7 years, 23 days

## Newtons Method in an Interval...

Maple

Hello, I'd like to use Maple to use Newton's Method in an interval to find multiple roots of 4xcos(3x)+(x-2)^2-2=0. What I have so far is:

with(Student[NumericalAnalysis]):
f := 4*x*cos(3*x)+(x-2)^2-2:
Newton(f,x=2,tolerance=10^(-4));

Other than trying out different initial guesses is there a way to do this?

## What does this notation mean: "0.824cos"...

Maple

I'm doing some stuff with Taylor Polynomials on Maple. In particular, I'm trying to find the second order Taylor Polynomial of e^x cos x. I'm using the "taylor" command.

This is what I have so far:

> f := proc (x) options operator, arrow; exp(x)*cos*x end proc;
x -> exp(x) cos x
> s2 := taylor(f(x), x = (1/3)*Pi, 2);
> p2 := convert(s2, polynom);
1 /1 \
- exp|- Pi| cos Pi
3 \3 /

/ /1 \ 1 /1 \ \ / 1 \
+ |exp|- Pi| cos + - exp|- Pi| cos Pi| |x - - Pi|
\ \3 / 3 \3 / / \ 3 /
> y1 := evalf(subs(x = .5, f(x)));
0.8243606355 cos
> y2 := evalf(subs(x = .5, p2));
-0.208092943 cos

Everything looks fine until the last two lines.

How do I interpret ".8243606355*cos" ? Cosine should have an argument. Am I messing up something with my code, or is this standard in Maple language?

## Ordinary Differential Equation DEplot...

Given the following system of first order ODE,

dx/dt=0.2x(1-0.5 x)-(1.5 xy)/(1+0.116 x),

dy/dt=(1.3 xy)/(1+0.1x)-0.8y.

Draw a DEplot (for t from 0 to 50) and indicate the particular

trajectory with the initial conditions x(0)=1,y(0)=2. If I

switched to forward Euler method,what would the DE plot look

like then? Is it possible to make the plot made by the

forward Euler method look close to the one which used the

default method?

## Solving ODEs without the Student package...

As it says in the title, I would like to solve the following ODE numerically using forward Euler method, without using the Student Package.

(dy(t))/(dt)=t(1-0.3t)-(ty)(1+0.6t)

with initial condition y(0)=1. I want to solve it for up to t=1, and then plot both the solution by Euler's method and the solution by "dsolve" on the same graph so I can compare them.

Also, can I make a separate DEplot with t extending to 5?

## Finding the Fourier Series for a functio...

Find the Fourier Series for the function f(x) defined as follows, and compare the graphs of some truncated Fourier series (try 1,2,3,5,6,30, terms) with the graph of f(x).

f(x)= min(|x|, pi/2), -pi less than or equal to x less than or equal to pi.

Also, let f(x) be periodic with a period of 2*pi. Thanks.

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