4001859090

新航道A-Level数学培训解题技巧:Numerical Methods

作者: 2022-06-20 19:41 来源:重庆编辑
收藏

  We havelearnedsome ofthe numericalmethodsin the P2 course, when we used the trapezium rule to approximate the area under a curve in thex-O-y plane. The trapezium rule divides the area into n parts. For each part we calculate the area of the corresponding trapezium to approximate the area of the bounded region. Thenwe summarise the results to approach the total area which is the value ofthe definiteintegral.

 

  Now we try to solve the rooting problem of a function in numerical wayFirst of alllets learn how to locate roots using the change-of-sign rule Hereisthetheorem:

  If the function f(x) is continuous in the

  interval [a,b]and f(a)and f(b) have opposite signs, then f(x) has at least one rootxwhich satisfiesa

 

  The special cases we need to pay attention to are:

  

 

  Now that we have locate the root ofthe

 

  function into a certain intervalnextwe make efforts to use numerical method toapproximate the root.

 

  If we want to find the roots ofa fucntionsuch as f(x)=0,we could rewrite the equation as g(x)=x.Then it is equivalent to finding the x- coordinate of the intersection point of the two curves with the equations y=g(x) andy=x. Therefore, like fugure 4 shows, if we set a start valuex,then followtheiterativeformulaxn+1=g(xn) we will get closer and closer to the intersection point. The way we approches the root of the function is called fixed point iteration which is a kind ofnumerical method.

  

 

  

姓名
电话
  • 品牌简介
  • 课程中心
  • 留学服务
  • 校区地图
  • 精品项目
  • 活动专区
热门活动

注册/登录

+86
获取验证码

登录

+86

收不到验证码?

知道了

找回密码

+86
获取验证码
下一步

重新设置密码

为您的账号设置一个新密码

保存新密码

密码重置成功

请妥善保存您的密码
立即登录

为了确保您的帐号安全

请勿将帐号信息提供给他人/机构