Showing posts tagged M32B

Math 32B Sample Questions

I’ve finished writing up some sample questions for the Math 32B final. The questions are available here and their solutions here. These questions are are my best guess of the sort of material that I feel is likely to appear on a final exam. As usual, feel free to let me know in the comments below if you find any errors.…

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Math 32B Final Review

I have written up a whirlwind review of the material covered in Math 32B this quarter. It is available here. The review is not meant to be entirely comprehensive, but I think it covers the bulk of the computational material from the course. The review is longer than I was hoping (6 pages) but it is certainly more condensed than the text which will hopefully be appealing to some students. As usual, let me know in the comments if you find errors or if anything in the text is unclear.…

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Homework 8 Hints

I’ve had a number of requests for hints and/or solutions to several of the homework problems for tomorrow. So here we go. 17.5 #30 This question asks us to compute the gravitational flux through a cylinder \(S\) from the gravitational field \[ \mathbf{F} = – G m \frac{\mathbf{e}_r}{r^2}. \] Here, \(S\) is the cylinder of radius \(R\) whose axis of symmetry is the \(z\)-axis with \(a \leq z \leq b\), and \(r = \sqrt{x^2 + y^2 + z^2}\) is the distance from \((x,…

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Explanation of 17.5 #48

In this problem, you are asked to compute the gravitational potential from uniform density spherical shell of total mass \(m\) and radius \(R\). In general, the gravitational potential of a massive surface \(S\) is given by \[ V(a, b, c) = – G \iint_S \frac{\rho, dS}{\sqrt{(x – a)^2 + (y – b)^2 + (z – c)^2}} \] where \(\rho\) is the density (mass per area) of the surface. In this case, \(\rho = m / (4 \pi R^2)\). The first part of the question asks you to reduce the problem to the…

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Math 32B/H Midterm 2 Review

I just finished writing up some review materials for the second midterm for Math 32B/H. There are two documents: the problems (here) and solutions (here). If you find any typos or points that need clarification, feel free to let me know in the comments below.…

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