Beyond Signals - Exploring Revolutionary Fourier Transform Applications
Fourier Transform is a fundamental mathematical framework that has revolutionized numerous scientific and technological domains. Beyond Signals - Exploring Revolutionary Fourier Transform Applications presents an in-depth analysis of its profound influence on modern research and industry. This volume explores advanced applications in signal processing, spectroscopy, quantum mechanics, biomedical imaging, nanomaterials, and renewable energy, illustrating how Fourier techniques enable precise data interpretation and system optimization. The book integrates theoretical foundations with practical implementations, offering insights into its role in material characterization, sensor technology, and computational modeling. Authored by distinguished experts, including Dr. Muhammad Bilal Tahir-recognized for his contributions to nanomaterials, optoelectronics, and applied physics-this work is a comprehensive resource for researchers, engineers, and scholars. By bridging classical theories with emerging advancements, Beyond Signals - Exploring Revolutionary Fourier Transform Applications highlights the transformative potential of Fourier Transform methodologies in solving complex scientific and engineering challenges.
Solution of Initial-Boundary Value Problems
Methods for solving problems of mathematical physics can be divided into the following four classes. Analytical methods (the method of separation of variables, the method of characteristics, the method of Green's functions, etc.) methods have a relatively low degree of universality, i.e. focused on solving rather narrow classes of problems. Approximate analytical methods (projection, variational methods, small parameter method, operational methods, various iterative methods) are more versatile than analytical ones. Numerical methods (finite difference method, direct method, control volume method, finite element method, etc.) are very universal methods. Probabilistic methods (Monte Carlo methods) are highly versatile. Can be used to calculate discontinuous solutions. However, they require large amounts of calculations and, as a rule, they lose with the computational complexity of the above methods when solving such problems to which these methods are applicable. Comparing methods for solving problems of mathematical physics, it is impossible to give unconditional primacy to any of them. Any of them may be the best for solving problems of a certain class. The proposed method of moving nodes for boundary value problems of differential equations combines a combination of numerical and analytical methods. In this case, we can obtain, on the one hand, an approximately analytical solution of the problem, which is not related to the methods listed above. On the other hand, this method allows one to obtain compact discrete approximations of the original problem. Note that obtaining an approximately analytical solution of differential equations is based on numerical methods. The nature of numerical methods also allows obtaining an approximate analytical expression for solving differential equations
Handbook of Calculus of Variations for Absolute Beginners
The book aims at endowing any student with a survival toolkit to start safely diving into the realm of Calculus of Variations. In summary, the latter is a part of mathematical analysis devoted to minimization/maximization problems. A great effort has been made to present the themes and methods considered in the book in the simplest possible way: the reader will not find here general statements or proofs based on general abstract theories. In contrast, the main focus of the book is on introducing some key concepts "from scratch", by means of simple and meaningful explicit examples (including for instance, the classical isoperimetric and brachistocrone problems, as well as the boundary value problem for harmonic functions). In particular, the book is mainly (but not exclusively) designed to smoothly introduce the reader to the so-called Direct Method of the Calculus of Variations, which is a central concept in the field. Accordingly, a good part of the book is devoted to discussing spaces of weakly differentiable functions (i.e., Sobolev and Lipschitz functions), which are essential tools of the Direct Method. A long list of problems will guide the student through the study of the subject. Almost all the problems come with their fully detailed solutions. The book is complemented by four appendices, which contribute to making it self-contained, as well as to deepening the study of certain parts. Despite being designed for students, even the researchers in the field could find a reading of the book profitable, at least for certain parts concerning the properties of Sobolev spaces, functional inequalities of the Sobolev-Poincar矇 type, tricks to handle nonlinear elliptic PDEs, and a gentle introduction to some techniques of modern regularity theory for elliptic PDEs.
Variance-Constrained Filtering for Stochastic Complex Systems
Game Theory for Applied Econometricians
Over the last 30 years the practice and use of game theory has changed dramatically, yet textbooks continue to present game theory with algebraic formalism and toy models. This book, on the other hand, illustrates game theory concepts using real-world data and analyses problems with real policy implications.
Unique Continuation Properties for Partial Differential Equations
Complex Analysis and Dynamics in One Variable with Applications
Metrical and Ergodic Theory of Continued Fraction Algorithms
This monograph presents the work of the authors in metrical theory of continued fractions in the last two decades. The monograph cuts a particular path through this extensive theory and describes the theory in its current form for three families of continued fractions, namely, θ-continued fractions, N-continued fractions, and generalized R矇nyi continued fractions. The book systematically lays out the required preliminaries, making the book easy to read. This monograph provides a solid introduction into the theory of continued fractions. The book is intended for researchers in metrical theory, as well as advanced graduate students and mathematicians interested in this field.
Bayesian Modelling of Suspended Solids in Oyo State Reservoirs
Construction of Advanced Machine Learning Models for Air Traffic
The Vedic Math Bible
The Vedic Math Way is more than a guide to faster calculations-it's a revolutionary journey into the timeless intelligence of ancient Indian mathematics, reimagined for today's learners, educators, and problem-solvers. Whether you're a student aiming to ace competitive exams, a teacher seeking innovative methods to spark numerical intuition, or an adult wishing to rekindle mental sharpness, this book delivers powerful techniques that are as practical as they are profound.Rooted in the 16 foundational Sutras of Vedic Mathematics, this book unveils a system that fosters mental clarity, speed, flexibility, and confidence-not by memorisation, but through intuitive insight. It breaks down complex arithmetic into effortless steps, nurtures logical thinking through pattern recognition, and builds numerical literacy without dependence on calculators or rote learning.What makes this book essential is its structure: every chapter is crafted to demystify the principles, offer real-world applications, and develop scalable skills through practice drills, brain games, and strategy frameworks tailored for timed tests and daily use. From basic operations to Olympiad-level challenges, the content evolves with the reader-making it a true "from beginner to master" experience.This book will be a game-changer for: Students preparing for competitive exams (SAT, GMAT, GRE, CAT, Olympiads, etc.)Educators looking to enrich classrooms with dynamic, ancient-meets-modern methodologyParents supporting their children's learning with logic-based strategiesLifelong learners who want to sharpen their minds and rediscover joy in numbersIn a world obsessed with shortcuts, The Vedic Math Way offers something deeper-a mindset of mastery. It's not just about how fast you solve; it's about how clearly you think. Whether you're battling number anxiety or aiming for mental agility, this book provides the tools, the history, and the roadmap to awaken the inner mathematician in you.
Probability, Statistics, and Reliability for Engineers and Scientists
This book helps engineering students and practicing engineers understand the fundamentals of probability, statistics, and reliability methods, especially their applications, limitations, and potential.
Causal Analysis for Climate Study
This book offers the theory of causal analysis and its applications. The authors have developed this book in relation its applications to four climatological phenomena, to prove the theory of causal analysis in time sequential data analysis.
Bridging Eigenvalue Theory and Practice - Applications in Modern Engineering
Combining Expert Knowledge and Deep Learning with Case-Based Reasoning for Predictive Maintenance
If a manufacturing company's main goal is to sell products profitably, protecting production systems from defects is essential and has led to vast documentation and expert knowledge. Industry 4.0 has facilitated access to sensor and operational data across the shop floor, enabling data-driven models that detect faults and predict failures, which are crucial for predictive maintenance to minimize unplanned downtimes and costs. Commonly, a universally applicable machine learning (ML) approach is used without explicitly integrating prior knowledge from sources beyond training data, risking incorrect rediscovery or neglecting already existing knowledge. Integrating expert knowledge with ML can address the scarcity of failure examples and avoid the learning of spurious correlations, though it poses technical challenges when combining Semantic Web-based knowledge graphs with neural networks (NNs) for time series data. For his research, a physical smart factory model with condition monitoring sensors and a knowledge graph was developed. This setup generated the required data for exploring the integration of expert knowledge with (Siamese) NNs for similarity-based fault detection, anomaly detection, and automation of root cause analysis. Patrick Klein applied symbolic and sub-symbolic AI techniques, demonstrating that integrating expert knowledge with NNs enhances prediction performance and confidence in them while reducing the number of learnable parameters and failure examples.
Floating Point Numerics for Games and Simulations
Floating point is ubiquitous in computers, where it is the default way to represent non-integer numbers. However, few people understand it. We all see weird behavior sometimes, and many programmers treat it as a mystical and imprecise system of math that just works until it sometimes doesn't.
Python for Mathematics
Python for Mathematics introduces readers to effective methods for doing mathematics using the Python programming language
Set Theory
Contemporary students of mathematics differ considerably from those of half a century ago. In spite of this, many textbooks written and now considered to be "classics" decades ago are still prescribed for students today. These texts are not suitable for today's students. This text is meant for and written to today's mathematics students.
Statistical Inference Via Data Science
Offers a comprehensive guide to learning statistical inference with data science tools widely used in industry, academia, and government. Ideal for those new to statistics or looking to deepen their knowledge, this edition provides a clear entry point into data science and modern statistical methods.
Analytic Methods of Spectral Representations of Non-Selfadjoint (Non-Unitary) Operators
Indirect Methods of Data Collection and Analysis from Surveys
