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Yang Dachun: Selected Lectures On
Functional Analysis: Spectral Theory Of

Selected Lectures On Functional Analysis: Spectral Theory Of Operators, Banach Algebras, And Semigroups Of Operators

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

This book offers a comprehensive treatment of the core mathematical topics required for a modern engineering degree. The book begins with an introduction to the basics of mathematical reasoning and builds up the level of complexity as it progresses.

Mathematics for Engineers

Textbooks in Mathematics

The textbook is designed for university students studying science and engineering. I have aimed for a comparatively short book that would give a sufficiently full exposition of the fundamentals of the theory of functions of a complex variable to prepare the student for various applications.

An Introduction to Complex Analysis and the Laplace Transform

Partial Differential Equations (PDEs) are fundamental in fields such as physics and engineering, underpinning our understanding of sound, heat, diffusion, electrostatics, electrodynamics, thermodynamics, fluid dynamics, elasticity, general relativity, and quantum mechanics. They also arise in areas like differential geometry and the calculus of variations.

This book focuses on recent investigations of PDEs in Sobolev and analytic spaces. It consists of twelve chapters, starting with foundational definitions and results on linear, metric, normed, and Banach spaces, which are essential for introducing weak solutions to PDEs. Subsequent chapters cover topics such as Lebesgue integration, Lp spaces, distributions, Fourier transforms, Sobolev and Bourgain spaces, and various types of KdV equations. Advanced topics include higher order dispersive equations, local and global well-posedness, and specific classes of Kadomtsev-Petviashvili equations.

This book is intended for specialists like mathematicians, physicists, engineers, and biologists. It can serve as a graduate-level textbook and a reference for multiple disciplines.

Partial Differential Equations In Sobolev And Analytic Spaces

This textbook focuses on the study of curves and surfaces, applying modern differential equation theory to geometric problems. By introducing isothermal parameters, it simplifies the fundamental equations of surface theory, leading to clear derivations of results like those of H Hopf and S Bernstein for surfaces of constant and vanishing mean curvature.Deviating from traditional approaches, the book first treats n-dimensional Riemannian spaces by a corresponding metric, then constructs Riemannian manifolds through transition conditions. The ultimate goal is to prove the Hadamard-Cartan theorem on the diffeomorphic character of the exponential mapping in Riemannian manifolds with nonpositive sectional curvature. By considering curves and surfaces in their optimal parametrization, the resulting ODEs and complex PDEs can be analytically solved, eliminating the need for intricate tensor calculus.The approach follows that of G Monge in his treatise L'Application de l'Analyse à la Géométrie, applying analytical techniques to geometric problems. Building on this foundation, the book uses modern theory of ODEs and PDEs to study the local and global results for curves and surfaces and their relevant curvatures.

Differential Geometry And Riemannian Manifolds

Advanced Topics in Biomaterials

Theory and Applications

Functional Analysis: Theory and Applications

Fractals And Dynamics In Mathematics, Science, And The Arts: Theory And Applications

Analysis on fractals began to take shape as a mathematical field in the late 1980s. Traditionally, the focus of analysis has been on finitely ramified fractals -- those where copies intersect at only finitely many points. To date, a comprehensive theory for infinitely ramified fractals remains elusive.This monograph outlines the theory of self-similar energies on finitely ramified self-similar fractals. Using these self-similar energies, one can construct Laplacians, harmonic functions, Brownian motion, and differential equations specific to these fractals.On finitely ramified fractals, self-similar energies are derived from eigenforms -- quadratic forms that are eigenvectors of a special nonlinear operator within a finite-dimensional function space. The monograph also explores conditions for the existence and uniqueness of these self-similar energies and addresses related problems. For certain cases, complete solutions are provided.

Self-similar Energies On Finitely Ramified Fractals

Signals and Systems Using MATLAB, Fourth Edition features a pedagogically rich and accessible approach to what can commonly be a mathematically dry subject. Historical notes and common mistakes combined with applications in controls, communications, and signal processing help students understand and appreciate the usefulness of the techniques described in the text. This new edition features more worked examples and a variety of new end-of-chapter problems, suggestions for labs, and more explanation of MATLAB code.

Signals and Systems Using MATLAB®

Adopting a student-cantered approach, this book anticipates and addresses the common challenges that students face when learning abstract concepts like limits, continuity, and inequalities. The text introduces these concepts gradually, giving students a clear pathway to understanding the mathematical tools that underpin much of modern science and technology. In addition to its focus on accessibility, the book maintains a strong emphasis on mathematical rigor. It provides precise, careful definitions and explanations while avoiding common teaching pitfalls, ensuring that students gain a deep understanding of core concepts. Blending algebraic and geometric perspectives to help students see the full picture. The theoretical results presented in the book are consistently applied to practical problems. By providing a clear and supportive introduction to real analysis, the book equips students with the tools they need to confidently engage with both theoretical mathematics and its wide array of practical applications.Features<ul> <li>Student-Friendly Approach making abstract concepts relatable and engaging</li> <li>Balanced Focus combining algebraic and geometric perspectives</li> <li>Comprehensive Coverage: Covers a full range of topics, from real numbers and sequences to metric spaces and approximation theorems, while carefully building upon foundational concepts in a logical progression</li> <li>Emphasis on Clarity: Provides precise explanations of key mathematical definitions and theorems, avoiding common pitfalls in traditional teaching</li> <li>Perfect for a One-Semester Course: Tailored for a first course in real analysis</li> <li>Problems, exercises and solutions</li> </ul>

An Invitation to Real Analysis

This surprisingly accessible book uses key math concepts and more than 500 short exercises to teach functional programming to experienced coders. Functional programming is a coding paradigm that emphasizes functions, repeatable computations that take input data and produce corresponding outputs. Functions are also important concepts in math, and a lot of deep mathematical insights shed light on functional computer programming. In this book, the author uses functional programming to introduce mathematical concepts – most notably set theory, abstract algebra, and category theory – and in turn uses that math to describe functional programming design patterns. The more than 500 short programming exercises included in the book will help you master functional programming and math skills alike, with code examples presented in the F# language.

Explore Set Theory, Abstract Algebra, and Category Theory with Functional Programming

The Book of Functions

AK Peters/CRC Recreational Mathematics Series

The Meditations in this book are the product of thousands of years of mathematical discourse. As you read through the book and work through the various exercises, you will discover new mechanisms that allow you to contemplate and understand some complex mathematical principles.

Mathematical Meditations

Series on Concrete & Applicable Mathematics

Differential evolution equations serve as mathematical representations that capture the progression or transformation of functions or systems as time passes. Currently, differential equations continue to be an active and thriving area of study, with continuous advancements in mathematical methodologies and their practical applications spanning diverse fields such as physics, engineering, and economics. In the late 20th century, the notion of "Differential Evolution Equations" emerged as a distinct field applied to optimization and machine learning challenges. Evolution equations hold immense importance in numerous realms of applied mathematics and have experienced notable prominence in recent times.

This book delves into the study of several classes of equations, aiming to investigate the existence of mild and periodic mild solutions and their properties such as approximate controllability, complete controllability and attractivity, under various conditions. By examining diverse problems involving second-order semilinear evolution equations, differential and integro-differential equations with state-dependent delay, random effects, and functional differential equations with delay and random effects, we hope to contribute to the advancement of mathematical knowledge and provide researchers, academicians, and students with a solid foundation for further exploration in this field. Throughout this book, we explore different mathematical frameworks, employing Fréchet spaces and Banach spaces to provide a comprehensive analysis. Our investigation extends beyond traditional solutions, encompassing the study of asymptotically almost automorphic mild solutions, periodic mild solutions, and impulsive integro-differential equations. These topics shed light on the behavior of equations in both bounded and unbounded domains, offering valuable insights into the dynamics of functional evolution equations.

Advanced Topics On Semilinear Evolution Equations

Selected Lectures On Functional Analysis: Spectral Theory Of ...

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