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Functional analysis --- Differential equations --- Mathematics --- differentiaalvergelijkingen --- mathematische modellen --- wiskunde --- Differential equations. --- 517.91 Differential equations --- Equacions diferencials funcionals --- Equacions diferencials ordinàries

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This study guide is designed for students taking courses in calculus. The textbook includes practice problems that will help students to review and sharpen their knowledge of the subject and enhance their performance in the classroom. Offering detailed solutions, multiple methods for solving problems, and clear explanations of concepts, this hands-on guide will improve student’s problem-solving skills and basic understanding of the topics covered in their calculus courses. Exercises cover a wide selection of basic and advanced questions and problems; Categorizes and orders the problems based on difficulty level, hence suitable for both knowledgeable and under-prepared students; Provides detailed and instructor-recommended solutions and methods, along with clear explanations; Can be used along with core calculus textbooks.

Engineering mathematics. --- Calculus. --- Differential equations. --- Partial differential equations. --- Engineering Mathematics. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Partial differential equations --- 517.91 Differential equations --- Differential equations --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Mathematical analysis --- Functions --- Geometry, Infinitesimal --- Engineering --- Engineering analysis --- Mathematics --- Methods.

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This book presents a concise, clear, and consistent account of the methodology of phase synchronization, an extension of modal analysis to decouple any linear system in real space. It expounds on the novel theory of phase synchronization and presents recent advances, while also providing relevant background on classical decoupling theories that are used in structural analysis. The theory is illustrated with a broad range of examples. The theoretical development is also supplemented by applications to engineering problems. In addition, the methodology is implemented in a MATLAB algorithm which can be used to solve many of the illustrative examples in the book. This book is suited for researchers, practicing engineers, and graduate students in various fields of engineering, mathematics, and physical science. Provides a concise review of classical decoupling techniques; Explains the physical intuition behind the method of phase synchronization; Illustrates the relationship between phase synchronization and classical decoupling theories and demonstrates the utility of phase synchronization; Reinforces concepts by illustrative examples; Provides a MATLAB algorithm for simulations.

Vibration. --- Dynamical systems. --- Dynamics. --- Differential equations. --- Partial differential equations. --- Phase transitions (Statistical physics). --- Vibration, Dynamical Systems, Control. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Phase Transitions and Multiphase Systems. --- Phase changes (Statistical physics) --- Phase transitions (Statistical physics) --- Phase rule and equilibrium --- Statistical physics --- Partial differential equations --- 517.91 Differential equations --- Differential equations --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Cycles --- Sound

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This textbook provides a graduate-level introduction to the spectral theory of linear operators on Banach and Hilbert spaces, guiding readers through key components of spectral theory and its applications in quantum physics. Based on their extensive teaching experience, the authors present topics in a progressive manner so that each chapter builds on the ones preceding. Researchers and students alike will also appreciate the exploration of more advanced applications and research perspectives presented near the end of the book. Beginning with a brief introduction to the relationship between spectral theory and quantum physics, the authors go on to explore unbounded operators, analyzing closed, adjoint, and self-adjoint operators. Next, the spectrum of a closed operator is defined and the fundamental properties of Fredholm operators are introduced. The authors then develop the Grushin method to execute the spectral analysis of compact operators. The chapters that follow are devoted to examining Hille-Yoshida and Stone theorems, the spectral analysis of self-adjoint operators, and trace-class and Hilbert-Schmidt operators. The final chapter opens the discussion to several selected applications. Throughout this textbook, detailed proofs are given, and the statements are illustrated by a number of well-chosen examples. At the end, an appendix about foundational functional analysis theorems is provided to help the uninitiated reader. A Guide to Spectral Theory: Applications and Exercises is intended for graduate students taking an introductory course in spectral theory or operator theory. A background in linear functional analysis and partial differential equations is assumed; basic knowledge of bounded linear operators is useful but not required. PhD students and researchers will also find this volume to be of interest, particularly the research directions provided in later chapters.

Functional analysis. --- Mathematical analysis. --- Analysis (Mathematics). --- Mathematical physics. --- Functional Analysis. --- Analysis. --- Mathematical Physics. --- Physical mathematics --- Physics --- 517.1 Mathematical analysis --- Mathematical analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Mathematics --- Spectral theory (Mathematics) --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Teoria espectral (Matemàtica) --- Anàlisi funcional --- Equacions en derivades parcials --- Successions espectrals (Matemàtica) --- Espais de Hilbert --- Differential equations. --- Differential Equations. --- 517.91 Differential equations --- Differential equations

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Differential equations --- Numerical solutions. --- 517.91 Differential equations --- Equacions diferencials --- Solucions numèriques --- Anàlisi numèrica --- Càlcul --- Funcions de Bessel --- Àlgebra diferencial --- Càlcul integral --- Càlcul operacional --- Equacions d'evolució --- Equacions de camp d'Einstein --- Equacions de Lagrange --- Equacions de Pfaff --- Equacions diferencials algebraiques --- Equacions diferencials ordinàries --- Equacions en derivades parcials --- Funcions de Green --- Funcions de Lyapunov --- Problemes de contorn --- Problemes inversos (Equacions diferencials) --- Teoria d'estabilitat (Matemàtica) --- Transformació de Laplace