Explorations in Numerical Analysis and Machine Learning with Julia (1版)

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【簡介】 The textbook is an expansion of Explorations in Numerical Analysis that includes new chapters covering topics from machine learning. It is intended for advanced undergraduate and early graduate students, with a focus on the connections between numerical analysis and machine learning.Topics covered include computer arithmetic, error analysis, solution of systems of linear equations by direct and iterative methods, least squares problems, eigenvalue problems, nonlinear equations, optimization, polynomial interpolation and approximation, numerical differentiation and integration, ordinary differential equations, partial differential equations, machine learning, classification, regression, and neural networks.Each problem is presented with derivations of solution techniques, analysis of their efficiency, accuracy and robustness, and detailed implementation using the Julia programming language. This book is suitable for a year-long course in numerical analysis, or for a one-semester course in numerical linear algebra (Part II) or machine learning (Part VI).

INTRODUCTION TO APPLIED NUMERICAL ANALYSIS, AN

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his book is based on lecture notes for a numerical analysis course designed mainly for senior undergraduate students majoring in mathematics, engineering, computer science and physical sciences. The book has two overarching goals. The first goal is to introduce different available numerical procedures for finding solutions to linear equations, roots of polynomial equations, interpolation and approximation, numerical differentiation and integration, differential equations, and error analysis. The second goal is to translate theory into practice through applying commonly used numerical methods in mathematics, physical sciences, biomedical sciences, and engineering. This book was crafted in an informal and user-friendly manner to motivate the study of the material being covered. Ample figures and numerical tables are presented to enhance the reader's ease of understanding of the material under consideration. Sample Chapter(s) Preface Chapter 7: Boundary Value Problems Contents: Preliminaries Solution of Linear System of Equations Roots of Nonlinear Equations Polynomial Approximation and Interpolation Differentiation and Integration Initial Value Problems Boundary Value Problems Partial Differential Equations Readership: Undergraduate students in Mathematics, Statistics, Physics, Engineering and Computer Science, biomedical, and any Course dealing with numerical calculations and computations.

Applied Numerical Methods with Python for Engineers and Scientists (1版)

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【簡介】 本書介紹 　　雖然MATLAB提供高品質與強大的運算平台，可是，採購的價格卻讓許多大學望而卻步，對此問題，作者 Chapra提供了另一種選擇方案，即「透過 Python 來學習數值方法」；本書是為工學院與理學院相關系所學生精心設計的核心教材，除了扎實的理論說明，在許多章節裡還附上許多工程應用的案例，從背景陳述到詳細的解題過程，協助學生能深刻的理解與應用；內容文筆與深度都十分容易閱讀，適合大學老師採用與指定為「數值方法」課程的學習課本。 【目錄】 Table of Contents PART ONE Modeling, Computers, and Error Analysis 1 Mathematical Modeling, Numerical Methods, and Problem Solving 2 Python Fundamentals 3 Programming in Python 4 Roundoff and Truncation Errors PART TWO Roots and Optimization 5 Roots: Bracketing Methods 6 Roots: Open Methods 7 Optimization PART THREE Linear Systems 8 Linear Algebraic Equations and Matrices 9 Gauss Elimination 10 LU Factorization 11 Matrix Inverse and Condition 12 Iterative Methods 13 Eigenvalues PART FOUR Curve Fitting 14 Straight-Line Linear Regression 15 General Linear and Nonlinear Regression 16 Fourier Analysis 17 Polynomial Interpolation 18 Splines and Piecewise Interpolation PART FIVE Integration and Differentiation 19 Numerical Integration Formulas 20 Numerical Integration of Functions 21 Numerical Differentiation PART SIX Ordinary Differential Equations 22 Initial-Value Problems 23 Adaptive Methods and Stiff Systems 24 Boundary-Value Problems

Numerical Approximations of Stochastic Maxwell Equations: via Structure-Preserving Algorithms

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The stochastic Maxwell equations play an essential role in many fields, including fluctuational electrodynamics, statistical radiophysics, integrated circuits, and stochastic inverse problems. This book provides some recent advances in the investigation of numerical approximations of the stochastic Maxwell equations via structure-preserving algorithms. It presents an accessible overview of the construction and analysis of structure-preserving algorithms with an emphasis on the preservation of geometric structures, physical properties, and asymptotic behaviors of the stochastic Maxwell equations. A friendly introduction to the simulation of the stochastic Maxwell equations with some structure-preserving algorithms is provided using MATLAB for the reader’s convenience. The objects considered in this book are related to several fascinating mathematical fields: numerical analysis, stochastic analysis, (multi-)symplectic geometry, large deviations principle, ergodic theory, partial differential equation, probability theory, etc. This book will appeal to researchers who are interested in these topics.

Numerical Modeling of Water Waves in Coastal and Ocean Engineering

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This unique compendium introduces the field of numerical modelling of water waves. The topics included the most widely used water wave modelling approaches, presented in increasing order of complexity and categorized into phase-averaged and phase-resolving at the highest level. A comprehensive state-of-the-art review is provided for each chapter, comprising the historical development of the method, the most relevant models and their practical applications. A full description on the method's underlying assumptions and limitations are also provided. The final chapter features coupling among different models, outlining the different types of implementations, highlighting their pros and cons, and providing numerous relevant examples for full context. The useful reference text benefits professionals, researchers, academics, graduate and undergraduate students in wave mechanics in general and coastal and ocean engineering in particular. Sample Chapter(s) Foreword Chapter 1: Introduction Contents: Introduction Phase-Averaging Approaches: Spectral Wave Models Phase-Resolving Approaches: Depth-Averaged Models Potential Flow Models Navier–Stokes Models Lattice–Boltzmann Models Wave Modeling Couplings: Couplings Between Wave Models Executive Summary Readership: Researchers, professionals, academics, undergraduate and graduate students in ocean/coastal engineering and fluid mechanics.