polynomials and numerical method ... help ?

[studiot]

 

 

 

 

 

 

 

 

 

f(x) = polynomial ??

 

f(x) = transcendental ??

 

f(x) = polynomial of degree one ?? therefore linear ?

 

f(x) = polynomial greater than degree one ?? therefore non linear ??

 

 

also all the above mentioned stuff about a linear change against a non linear change ???

 

Yes x is the independent variable and y the dependent variable.

 

So can I assume you are now responding directly to my posts?

 

If so the rest of what you posted is quite irrelevent.

 

Please don't try to go beyond a simple answer to a simple question.

Especially as you have only answered the first one.

 

To help I will examine a few functions (of x) in the light of my definition of linear.

 

Here are a few functions.

 

y = x

y = x²

y = sin(x)

y = x + 10

 

 

Calculate y for x = 1 and for x = 5 that is for x₁=1 and for x₂=5. or x₂ = 5x₁

 

y = x So that y(1) = 1; y(5) = 5

y = x² So that y(1) = 1; y(5) = 25

y = sin(x) So that y(1) = 0.84; y(5) = -0.96

y = x + 10 So that y(1) = 11; y(5) = 20

 

Now my definition of linear is that

 

y(5x) = 5y(x)

 

For which of these functions is this true?

 

Can you now answer my questions 2 and 3 in post49?

Edited December 9, 2015 by studiot

[bimbo36]

In y = f(x) do you understand what is meant by the independent variable and the dependent variable; please state which is which?

For the function is y = 5 does my definition make the function linear or nonlinear?

Is this true for any y = a constant?

 

 

x is independent ,y is dependent

y=5 is linear and for any value of a yes it is linear

for any value of 'a', yes it is linear

 

 

let me rearrange few things one more time ....

 

 

 

f(x) = polynomial ??

 

f(x) = transcendental ??

 

f(x) = polynomial of degree one ?? therefore linear ? Solution of Linear Equations? Direct Methods ? http://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/12-LinEqs_Direct.pdf

 

 

f(x) = polynomial of degree one ?? therefore linear ? Solution of Linear Equations? Indirect Methods ? http://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/13-LinEqs_Indirect.pdf

 

f(x) = polynomial greater than degree one ?? therefore non linear ?? solving nonlinear equations ? Fixed Point ?http://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/14-NonlinearEquations_1_FixedPoint.pdf

 

f(x) = polynomial greater than degree one ?? therefore non linear ?? solving nonlinear equations ? Bisection ? http://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/14-NonlinearEquations_2_Bisection.pdf

 

f(x) = polynomial greater than degree one ?? therefore non linear ?? solving nonlinear equations ? Newton ? http://www.ce.utexas.edu/prof/mckinney/ce311k/Overheads/14-NonlinearEquations_3_Newton.pdf

 

 

 

is this right so far ??

 

its better than getting stuck .... atleast things are going to get better in 2016 ....

Edited December 10, 2015 by bimbo36

[studiot]

I am sorry, I am clearly wasting my time.

 

We have a saying in English.

 

You can lead a horse to water.

But you can't make him drink.

 

I feel exactly this way seeing your last post.

[bimbo36]

hello studiot , thanks for all the help , support and questions...

 

why i dont work with problems right now is because , i was a bit weak in algebra in general ...

 

i was also looking for small problems to begin working with examples ...

 

thank god , i found this excellent beginner book on algebra ....

 

 

Peter Selby, Steve Slavin-Practical Algebra_ A Self-Teaching Guide-John Wiley & Sons (1991)

 

i am also ... going to buy two more books from an online store ...

 

 

How to Ace Calculus: The Streetwise Guide

 

 

with the help of those two books .. i am going to work on examples of algebra and calculus ....

 

 

later , after i get those books... i will start working on differential equations too ... right now i am not touching that subject ....

 

 

i am glad i got a better overall picture of this subject ...

 

now its time to practise from basics.... with the help of those books ....