MakerYang

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在现代科技发展的时代，前端技术作为构建用户界面的核心扮演着关键角色。为了帮助个体或企业提升技术水平，提供一套高效的前端基础培训课程显得尤为重要。通过系统学习，学员可以深入了解HTML、CSS和JavaScript等前端技术栈的基础知识，掌握响应式设计、浏览器兼容性等实用技能。培训内容将涵盖从基础到进阶的层层深入，确保学员具备解决实际问题的能力。此外，课程还将通过项目实战的方式，让学员在实际项目中巩固所学知识，提高应用能力。在培训过程中，注重理论与实践相结合，通过案例分析、编码实践等形式，激发学员的学习兴趣，帮助他们更好地掌握前端开发的核心技能。

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2023-12-13 12:30

RxJS响应式编程

响应式编程,使用RxJS来编程异步的JavaScript代码!!

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3.17MB

2020-08-20 20:27

RxJS实战pdf

异步控制流程Rxjs，最新2017版本，书中给出完整的事例和讲解，为什么要使用RxJS，RxJS能解决什么问题，最后结合一个具体的实例来演示如何使用

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5.65MB

2019-09-03 20:13

Anintroductiontonumericalanalysis

英文原版，哈佛大学教授编写。数组分析导论PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGEThe Pitt Building, Trumpington Street, Cambridge, United KingdomCAMBRIDGE UNIVERSITY PRESSThe Edinburgh Building, Cambridge CB2 2RU, UK40 West 20th Street. New York, NY 10011-4211USA477 Williamstown Road. port Melbourne. viC 3207, AustraliaRuiz de Alarcon 13, 28014 Madrid, SpainDock house, The Water front, Cape Town 8001, South Africahttp://www.cambridgc.orgO Cambridge University Press, 2003This book is in copyright. Subject to statutory exceptionand to the provisions of relevant collective licensing agreementsno reproduction of any part may take place withoutthe written permission of Cambridge University PressFirst published 2003Printed in the United Kingdom at the University Press, Cambridgeypeface CMR 10/13 pt System. IATEX 22 TBa catalogue record fuy thuis book is available fromn the British LibraryLibrary of Congress Cataloguing 2n Pablication dataISBN 0 521 81026 4 hardbackISBN 0 521 00794 1 paperbackContentsSolution of equations by iteration1.1 Iutroduction1.2 Simple iterate1. Iterative solution of equation171.4 Relaxation and Newton' s method191.5 The secant method251.6 The bisection method21. 7 Global beh1. 8 NotesFxercises2 Solution of systems of linear equations2.1nt2. 2 Gaussian elimination2.3 LU facto482.4 Pivoting522.5 Solution of systems of equations26Ctational work562.7 Norms and condition numbers582. 8 Hilbert matrix2.9 Least squares method2.10 NotesExercises3 Special matrices3.1 Introduction3.2 SyInIletric positive definite matrices3.3 Tridiagonal and band matrices93IVContents3.4 Monotone matrices983.5 Notes101Exercises1024Simultaneous nonlinear equations1044.1 Introduction1044.2 Simultaneous iteration1064.3 Relaxation and Newton's method4.4 Global convergence45N124ExercisesEigenvalues alld eigenvectors of a syInlletric matrix 1335.1 Introduction1335.2 The characteristic polynoInlial5.3 Jacobi’ s method1375.4 The Gerschigorin the1455.5 Householder' s method1505. 6 Eigenvalues of a tridiagonal matrix1565.7 Thc QR algorithm5.7.1 The QR factorisation revisited1625.7.2 The dcfinition of thc QR algorithm1645. 8 Inverse iteration for the eigenvectors1665. 9 The Rayleigh5.10 Perturbation analysis1725.11 Notes1746 Polynomial interpolation1796.1 Introduction1796.2 Lagrange interpolation1806.3 Conve6.4 Hermite interpolati86.5 Differentiation1916.6 NoteExercises1957 NuMerical integration7.1 Introduction2007.2 Newton-Cotes formulae7.3 Error estimates7.4 The Runge phenomenon revisited2087.5 Composite formulae209Conte7.6 The Euler-Maclaurin expansion7.7 Extrapolation methods2157. 8 Notes219Exercises2208 Polynomial approximation in the oo-norm8.1 Introduction2248.2 Normed linear spaces2248.3 Best approximation in the x-norm8.4 Chebyshev polynomials8.5 Interpolation8. 6 Notes247Exercises2489 Approxilllation in the 2-1lorIll2529.1 Introduction2529.2 Inner product spaces2539.3 Best approximation in the 2-norm2569.4 Orthogonal polynomials9.5 Comparisons9.6 NotesExercises10 Numerical integration -Il10. 1 Introduction10.2 Construction of Gauss quadrature rules27710.3 Direct construction28010.4 Error estimation for Gauss quadrature210.5 Composite Gauss formulae28510.6 Radau and Lobatto quadrature28710.7 NoteExercises11 Piecewise polynomial approximation29211. 1 Introduction11.2 Linear interpolating splines29311.3 Basis functions for t he linear spline29711.4 Cubic splines11.5 Hermite cubic splines11.6 Basis functions for cubic splines11.7 Notes306307Contents12 Initial value problems for ODEs31012.1 Introduction1012.2 One-ste31712.3 Consistency and convergence32112. 4 All iMplicit one-step Inethod32412.5 Runge Kutta methods12.6 Linear Multistep inethods32912.7 Zero-stability12.9 Dahlquist's theorems34012.10 Systems of34112.11 Stiff systcms34312.12 Implicit Runge-Kutta methods34912.13 Notes353Exercises13 Boundary value problems for ODEs36113.1 Introducti13.2 A model problem13.3 Error analysis13.4 Boundary conditions involving a derivativegene37013.6 The Sturm-Liouville eigenvalue problem37313.7 The shoot13.8 Not14 The finite element method14.1 Introduction: the model problem14.2 Rayleigh-Ritz and Galerkin principles38814.3 Formulation of the finite element method39114.4 Error analysis of the finite element method39714.5 A posteriori error analysis by duality40314.6Nt412Exercises414Appendise a An overview of results from real allalysis 41Adiabwww.BibliographySolution of equations by iteration1.1 IntroductionEquations of various kinds arise in a range of physical applications anda substantial body of mathematical research is devoted to their studySome equations are rather simple: in the early days of our mathematicaleducation we all encountered the single linear equation a C+b=0, wherea anb are real numbers and a#0, whose solution is given by theformula r=-6/a. Many equations. however, are nonlinear. a simpleexample is a+b.+c=0, involving a quadratic polynomial with realcoefficients a, b, G, and a+0. The two solutions to this equation, labelle.I and 2, are found in terms of the coefficients of the polynomial fromthe familiar formulaeb+√b2-4acb-√b2-4ac(1.1)It is less likely that you have seen the Inore intricate forMulae for thesolution of cubic and quartic polynomial equations due to the sixteenthcentury Italian mlatheinaticians Niccolo Fontana Tartaglia(1499-1557)and Lodovico Ferrari(1522 1565). respectively, which were publishedby Girolamo Cardano(1501-1576) in 1545 ill his Ar tis magnae sive deregulis algebraicis liber unus. In any case, if you have been led to believethat similar expressions involving radicals (roots of sums of products ofcoefficients) will supply the solution to any polynomial equation, thenou should brace yourself for a surprise: no such closed formula existsfor a general polynomial equation of degree n when n >> 5. It transpiresthat for each n> 5 there exists a polynomial equation of degree n withSolution of equations by iterationinteger coefficients which cannot be solved in terms of radicals: such is20Since there is no general formula for the solution of polynomial equations,no general formula will exist for the solution of an arbitrary non.linear equation of the form /(x)=0 where is a continuous real-valuedfunction. How can we then decide whether or not such an equationpossesses a solution in the set of real nunbers, and how can we find aThe present chapter is devoted to the study of these questiOns. Ourgoal is to develop simple numerical methods for the approximate solutionof the equation f()=0 where f is a real-valued function, defined andcontinuous on a bounded and closcd interval of the rcal linc. Mcthodsof the kind discussed here are iterative in nature and produce sequencesof rcal numbcrs which, in favourable circumstances, convcrge to therequired solution1.2 Simple iterationSuppose that f is a real-valued function, defined and continuous on abounded closed interval a, b of the real line. It will be tacitly assumedthroughout the chapter that a <6, so that the interval is nonempty. Wewish to find a real number E e a, b] such that f(s)=0. If such s existsit is called a solution to the equation f()=0Even some relatively simple equations may fail to have a solution inthe set of real numbers. Consider for examplef:x2+1Clearly f(a)=0 has no solution in any interval a, b of the real lineIndeed, according to(1. 1), the quadratic polynomial +I has two roots1=V-1= and 2=-V-1=-. However, these belong to the setof imaginary numbers and are therefore excluded by our definition ofsolution which only admits real numbers. In order to avoid difficultiesof this kindgimof solutions to thequation f(a)=0 in the set of real nunbers. Our first result in thisdirection is rathcr simplc1 This result was proved in 1824 by the Norwegian mathematician Niels IIenrik abel(1802-1829), and was further refined in the work of Evariste Galois(1811-1832who clarified t, he circumst. ances in which a closed formula may exist for the solutionuf a polynomial equation of degree TL in terns of radicals1. 2 Simple iteration3Theorem 1.1 Let f be a real-valued function, defined and continuouson a bounded closed interval [a, b of the real line. Assume, further, thatf(a)f(b)<0: then, there exists s in [a b] such that f($)=0Proof If f(a)=0 or /(b)=0 then &=a or $=b, respectively, alld theproof is complete. Now, suppose that f(a)f(b)+0. Then, f(a).f(b)<in other words, 0 belongs to the open interval whose endpoints are f(a)and f(b). By the Intermediate Value Theorem(Theorem A1),thereexists s in the openl interval (a, b )such that f(S)=0To pa.raphrase Theorem 1.1, if a continuous function f has oppositesigns at the endpoints of the interval a, b, then the equation f(c)=0as a SoliTion in cThe converse statement is. of course falseConsider, for example, a continuous function defined on [a, b whichchanges sign in the open interval(a, b) an even number of times, withf(a)f(b),0; then. f(a)f(b)>0 even though f(a)=0 has solutionsinside a, b. Of course, in the latter case, there exist an even numberof subintervals of (u, b) at the endpoints of each uf which f does haveopposite signs. However, finding such subintervals may not always beTo illustrate this last point, consider the rather pathological functiona H>21+M|m-1.05(1.2)depicted in Figure 1. 1 for m in the closed interval [ 0.8, 1. 8 and M=200The solutions 1=1.05-(1/ M)and 22=1.05+(1/M) to the equationf (r)=0 are only a distance 2/M apart and, for large and positive Mlocating them computationally will be a challenging taskRemark 1.1 If you have access to the mathematical software packagMaple, plot the function f by typingplot(1/2-1/(1+200*abs(x-1.05)),x=0.8..1.8,y=-0.5..0.6);at the Maple com.man.d line, and then repeat this erperiment by choosingM=2000,20000,2000,2000.0a20000000 place of the number 200. What do you observe For the last two values of M, replot thefunction f foru in the subinter val[1.04999, 1.05001An alternative sufficient condition for the existence of a solution tothe equation f(x)=0 is arrived at by rewriting it in the equivalentform a-g()=0 where g is a certain real-valued function, defined

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9.12MB

2019-05-20 10:54

theCProgramminglanguage4th

c++经典书籍

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8.09MB

2019-01-08 16:59