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For questions about differential and integral calculus with more than one independent variable.

1
vote
I like stressing the connection between rates of change and integrals, and I carry this into multiple integrals as well. As an example, you could talk about a row of apple trees producing (on average …
answered Feb 7 by Steven Gubkin
2
votes
My proof is basically the same as yours, but perhaps this will be a bit more intuitive. We want to find the volume of a $k$-parallelepiped spanned by $v_1,v_2,...,v_k$ in $\mathbb{R}^k$. We are arme …
answered Jan 18 '16 by Steven Gubkin
14
votes
A place that Lagrange Multipliers comes up is in the proof of the real spectral theorem. Namely, let $A$ be a symmetric matrix. Define $f: \mathbb{R}^n \to \mathbb{R}$ by $f(v) = v^\top A v$. If yo …
answered Jul 8 '15 by Steven Gubkin
1
vote
Solving systems of polynomial equations is hard in general. The examples in the textbook are specially cooked up to be possible. I am not sure that developing skill at solving such systems is a good …
answered Mar 1 '18 by Steven Gubkin
2
votes
I am also vaguely aware that in economics, the actual value of $\lambda$ is often important. Say you have a function $f$ which needs to be optimized subject to a constraint $g = c$. Then it turns ou …
answered Jul 9 '15 by Steven Gubkin
6
votes
A question with two constraints might make the method seem preferable to finding a parameterization (which I assume is the "easier" technique you refer too in the OP). For example, maximizing $f(x,y, …
answered Jul 9 '15 by Steven Gubkin