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"This book is an introduction to numerical methods for students in engineering. It covers solution of equations, interpolation and data fitting, solution of differential equations, eigenvalue problems and optimisation. The algorithms are implemented in Python 3, a high-level programming language that rivals MATLAB in readability and ease of use. All methods include programs showing how the computer code is utilised in the solution of problems. The book is based on Numerical Methods in Engineering with Python, which used Python 2. This new edition demonstrates the use of Python 3 and includes an introduction to the Python plotting package Matplotlib. This comprehensive book is enhanced by the addition of numerous examples and problems throughout" [Publisher]
Engineering mathematics --- Python (Computer program language) --- Data processing --- 681.3*G4 --- 519.6 --- Mathematical software: algorithm analysis; certification and testing; efficiency; portability; reliability and robustness; verification --- Computational mathematics. Numerical analysis. Computer programming --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 681.3*G4 Mathematical software: algorithm analysis; certification and testing; efficiency; portability; reliability and robustness; verification --- Mathématiques de l'ingénieur --- Python (Langage de programmation) --- Data processing. --- Informatique --- Mathématiques de l'ingénieur --- Scripting languages (Computer science) --- Python (langage de programmation) --- Informatique.
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The present book provides an introduction to using space-filling curves (SFC) as tools in scientific computing. Special focus is laid on the representation of SFC and on resulting algorithms. For example, grammar-based techniques are introduced for traversals of Cartesian and octree-type meshes, and arithmetisation of SFC is explained to compute SFC mappings and indexings. The locality properties of SFC are discussed in detail, together with their importance for algorithms. Templates for parallelisation and cache-efficient algorithms are presented to reflect the most important applications of SFC in scientific computing. Special attention is also given to the interplay of adaptive mesh refinement and SFC, including the structured refinement of triangular and tetrahedral grids. For each topic, a short overview is given on the most important publications and recent research activities.
Computer science --- Curves on surfaces. --- 519.6 --- 514.1 --- Surfaces, Curves on --- Computational mathematics. Numerical analysis. Computer programming --- General geometry --- Covering spaces (Topology). --- Curves of double curvature. --- Geometry, Differential. --- Curves --- Curves on surfaces --- Mathematics --- Physical Sciences & Mathematics --- Mathematics - General --- Geometry --- Mathematical models --- 514.1 General geometry --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Convex surfaces. --- Convex areas --- Mathematics. --- Applied mathematics. --- Engineering mathematics. --- Algorithms. --- Computer mathematics. --- Computational Science and Engineering. --- Applications of Mathematics. --- Math Applications in Computer Science. --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Algorism --- Algebra --- Arithmetic --- Engineering --- Engineering analysis --- Mathematical analysis --- Math --- Science --- Foundations --- Convex domains --- Surfaces --- Computer science. --- Informatics --- Mathematical models. --- Computer science—Mathematics.
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Originally published in 1999, Wavelets Made Easy offers a lucid and concise explanation of mathematical wavelets. Written at the level of a first course in calculus and linear algebra, its accessible presentation is designed for undergraduates in a variety of disciplines—computer science, engineering, mathematics, mathematical sciences—as well as for practicing professionals in these areas. The present softcover reprint retains the corrections from the second printing (2001) and makes this unique text available to a wider audience. The first chapter starts with a description of the key features and applications of wavelets, focusing on Haar's wavelets but using only high school mathematics. The next two chapters introduce one-, two-, and three-dimensional wavelets, with only the occasional use of matrix algebra. The second part of this book provides the foundations of least-squares approximation, the discrete Fourier transform, and Fourier series. The third part explains the Fourier transform and then demonstrates how to apply basic Fourier analysis to designing and analyzing mathematical wavelets. Particular attention is paid to Daubechies wavelets. Numerous exercises, a bibliography, and a comprehensive index combine to make this book an excellent text for the classroom as well as a valuable resource for self-study.
Wavelets (Mathematics) --- 519.6 --- 519.65 --- 519.65 Approximation. Interpolation --- Approximation. Interpolation --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- Wavelet analysis --- Harmonic analysis --- Wavelets (Mathematics). --- Civil & Environmental Engineering --- Operations Research --- Applied Mathematics --- 517.518.8 --- 517.518.8 Approximation of functions by polynomials and their generalizations --- Approximation of functions by polynomials and their generalizations --- Ondelettes --- Mathematics. --- Harmonic analysis. --- Fourier analysis. --- Applied mathematics. --- Engineering mathematics. --- Computer mathematics. --- Electrical engineering. --- Abstract Harmonic Analysis. --- Fourier Analysis. --- Electrical Engineering. --- Applications of Mathematics. --- Computational Mathematics and Numerical Analysis. --- Algebra --- Harmonic analysis. Fourier analysis --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Computer engineering. --- Computer science --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Math --- Science --- Computers --- Analysis, Fourier --- Design and construction --- Ondelettes. --- Engineering --- Engineering analysis --- Electric engineering --- Functional analysis. --- Functional Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations
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