THERMAL PHYSICS(台灣版) (2版)

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【原文書】 書名：Thermal Physics 2/E 作者：Charles Kittel ISBN：0716710889 Synopsis CONGRATULATIONS TO HERBERT KROEMER, 2000 NOBEL LAUREATE FOR PHYSICS For upper-division courses in thermodynamics or statistical mechanics, Kittel and Kroemer offers a modern approach to thermal physics that is based on the idea that all physical systems can be described in terms of their discrete quantum states, rather than drawing on 19th-century classical mechanics concepts. "synopsis" may belong to another edition of this title.

Modern Classical Mechanics (2版)

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MODERN CLASSICAL MECHANICS 2E 2020 (H) ISBN： 9781108834971 類別： 物理學Physics 出版社： CAMBRIDGE UNIVERSITY PRESS 作者： HELLIWELL 年份： 2020 裝訂別： 精裝 頁數： 704頁 內容簡介

Brownian Motion and Potential Theory, Modern and Classical (1版)

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【簡介】 In this book, potential theory is presented in an inclusive and accessible manner, with the emphasis reaching from classical to modern, from analytic to probabilistic, and from Newtonian to abstract or axiomatic potential theory (including Dirichlet spaces). The reader is guided through stochastic analysis featuring Brownian motion in its early chapters to potential theory in its latter sections. This path covers the following themes: martingales, diffusion processes, semigroups and potential operators, analysis of super harmonic functions, Dirichlet problems, balayage, boundaries, and Green functions. The wide range of applications encompasses random walk models, especially reversible Markov processes, and statistical inference in machine learning models. However, the present volume considers the analysis from the point of view of function space theory, using Dirchlet energy as an inner product. This present volume is an expanded and revised version of an original set of lectures in the Aarhus University Mathematics Institute Lecture Note Series. 【目錄】 Contents: Introduction Martingales and Markov Processes Brownian Motion and Ito-Calculus Semi-Groups of Operators, Potentials, and Diffusion Equations Harmonic Functions, Dynkin, and Transforms Superharmonic Functions and Riesz Measures Green Functions, Boundary Value Problems, and Kernels Potential Theory, Capacity, Boundaries, Dirichlet Spaces, and Applications Appendix: Kernels and More General Classes of Gaussian Processes

CLASSICAL AND MODERN OPTIMIZATION

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The quest for the optimal is ubiquitous in nature and human behavior. The field of mathematical optimization has a long history and remains active today, particularly in the development of machine learning. Classical and Modern Optimization presents a self-contained overview of classical and modern ideas and methods in approaching optimization problems. The approach is rich and flexible enough to address smooth and non-smooth, convex and non-convex, finite or infinite-dimensional, static or dynamic situations. The first chapters of the book are devoted to the classical toolbox: topology and functional analysis, differential calculus, convex analysis and necessary conditions for differentiable constrained optimization. The remaining chapters are dedicated to more specialized topics and applications. Valuable to a wide audience, including students in mathematics, engineers, data scientists or economists, Classical and Modern Optimization contains more than 200 exercises to assist with self-study or for anyone teaching a third- or fourth-year optimization class. Sample Chapter(s) Preface Chapter 1: Topological and Functional Analytic Preliminaries Request Inspection Copy Contents: Topological and Functional Analytic Preliminaries: Metric Spaces Normed Vector Spaces Banach Spaces Hilbert Spaces Weak Convergence On the Existence and Generic Uniqueness of Minimizers Exercises Differential Calculus: First-Order Differential Calculus Second-Order Differential Calculus The Inverse Function and Implicit Function Theorems Smooth Functions on ℝd, Regularization, Integration by Parts Exercises Convexity: Hahn–Banach Theorems Convex Sets Convex Functions The Legendre Transform Exercises Optimality Conditions for Differentiable Optimization: Unconstrained Optimization Equality Constraints Equality and Inequality Constraints Exercises Problems Depending on a Parameter: Setting and Examples Continuous Dependence Parameter-Independent Constraints, Envelope Theorems Parameter-Dependent Constraints Discrete-Time Dynamic Programming Exercises Convex Duality and Applications: Generalities Convex Duality with Respect to a Perturbation Applications On the Optimal Transport Problem Exercises Iterative Methods for Convex Minimization: On Newton's Method The Gradient Method The Proximal Point Method Splitting Methods Exercises When Optimization and Data Meet: Principal Component Analysis Minimization for Linear Systems Classification Exercises An Invitation to the Calculus of Variations: Preliminaries On Integral Functionals The Direct Method Euler–Lagrange Equations and Other Necessary Conditions A Focus on the Case d = 1 Exercises Readership: Thought-leaders, executives, industry strategists, research scientists, graduate students, advanced undergraduate students, policy-makers, research funding agencies, private research institutions, government regulators, investors, corporate managers, purchasing agents, and entrepreneurs in the areas of computer science, quantum computing, information theory, neuroscience, and physics.

Fundamentals of Classical and Modern Error-Correcting Codes

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Using easy-to-follow mathematics, this textbook provides comprehensive coverage of block codes and techniques for reliable communications and data storage. It covers major code designs and constructions from geometric, algebraic, and graph-theoretic points of view, decoding algorithms, error control additive white Gaussian noise (AWGN) and erasure, and dataless recovery. It simplifies a highly mathematical subject to a level that can be understood and applied with a minimum background in mathematics, provides step-by-step explanation of all covered topics, both fundamental and advanced, and includes plenty of practical illustrative examples to assist understanding. Numerous homework problems are included to strengthen student comprehension of new and abstract concepts, and a solutions manual is available online for instructors. Modern developments, including polar codes, are also covered. An essential textbook for senior undergraduates and graduates taking introductory coding courses, students taking advanced full-year graduate coding courses, and professionals working on coding for communications and data storage.