are supplemented by exercises ranging from direct applications of the notions introduced in the corresponding chapter to elaborate problems involving concepts from different chapters, as well as numerical explorations.

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Book SynopsisThis textbook gives a unified treatment of the solution of various linear equations that arise in science and engineering with examples. It is based on a course taught by the first author for over thirty years. Some unique features include: Use of symbolic software for illustrating and enhancing the impact of physical parameter changes on solutions. Multi-scale analysis of engineering problems with physical interpretation of time and length scales in terms of eigenvalues and eigenvectors/eigenfunctions. Discussion of compartment models for various finite dimensional problems. Evaluation and illustration of functions of matrices (and use of symbolic manipulation) to solve multi-component diffusion-convection-reaction problems. Illustration of the techniques and interpretation of solutions to several classical engineering problems. Emphasis on the connection between discrete (matrix algebra) and continuum. Physical interpretation of adjoint operator and adjoint systems. Use of complex analysis and algebra in the solution of practical engineering problems.

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Book SynopsisThe work shows, by means of examples coming from different corners of physics, how physical and mathematical questions can be answered using a computer. Starting with maps and neural networks, applications from Newton's mechanics described by ordinary differential equations come into the focus, like the computation of planetary orbits or classical molecular dynamics. A large part of the textbook is dedicated to deterministic chaos normally encountered in systems with sufficiently many degrees of freedom. Partial differential equations are studied considering (nonlinear) field theories like quantum mechanics, thermodynamics or fluid mechanics. In the second edition, a new chapter gives a detailed survey on delay or memory systems with a direct application to epidemic and road traffic models. Most of the algorithms are realized in FORTRAN, a language most suitable for effectively solving the discussed problems. On the other hand, the codes given and presented on the book’s homepage can be easily translated into other languages. Moreover, several MATLAB examples are presented, mainly for didactic reasons. The book is addressed to advanced Bachelor or Master students of physics, applied mathematics and mechanical engineering.

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Book SynopsisMathematical models cannot be solved using the traditional analytical methods for dynamic equations on time scales. These models must be dealt with using computational methods. This textbook introduces numerical methods for initial value problems for dynamic equations on time scales. Hands-on examples utilizing MATLAB and practical problems illustrate a wide variety of solution techniques.

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Book SynopsisOrdinary differential equations (ODEs) and differential-algebraic equations (DAEs) are widely used to model control systems in engineering, natural sciences, and economy. Optimal control plays a central role in optimizing such systems and to operate them effi ciently and safely. The intention of this textbook is to provide both, the theoretical and computational tools that are necessary to investigate and to solve optimal control problems with ODEs and DAEs. An emphasis is placed on the interplay between the optimal control problem, which typically is defi ned and analyzed in a Banach space setting, and discretizations thereof, which lead to finite dimensional optimization problems. The theoretical parts of the book require some knowledge of functional analysis, the numerically oriented parts require knowledge from linear algebra and numerical analysis. Practical examples are provided throughout the book for illustration purposes. The book addresses primarily master and PhD students as well as researchers in applied mathematics, but also engineers or scientists with a good background in mathematics. The book serves as a reference in research and teaching and hopefully helps to advance the state-of-the-art in optimal control.

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Book SynopsisPrecision and uniformity are indispensable when working with physical quantities, units and formula symbols. Only through unambiguous and authoritative notation is interdisciplinary cooperation possible. The book gives an overview of all common quantities and units, which are needed in studies and teaching as well as in everyday work. All printed quantities and units are currently valid and standardized in ISO/IEC. The book includes: _brief introduction to the development of the system of units _overview on the system of quantities and units _calculating with quantity values _units (international system of units, SI) _notation of numbers _mathematical symbols _Standardized symbols for quantities (mechanics, space and time, radiation, solid state physics, etc.), elements, nuclides, particles and quantum states. _Appendix: conversion to the U.S. customary system of units.

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Book SynopsisEvery age and every culture has relied on the incorporation of mathematics in their works of architecture to imbue the built environment with meaning and order. Mathematics is also central to the production of architecture, to its methods of measurement, fabrication and analysis. This two-volume edited collection presents a detailed portrait of the ways in which two seemingly different disciplines are interconnected. Over almost 100 chapters it illustrates and examines the relationship between architecture and mathematics. Contributors of these chapters come from a wide range of disciplines and backgrounds: architects, mathematicians, historians, theoreticians, scientists and educators. Through this work, architecture may be seen and understood in a new light, by professionals as well as non-professionals.Volume I covers architecture from antiquity through Egyptian, Mayan, Greek, Roman, Medieval, Inkan, Gothic and early Renaissance eras and styles. The themes that are covered range from symbolism and proportion to measurement and structural stability. From Europe to Africa, Asia and South America, the chapters span different countries, cultures and practices.Trade Review“It presents several alternative historical and theoretical contexts of the relationship between architecture and mathematics which has been pushed to the foreground during the past decades with the increasing use of computer-aided design in their profession … . Historians of mathematics, too, will no doubt find useful material here for their research, especially if they are interested in the more practical concerns that have shaped the development of their field … .” (Yelda Nasifoglu, BSHM Bulletin, Vol. 31 (3), October, 2016)“The study of connections between mathematics and the arts has grown considerably in recent decades, influenced by the work of Doris Schattschneider, Jay Kappraff, and Michele Emmer, among others. The use of mathematics is particularly a necessity in architecture, so the present set is welcome. … This is a valuable resource for mathematics, architecture, and the arts in general. Summing Up: Highly recommended. All readers.” (C. A. Gorini, Choice, Vol. 53 (2), October, 2015)“The ambitious goal is to describe both the intimate relation but also the alienation between mathematics and architecture and between mathematicians and architects. … It is an important and highly inspiring collection of papers that will be of interest to researchers from as many disciplines as illustrated by the diversity of the background of the authors. … Highly recommended for readers who do not want to drown or hide in their own abyss of specialization.” (Adhemar Bultheel, euro-math-soc.eu, June, 2015)Table of ContentsPart I: Introduction.- Part II: From 2000 BC to 300AD.- Part III: Theories of Measurement and Structure.- Part IV: From 1100 AD to 1400 AD.- Part V: Theories of Proportion, Symmetry, Periodicity.- Part VI: From 1500 AD to 1600 AD.- Index.- Acknowledgements.

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Book SynopsisEvery age and every culture has relied on the incorporation of mathematics in their works of architecture to imbue the built environment with meaning and order. Mathematics is also central to the production of architecture, to its methods of measurement, fabrication and analysis. This two-volume edited collection presents a detailed portrait of the ways in which two seemingly different disciplines are interconnected. Over almost 100 chapters it illustrates and examines the relationship between architecture and mathematics. Contributors of these chapters come from a wide range of disciplines and backgrounds: architects, mathematicians, historians, theoreticians, scientists and educators. Through this work, architecture may be seen and understood in a new light, by professionals as well as non-professionals.Volume II covers architecture from the Late Renaissance era, through Baroque, Ottoman, Enlightenment, Modern and contemporary styles and approaches. Key figures covered in this volume include Palladio, Michelangelo, Borromini, Sinan, Wren, Wright, Le Corbusier, Breuer, Niemeyer and Kahn. Mathematical themes which are considered include linear algebra, tiling and fractals and the geographic span of the volume’s content includes works in the United States of America and Australia, in addition to those in Europe and Asia.Trade Review“It presents several alternative historical and theoretical contexts of the relationship between architecture and mathematics which has been pushed to the foreground during the past decades with the increasing use of computer-aided design in their profession … . Historians of mathematics, too, will no doubt find useful material here for their research, especially if they are interested in the more practical concerns that have shaped the development of their field … .” (Yelda Nasifoglu, BSHM Bulletin, Vol. 31 (3), October, 2016)Table of ContentsPart VII: Theories of Representation.- Part VIII: From 1600 AD to 1900 AD.- Part IX: 1900–2000.- Part X: Contemporary Approaches to Design and Analysis.- Part XI: Theories and Applications of Computer Sciences.- Index.- Acknowledgements.​

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Book SynopsisOffering a concise but complete survey of the common features of the microstructure of electricity markets, this book describes the state of the art in the different proposed electricity price models for pricing derivatives and in the numerical methods used to price and hedge the most prominent derivatives in electricity markets, namely power plants and swings. The mathematical content of the book has intentionally been made light in order to concentrate on the main subject matter, avoiding fastidious computations. Wherever possible, the models are illustrated by diagrams. The book should allow prospective researchers in the field of electricity derivatives to focus on the actual difficulties associated with the subject. It should also offer a brief but exhaustive overview of the latest techniques used by financial engineers in energy utilities and energy trading desks.Table of Contents​Introduction.- Electricity Markets.- Electricity Features.- Markets Microstructure.- Real Derivatives.- Conclusion.- Price Models.- Preliminary Remarks.- HJM Style Forward Curve Models.- One-Factor Spot Models.- Multi-Factor Spot Models.- Structural Models.- Derivatives.- Spreads.- Power Plants and Tollings.- Storage and Swings.- Retail Contracts.- Weather Derivatives.- Conclusion.

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Book SynopsisThe book offers a detailed, robust, and consistent framework for the joint consideration of portfolio exposure, risk, and performance across a wide range of underlying fixed-income instruments and risk factors. Through extensive use of practical examples, the author also highlights the necessary technical tools and the common pitfalls that arise when working in this area. Finally, the book discusses tools for testing the reasonableness of the key analytics to help build and maintain confidence for using these techniques in day-to-day decision making. This will be of keen interest to risk managers, analysts and asset managers responsible for fixed-income portfolios.Table of ContentsWhat Is Portfolio Analytics?- From Risk Factors to Returns: Computing Exposures.- A Useful Approximation.- Extending Our Framework.- The Yield Curve: Fitting Yield Curves.- Modelling Yield Curves.- Performance: Basic Performance Attribution.- Advanced Performance Attribution.- Traditional Performance Attribution.- Risk: Introducing Risk.- Portfolio Risk.- Exploring Uncertainty in Risk Measurement.- Risk and Performance: Combining Risk and Return.- The Ex-Post World.- Appendix: Some Mathematical Background.- A Few Thoughts on Optimization.- Index.

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Book SynopsisConsidering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equations the present book introduces a new method for modeling the states of complex systems perturbed by random sources over time, such as interest rates in financial markets or temperature distributions in a specific region. It studies properties of the solutions of the stochastic equations, observing the long-term behavior and the sensitivity of the solutions to changes in the initial data. The authors consider an integration theory of measurable and adapted processes in appropriate Banach spaces as well as the non-Gaussian case, whereas most of the literature only focuses on predictable settings in Hilbert spaces. The book is intended for graduate students and researchers in stochastic (partial) differential equations, mathematical finance and non-linear filtering and assumes a knowledge of the required integration theory, existence and uniqueness results and stability theory. The results will be of particular interest to natural scientists and the finance community. Readers should ideally be familiar with stochastic processes and probability theory in general, as well as functional analysis and in particular the theory of operator semigroups. ​Table of Contents1.Introduction.- 2.Preliminaries.- 3.Stochastic Integrals with Respect to Compensated Poisson Random Measures.- 4.Stochastic Integral Equations in Banach Spaces.- 5.Stochastic Partial Differential Equations in Hilbert Spaces.- 6.Applications.- 7.Stability Theory for Stochastic Semilinear Equations.- A Some Results on compensated Poisson random measures and stochastic integrals.- References.- Index.

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Book SynopsisThis book offers readers a primer on the theory and applications of Ordinary Differential Equations. The style used is simple, yet thorough and rigorous. Each chapter ends with a broad set of exercises that range from the routine to the more challenging and thought-provoking. Solutions to selected exercises can be found at the end of the book. The book contains many interesting examples on topics such as electric circuits, the pendulum equation, the logistic equation, the Lotka-Volterra system, the Laplace Transform, etc., which introduce students to a number of interesting aspects of the theory and applications. The work is mainly intended for students of Mathematics, Physics, Engineering, Computer Science and other areas of the natural and social sciences that use ordinary differential equations, and who have a firm grasp of Calculus and a minimal understanding of the basic concepts used in Linear Algebra. It also studies a few more advanced topics, such as Stability Theory and Boundary Value Problems, which may be suitable for more advanced undergraduate or first-year graduate students. The second edition has been revised to correct minor errata, and features a number of carefully selected new exercises, together with more detailed explanations of some of the topics.A complete Solutions Manual, containing solutions to all the exercises published in the book, is available. Instructors who wish to adopt the book may request the manual by writing directly to one of the authors.Trade Review“This is the second edition of an undergraduate introduction to ordinary differential equations suitable for mathematicians and engineers. … The style is clean and concise with many examples and exercises. Basic results are proven, more involved results are only stated. The new edition features some new exercises and better explanations at various points. So if you are looking for an application oriented introduction which is still concise and rigorous, this book might be just right for you.” (G. Teschl, Monatshefte für Mathematik, 2016)Table of Contents1 First order linear differential equations.- 2 Theory of first order differential equations.- 3 First order nonlinear differential equations.- 4 Existence and uniqueness for systems and higher order equations.- 5 Second order equations.- 6 Higher order linear equations.- 7 Systems of first order equations.- 8 Qualitative analysis of 2x2 systems and nonlinear second order equations.- 9 Sturm Liouville eigenvalue theory.- 10 Solutions by infinite series and Bessel functions.- 11 Laplace transform.- 12 Stability theory.- 13 Boundary value problems.- 14 Appendix A. Numerical methods.- 15 Answers to selected exercises.

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