Download presentation

Presentation is loading. Please wait.

Published byGordon Trueblood Modified over 2 years ago

1
Suggested problems from text (6 th edition) Chapter 3.1 p85 Problems 1, 4, 9, 10 Computer problems 1, 2, 4, 7 Chapter 3.2 p101 Problems 4, 15, 17, 19 Computer problems 1, 2, 4, 8, 9, 14 Chapter 3.3 p119 Problems 2, 3, 5 Computer problems 1, 3, 5, 6, 7

2
p3.1-1: find intersection of y = 3x and y = exp(x) How is this problem related to finding roots of a function?

3
p3.1-4 p85: solve the equation ln(x+1) + tan(2x) = 0

4
X f(x) = ln(x+1) + tan(2x) Where are the roots?

5
P3.1-9 p86 f(x) = cos(x) - cos(3x) Which roots will be easy to find? Which roots will be hard to find? Write a MabLab program for graphical solution.

6
X f(x) = cos(x) – cos(3x) What are the multiplicities of these roots?

7
y = inline(‘log(x+1)/(1-x.*x)’); x = linspace(-0.5, 2, 100); plot(x,y(x)) What is wrong with this MatLab code? With fplot we don’t need to create a vector of x values. P3.1-10 p86: y=log(x+1)/(1-x 2 ); Where are the roots?

8
What is wrong with this plot? >> p1031=inline('log(1+x)/(1-x^2)'); >> fplot(p1031,[0,2]);

9
X f1031(x) = ln(x+1)/(1-x 2 ) x(1)=-0.5; y(1)=f1031(x(1)); for i=2:149 x(i)=x(i-1)+0.01; y(i)=f1031(x(i)); end x(150)=1.01; y(150)=f1031(x(150)); for i=151:199 x(i)=x(i-1)+0.01; y(i)=f1031(x(i)); end plot(x,y)

10
Computer problems 1, 2, 4, 7 will give you practice with your bisection code. Ignore details like those in #7 “one run”, “full machine precision”, “correct number of steps” and “false positive method” How can you be sure that your code is giving correct answers?

11
Suggested problems from text Chapter 3.1 p85 Problems 1, 4, 9, 10 Computer problems 1, 2, 4, 7 Chapter 3.2 p101 Problems 4, 15, 17, 19 Computer problems 1, 2, 4, 8, 9, 14 Chapter 3.3 Problems 2, 3, 5 Computer problems 1, 3, 5, 6, 7

12
>> f324=@(x) x.^4+2*x.^3-7*x.^2+3'; >> df324=@(x) 4*x.^3+6*x.^2-14*x; >> fplot(f324,[-4,2]) >> [r,fr,~]=newtfun(f324,df324,-1); >> disp([r,fr]) -0.6180 -0.0000 >> [r,fr,~]=newtfun(f324,df324,0.75); >> disp([r,fr]) 0.7913 -0.0000 >> [r,fr,~]=newtfun(f324,df324,1.7); >> disp([r,fr]) 1.6180 -0.0000 >> [r,fr,~]=newtfun(f324,df324,-4); >> >> disp([r,fr]) -3.7913 -0.0000 Problem 3.2-4 page 101: find all the zeros of x 4 +2x 3 -7x+3

13
P3.2-15: f(x) = x 3 - x +1 if x 0 in newton’s method is 1, what is x 1 ? P3.2-17 f(x) = x 5 – x 3 +3 if x n in newton’s method is 1, what is x n+1 ? See slide 10 Lecture on finding zeros

14
P3.2-19 f(x) = x 2 /(1 + x 2 ) from what starting values will newton’s method converge?

15
f(x) = x 2 /(1+x 2 ) X Symmetry can cause cycling of Newton’s method Find analytical solution for when Newton’s method will converge.

16
From solution manual for text

17
Computer problems 1, 2, 4, 8, 9, 14 will give you practice with your newton code.

18
Suggested problems from text Chapter 3.1 p85 Problems 1, 4, 9, 10 Computer problems 1, 2, 4, 7 Chapter 3.2 p101 Problems 4, 15, 17, 19 Computer problems 1, 2, 4, 8, 9, 14 Chapter 3.3 p119 Problems 2, 3, 5 Computer problems 1, 3, 5, 6, 7

19
P3.3-2: f(x) = x 3 - 2x +2 if x 0 = 0 and x 1 = 1 in secant method, what is x 2 ? P3.3-3 f(x) = x 5 + x 3 +3 if x n-2 = 0 and x n-1 = 1 in secant method, what is x n ? See slide 33 in Lectures on finding zeros.

20
P3.3-5: find the largest positive root of x 3 - 5x +3 by bisection, newton’s and secant methods

21
Computer problems 1, 3, 5, 6, 7 will give you practice with your secant code. I think cp3.3-3 is referring to functions on p77 of text. I think cp3.3-5 is referring to example 1 on p113 of text f(x) = x 5 + x 3 +3

Similar presentations

OK

3.1 Solving equations by Graphing System of equations Consistent vs. Inconsistent Independent vs. Dependent.

3.1 Solving equations by Graphing System of equations Consistent vs. Inconsistent Independent vs. Dependent.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on power system protection and switchgear Ppt on water cycle for kindergarten Ppt on holographic technology schools Ppt on index numbers definition 7 habits of highly effective kids ppt on batteries Free ppt on save environment Ppt on one self i sing by walt whitman Ppt on save environment in hindi Ppt on cse related topics in biology Ppt on film industry bollywood songs