tag:blogger.com,1999:blog-7225373.post8832048719511876643..comments2024-02-29T03:34:23.190-05:00Comments on Who Were the Sea Peoples?: An Uncomfortable Teachergcallahhttp://www.blogger.com/profile/10065877215969589482noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-7225373.post-25806931214788038662007-08-27T02:54:00.000-04:002007-08-27T02:54:00.000-04:00It's always fun to con students into trying to sol...It's always fun to con students into trying to solve a non-elementary integral that, superficially, doesn't look any harder than the integrals they know how to do.shonkhttps://www.blogger.com/profile/17369367271546487712noreply@blogger.comtag:blogger.com,1999:blog-7225373.post-78871208759282891602007-08-26T17:51:00.000-04:002007-08-26T17:51:00.000-04:00shonk: ain't it the truff? It's much like making u...shonk: ain't it the truff? It's much like making up your own integrands to integrate.Wabulonhttps://www.blogger.com/profile/16838347174718251102noreply@blogger.comtag:blogger.com,1999:blog-7225373.post-36754617058946046402007-08-23T23:29:00.000-04:002007-08-23T23:29:00.000-04:00Are you serious or ridiculing the premise of my po...<I>Are you serious or ridiculing the premise of my post?</I><BR/><BR/>I was being quite serious. We lie all the time when explaining to freshmen how things work or why they're true. It makes me cringe every time I get to the section on the Fundamental Theorem of Calculus and completely gloss over why it's true.<BR/><BR/>Of course, a bigger lie is the implication that the techniques you learn in the Differential Equations section of Calc. II (or even in a first "real" Diff Eq. class) are actually useful for anything other than solving the problems your teacher assigns you. There's a reason making up your own DEs to solve as practice for the exam never seems to work.shonkhttps://www.blogger.com/profile/17369367271546487712noreply@blogger.comtag:blogger.com,1999:blog-7225373.post-1897744151895770612007-08-22T17:35:00.000-04:002007-08-22T17:35:00.000-04:00Here's something I handed my calculus teacher in H...Here's something I handed my calculus teacher in High School:<BR/><BR/>Solve: A d2y/dx2 + B dy/dx + Cy = 0<BR/><BR/>Multiplying through by dx2:<BR/>A d2y + B dy dx + C y dx2 = 0<BR/><BR/>This is a quadratic in dx:<BR/>dx=(-Bdy+-sqrt(B2dy2-4ACyd2y))/2Cy<BR/><BR/>Therefore<BR/>dx/dy=(-B+-sqrt(<BR/> B2-4ACyd2y/dy2))/2Cy<BR/><BR/>But d2y/dy2 = d/dy (dy/dy) = 0<BR/><BR/>Therefore<BR/>dx/dy=(-B+-sqrt(B2))/2Cy<BR/> =(-B +- B)/2Cy<BR/> = 0 OR -2B/2Cy=(-B/C)(1/y)<BR/><BR/>Therefore<BR/> EITHER x is constant (doubtful)<BR/> OR x = (-B/C) log y + K<BR/> SO y = exp((-C/B)(x - K))<BR/> = K'exp(-(C/B)x)<BR/><BR/>DONE!<BR/><BR/>Needless to say, I did not receive a convincing explanation of why this derivation was invalid.Wabulonhttps://www.blogger.com/profile/16838347174718251102noreply@blogger.comtag:blogger.com,1999:blog-7225373.post-23605461805545141262007-08-20T00:32:00.000-04:002007-08-20T00:32:00.000-04:00Are you serious or ridiculing the premise of my po...Are you serious or ridiculing the premise of my post? Because I think that that might be true, that when you teach calc to freshmen you end up saying things without caveats that you'd give to grad students.Bob Murphyhttps://www.blogger.com/profile/04001108408649311528noreply@blogger.comtag:blogger.com,1999:blog-7225373.post-84038252290802280122007-08-18T22:55:00.000-04:002007-08-18T22:55:00.000-04:00I used to think it must be nice to be a math profe...<I>I used to think it must be nice to be a math professor, because then everything you taught would be rigorously correct.</I><BR/><BR/>I don't know, I find myself lying quite a bit when I teach freshman calculus.shonkhttps://www.blogger.com/profile/17369367271546487712noreply@blogger.com