looking for where can i learn this problems of numerical analysis (specifically problem 2)

[imranmx]

 

[HallsofIvy]

For (2) what are $\displaystyle \nabla$ and $\displaystyle \Delta$? How are they defined in your text book?

 

[imranmx]

its nabla and delta
i couldn't find any definition
i dont even understand what thay are !

 

[HallsofIvy]

Are you taking a course? Do you have a textbook? What about a teacher? "Nabla" is defined here: Nabla -- from Wolfram MathWorld .

Nabla, $\displaystyle \nabla$, is a "differential operator" that, in an xy-coordinate system is $\displaystyle \frac{\partial}{\partial x}+ \frac{\partial}{\partial y}$ and in an xyz-coordinate system is $\displaystyle \frac{\partial}{\partial x}+ \frac{\partial}{\partial y}+ \frac{\partial}{\partial z}$.

For example, $\displaystyle \nabla f(x,y,z)$ where f is a scalar valued of x, y, and z is $\displaystyle \frac{\partial f}{\partial x}+ \frac{\partial f}{\partial y}+ \frac{\partial f}{\partial z}$ (called "grad f", "gradient of f") and is the vector that points in the direction of fastest increase of f and has length the rate of increase (derivative) in that direction.

Or, if $\displaystyle \vec{f}= f_1(x,y,z)\vec{i}+ f_2(x,y,z)\vec{j}+ f_3(x,y,z)\vec{k}$ is a vector valued function the "dot product" of $\displaystyle \nabla$ and $\displaystyle \vec{f}$, $\displaystyle \nabla\cdot \vec{f}= \frac{\partial f_1}{\partial x}+ \frac{\partial f_2}{\partial y}+ \frac{\partial f_3}{\partial z}$ (called "div f", divergence), measures how fast the vector functions spreads out. Finally, the cross product of $\displaystyle \nabla$ and $\displaystyle \vec{f}= \left(\frac{\partial f_2}{\partial z}- \frac{\partial f_3}{\partial f_2}{\partial z}\right)\vec{i}+ \left(\frac{\partial f_3}{\partial x}- \frac{\partial f_1}{\partial z}\right)\vec{j}+ \left(\frac{\partial f_1}{\partial y}- \frac{\partial f_2}{\partial x}\right)\vec{k}$. The "curl" measures the rotation of the vector field.

$\displaystyle \Delta$ is much simpler. In introductory Calculus $\displaystyle \Delta x$ is used to mean a small change in x. For example, the derivative of y(x) can be defined by $\displaystyle \frac{dy}{dx}=$$\displaystyle \lim_{\Delta x \to 0}\frac{\Delta y}{\Delta x}$$\displaystyle = \lim_{\Delta x\to 0}\frac{y(x+\Delta x)- y(x)}{\Delta x}$. That is, $\displaystyle \Delta x$ is a small change in x and $\displaystyle \Delta y$ is a small change in y, the change from $\displaystyle y(x)$ to $\displaystyle y(x+ \Delta x)$.

 

[imranmx]

i am really bad at math (really bad might be an understatement) but i want to learn
but couldn't get the courage to learn from the beginning.. because i have start from high school again.
Are you taking a course >>> yes (BSC in CSE)
Do you have a textbook >>> yes (Numerical Analysis Richard L. Burden, J. Douglas Faires, Annette M. Burden)
What about a teacher? >>> yes but too busy.... and cant access other resources because of covid.
i took some notes from class.
i understood what my teacher taught me but when it come to solve anything i just cant.
but i feel like somethings missing that i should have known from the start.
but i don't know what.
i feel so lost and the shear amount of things i have to learn just freezes me.
if i am not climbing i am falling.