In my opinion learning numerical methods without even "touching" calculus is almost impossible, particularly when these methods concern fixed point iteration. Maybe you can learn some numerical linear algebra without calculus, but then I still have my sincere doubts. Actually, my doubts are so serious that I take the liberty to offer you this link: https://www.physicsforums.com/insights/self-study-calculus/

The author of that text offers good advice on learning mathematics, so you might find other texts by him useful, too.

I don't know... Learning numerical methods is maybe not the best thing to adopt as your "aim of life". Why don't you aim to be happy and content, alone or together with others, whichever you prefer? Numerical methods will come along the way, if you make a well-planned effort.

thanks for the advice ... and the link for calculus ..

actually i was having plans to buy this book too this year for some reference ...

i found this nice link .. its about numerical methods and it has some examples of fixed point iteration method for different types of equations ...

it was a bit hard to get some sort of flow for this subject .. which is why learning this was a bit depressive ... there are always more pre requisites to fullfill to understand these methods properly ...

from page 11 , of that pdf ... they describe the fixed point iteration method ...

i need to understand all those somehow ... it feels better because it has some simple looking equations where this fixed point iteration method can be applied ... even though i dont completly understand the definition .. or why the phi is used ... or what it actually mean by "take an arbitrary x0.....

i have a doubt if i am confusing simultaneous equations with systems of linear equations ??
or all these three things .. the linear equation , the systems of linear equations and simultaneous equations different ????

and i think the methods described in these two links below , could be used to solve ... the linear equation , the systems of linear equations and simultaneous equations ....

You can start with a wild guess, or with a more reasoned guess, or with a rough estimate after trying a few values on your calculator or after sketching a graph.

As a general rule, for a given rearrangement the closer your initial value is to the exact solution, the fewer the required number of iterations to achieve the accuracy desired.

I suggest that you set yourself some exercises using equations for which you already know the exact solution, so you can see how iteration converges towards the solution (or not, as the case may be). For example, you can see in advance the solutions to this quadratic: (x-7)(x+3)=0
which can be written x^{2} - 4x - 21 = 0

the things i were following were these numerical methods ...

then i found a simple example to work with ...

then i was trying to figure out a way to solve it ...

i have a little bit of confusions here ...

i think i figured it out that the initial guess ,(the initial root )... the answer of the question ... is like f(1.618) ... which makes the equation close to zero ... ??

this positive root is called a golden ratio ... right ??

is this like an answer to the question already ???

should i be looking for more values which makes the equation closer to zero ?

is that why we use numerical methods such as fixed point iteration ... ??

anyway then you put the values to fit the formulas of iteration methods ...

to get more approximate values which makes the equation closer to zero ???

yea..lol ... i was just trying to figure out the steps .. the syllabus wants me to put the numerical methods to a computer program in c ...so i was just confused about the steps involved ...