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Catalogue complet

Han H: Mathematical Foundation of the
Boundary Integro-Differential Equation

Mathematical Foundation of the Boundary Integro-Differential Equation Method

The book is devoted to contemporary variance reduction methods for Monte Carlo and Markov Chain (MCMC) with Machine Learning and Finance applications. We present new approaches based on martingale representations, and Stein control variates besides the standard techniques. In addition, the book focuses on developing new variance reduction algorithms in MCMC and their theoretical analysis. Readers will find numerical examples that illustrate all proposed algorithms.

Advanced Variance Reduction Techniques For Mcmc

Universitext

This textbook provides a thorough-yet-accessible introduction to function spaces, through the central concepts of integrability, weakly differentiability and fractionally differentiability.In an essentially self-contained treatment the reader is introduced to Lebesgue, Sobolev and BV-spaces, before being guided through various generalisations such as Bessel-potential spaces, fractional Sobolev spaces and Besov spaces. Written with the student in mind, the book gradually proceeds from elementary properties to more advanced topics such as lower dimensional trace embeddings, fine properties and approximate differentiability, incorporating recent approaches. Throughout, the authors provide careful motivation for the underlying concepts, which they illustrate with selected applications from partial differential equations, demonstrating the relevance and practical use of function spaces.Assuming only multivariable calculus and elementary functional analysis, as conveniently summarised in the opening chapters,&nbsp;A Course in Function Spaces&nbsp;is designed for lecture courses at the graduate level and will also be a valuable companion for young researchers in analysis.

I: Spaces of continuous and integrable functions

A Course on Function Spaces

Petroleum Production Engineering with Data Science

Ultrasonic Measurement and Characterization of Liquid-Particle Flow

Dieses Buch richtet sich an Studierende in MINT-Studiengängen, die die Mathematik-Grundvorlesungen der ersten beiden Semester absolviert haben. Es vermittelt ein grundlegendes Verständnis der mehrdimensionalen Differentialrechnung und gewöhnlichen Differentialgleichungen und führt schlüssig zur Approximationstheorie und Variationsrechnung. Der Fokus liegt auf den Anwendungsbereichen der Integraltransformationen für die Signalverarbeitung und Systemtheorie sowie einer Einführung zur Modellbildung und Simulation. Zahlreiche Beispiele und etwa 300 Abbildungen unterstützen den Lernprozess.Der AutorWolfgang Högele lehrt als Professor für&nbsp;Angewandte Mathematik&nbsp;mit Schwerpunkt&nbsp;Computational Sciences an der Fakultät für Informatik und Mathematik an der Hochschule München.

Vom Verständnis zum praktischen Werkzeug

Aufbruch in die Angewandte Mathematik

Tutorials, Schools, and Workshops in the Mathematical Sciences

This book presents selected lectures from the Wis¿a 22 Winter School and Workshop organized by the Baltic Institute of Mathematics that illustrate the power of geometric methods in understanding complex physical systems.&nbsp; Chapters progress from foundational mathematical structures to concrete applications in fluid dynamics and mechanical systems, highlighting the profound connection between differential geometry and physical phenomena.
The first chapter investigates differentiable structures on a non-Hausdorff line with two origins, setting the stage for the applications that follow.&nbsp; The next chapter transitions to fluid mechanics through a study of generalized geometry in two-dimensional incompressible fluid flows, establishing the mathematical framework needed for analyzing fluid systems through geometric lenses.&nbsp; Building on these foundations, the third chapter expands the perspective with a comprehensive treatment of nonlinear differential equations in fluid mechanics, utilizing concepts from contact and symplectic geometry to illuminate singular properties of fluid dynamics solutions.&nbsp; Finally, the fourth chapter demonstrates how geometric methods extend beyond fluid mechanics to mechanical systems with nonholonomic constraints, revealing how geometric formulations can address challenging phenomena like discontinuities, collisions, and the counterintuitive stabilization of inverted pendulums.
Geometric Methods in Physical Systems is ideal for graduate students and researchers working in these areas. A basic understanding of differential geometry and mathematical analysis is assumed.

The Wisła 22 Winter School and Workshop

Geometric Methods in Physical Systems: From Differentiable Structures to Applications

Learn to build robust, scalable financial models to position yourself as an expert in computational finance. At a time when the financial industry demands an increasingly complex and accurate mode, this book ensures you stay ahead of the curve by leveraging the latest advancements in programming to develop faster, more reliable, and maintainable financial software.
To begin, you’ll explore key features of C++23, object-oriented programming, and template-based design patterns critical for building reusable financial components. From there, dive into a range of numerical methods, including Monte Carlo simulations, binomial and trinomial trees, and finite difference schemes. Special attention is given to practical implementation details. Every chapter is designed to guide you step by step in transforming mathematical models into efficient, production-level C++ code. You will also learn to handle exotic derivatives, stochastic volatility, and jump-diffusion models, bridging the gap between theory and practice.
In the end, you’ll be equipped with the technical foundation and practical tools needed to design, implement, and analyze complex financial products. You will also be well-prepared to tackle the advanced interest rate and credit derivatives covered in further depth in De La Rosa’s Advanced Quantitative Finance with Modern C++. 
What You Will Learn:&nbsp;
<ul>
<li>Master modern C++23 syntax and features, including object-oriented and generic programming.</li>
<li>&nbsp;Design flexible option payoff hierarchies for code reuse.</li>
<li>Apply advanced numerical techniques such as Monte Carlo, binomial/trinomial trees, and finite difference methods.</li>
<li>Calculate and interpret option sensitivities (Greeks).</li>
<li>Model and price exotic options, including stochastic volatility and jump-diffusion models.</li>
<li>Integrate mathematical finance concepts into production-quality C++ code.</li>
</ul>
Who This Book is for: 
Quantitative analysts, financial engineers, researchers, and advanced developers who seek to deepen their knowledge of derivative pricing and computational finance using modern C++. Also suited for graduate students in quantitative finance or applied mathematics who want to complement their theoretical studies with robust coding skills.

Foundations, Derivatives, and Computational Methods

Mastering Quantitative Finance with Modern C++

SpringerBriefs in Mathematics

This book explores the topological properties of connected and path-connected solution sets for nonlinear equations in Banach spaces, focusing on the distinction between these concepts. Building on Rabinowitz's dichotomy and classical results on Peano continua, the authors introduce "congestion points"—where connected sets fail to be weakly locally connected—and examine the extent to which their presence is compatible with path-connectedness. Through rigorous analysis and examples, the book provides new insights into global bifurcations.

Structured into seven chapters, the book begins with an introduction to global bifurcation theory and foundational concepts in set theory and metric spaces. Subsequent chapters delve into connectedness, local connectedness, and congestion points, culminating in the construction of intricate examples that highlight the complexities of solution sets. The authors' careful selection of material and fluent writing style make this work a valuable resource for PhD students and experts in functional analysis and bifurcation theory.

Connected Sets in Global Bifurcation Theory

This textbook is relevant to BSc/MSc students interested in mathematical modeling and simulation. It brings together analysis, calculus and numerical methods presented in a single coherent volume. Particular attention is given to engineering mathematics, addressing modeling, analysis, method development, implementation and testing of algorithms, as well as application to actual problems and critical interpretation of the results. The book can be used throughout bachelor programs and parts of masters programs, presenting a comprehensive suite of courses that link formal abstract thinking on the one hand to intuitive model formulation, critical algorithm development and interpretation of results on the other hand. The books contains numerous examples of practical applications from physics, technology, biology and chemistry. It also contains an introduction to Matlab and C for algorithm development and computational analysis.&nbsp;Software and solutions to selected problems are included.

Mathematical Modeling and Simulation

The Navier-Stokes equations - modeling the motion of viscous, incompressible Newtonian fluids - have been capturing the attention of an increasing number of mathematicians over the years and has now become one of the most intensely studied subjects in applied analysis. This project is dedicated to a complete and updated mathematical analysis of fundamental topics related to these equations. Every subject will be analyzed using different approaches. The main ideas behind them as well as their differences will also be emphasized and discussed. The book aims at being self-contained, however, it will also be supported by a vast bibliography for further reading.

Navier-Stokes Equations: A Mathematical Analysis

Scientific Facts with Philosophical Considerations and Contributions

Mankind's Problem: Climate Change

This second edition of Linear Operator Equations: Approximation and Regularization provides a modern, accessible, and student-friendly introduction to the theory and numerical treatment of linear operator equations, both well-posed and ill-posed.With rewritten and expanded proofs, a more consistent structure, and numerous new exercises and examples, the book offers clear pathways for learning approximation theory, regularization techniques, and applications of functional analysis to inverse problems. New topics include truncated singular value decomposition, generalized Tikhonov regularization with stabilizing operators, and a deeper treatment of discrete projection methods for operator equations.Designed for students and researchers alike, the book balances theoretical rigor with practical insights, making it a valuable resource for courses in numerical functional analysis, inverse problems, and operator theory, or for self-study by applied mathematicians, engineers, and computational scientists.A newly expanded bibliography, revised notation, and systematic numbering make this edition even more usable as a reference and teaching tool.

Well-posed And Ill-posed Equations: Approximation And Regularization

Numerical Methods for Engineering and Data Science guides students in implementing numerical methods in engineering and in assessing their limitations and accuracy, particularly using algorithms from the field of machine learning.

Numerical Methods for Engineering and Data Science

Mathematical Foundation of the Boundary Integro-Differential Equation Method

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