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Hi there. I just want to know which book would you recommend to someone who is familiar with the basics and up to acquire a deeper understanding of the concepts of Linear Algebra and its applications?

Thank you!

Is there a general rule to solve this kind of problems, given two surfaces that bound a solid and its density function ?

Can you help me calculate the mass of the solid bounded by the surfaces $x^2+y^2=2y$ and $z=\sqrt{x^2+y^2}$ given its density function $m(x,y,z)=\sqrt{x^2+y^2}$ ?

Yes, this typo confused me. Thank you again for everything you've done!

Oh, I see...The example was taken from Marsden-Tromba's Vector Calculus. These books aren't the gospel truth after all!

I tried drawing D but I got confused. I represent $x=\sqrt{y}$ as $y=x^2$ and plot the lines $y=2$, $x=1$. It seems to me that D is divided in two sections: $0\leq x\leq1$ , $0\leq y\leq x^2$ and $1\leq x\leq\sqrt{2}$ , $x^2\leq y\leq 2$ , because the curve intersects the vertical line. Is this poss...

Can you show me how to change the order of integration to the following integral (how to find the new limits of integration)?

$\int_{0}^{2}\int_{\sqrt{y}}^{1} (x^2+y^3x) dxdy$

Thank you, your help was invaluable!

How can I calculate the volume between the surfaces given below using double/triple integrals and polar coordinates?

$$\begin{Bmatrix}
F_2(x, y) & = & 2-x^2-y^2 \\\\
F_1(x, y)& = & \sqrt{x^2+y^2}
\end{Bmatrix}$$