Back in nerd school, we did PDE out of a Well Respected (tm) brutal textbook that I will not name because who knows what roving bands of mathozoids with an axe to grind are up to these days. And it's more fun if you can guess.
Despite getting good grades both semesters, to this day I have no idea how to solve a PDE. Not even a game plan. Contrast me facing off agin' an ODE, which I also probably cannot solve but can at least get a few pokes in before it chews my arms and legs off.
Whereas ODE offer a welcome buzz, PDE are all hangover. The difference between sipping a nice Malbec by the fire and forcing down shots of homebrew teen LabKitty made using a contraption described in the yellowing pages of a Cold War era Reader's Digest found in the basement of the Circle Pines library, back when there were still libraries in a time before nomenclature was and each was all. It burned going in, burned coming out, and in between did enough chromosome damage that one temporarily qualified as a protected wetland species, genetically, before corrective nucleases had worked the necessary extra shifts to put your phenome back on the sapien branch. X-Men, indeed.
But I digress.
Our course textbook was all Hilbert space this and self-adjoint that, and I guess they do that sort of thing but it did not serve us well, "us" here being the unmutated who view mathematics as a tool and not a status club (in either sense of the word).
The net effect was all tree and no forest. Perhaps that has something to do with the net effect. We happy few, donning jorts and field glasses, stood nose-to-bark for the better part of a year while the professor regaled us with tales of the vascular cambiumand periderm, the various coverings, spices, flavorings, tannins, resin, latex, medicines, and most of all poisons it offered. Textures and colorings, description and decortications.
Meanwhile the rich PDE landscape spread around us unseen, vistas and dells not visited nor even divulged. The kingdom of the father spread upon the earth and men do not see it; Thomas an engineering student at heart.
As such, were I today to encounter a PDE in the wild, my solution would consist of panic and pee. Sure, I can throw it on the computerzoid and do the finite elements maybe, but I sing here of analytics -- the cozy comfort of a pen and paper solution, wherein nature and nature's god are made to squeal using tools known to any post-Newtonian primitive. These lay beyond my ken and grasp where PDE are involved.
Until recently, that is. Enter Stanley Farlow.
Farlow's book was first published in 1982 and I don't know how it eluded me until now. Perhaps prior trauma gifted me a kind of hysterical PDE blindness, like Blythe collapsing in a Carentan alley.
Partial Differential Equations for Scientists and Engineers, with the title on the cover in bold Cabin in the Woods font, is a welcome relief to the dirge of Well Respected (tm) brutal PDE textbooks.
Farlow organizes his presentation into 47 bite-sized "lessons," each opening with a boxed motivation, then: material, solved problems, exercises (with solutions), and a short list of recommended go-next references. Globally the topics build upon what came before, as they should: the parabolic leads to the hyperbolic leads to the elliptic (yes, Farlow, too, focuses on the heat equation, wave equation, and Poisson's equation -- PDEs are the math equivalent of a cover band: You study equations other people have solved because there aren't any other kinds). Here we tour all of the great PDE vistas: separation of variables, superposition, characteristics, transform solutions, Duhamel's principle, spherical harmonics. Take a picture, it will last longer.
The fourth and final section is a quick recapitulation vis-a-vis numerical methods, wherein we arrive at my only complaint: no finite element, even though Farlow ends on variational techniques (dude, FE was RIGHT THERE). But 'tis but a small offense.
An appendix even includes a PDE crossword puzzle (suck it, NYT).
The presentation is breezy enough that the big picture emerges rapidly (you could read the whole thing in two weeks of evenings if you skim occasionally) and the big picture is the point. I dare say the read is enjoyable, believe it or not, especially if Farlow is playing the Robin Williams to your Matt Damon, someone at last explaining a borked PDE psyche is Not Your Fault.
Full digestion of this topic, of course, takes longer (approximately: the lifetime of the reader), but arriving at the end of Farlow brings a calmness, a relaxing of the shoulders, an easing of a furrowed brow. Partial differential equations will always be unpleasant, always formidable, mean and strong like the people of South Alabama, but by Farlow made less a horror and more mere horror-show.
Buy Farlow on Amazon.
Despite getting good grades both semesters, to this day I have no idea how to solve a PDE. Not even a game plan. Contrast me facing off agin' an ODE, which I also probably cannot solve but can at least get a few pokes in before it chews my arms and legs off.
Whereas ODE offer a welcome buzz, PDE are all hangover. The difference between sipping a nice Malbec by the fire and forcing down shots of homebrew teen LabKitty made using a contraption described in the yellowing pages of a Cold War era Reader's Digest found in the basement of the Circle Pines library, back when there were still libraries in a time before nomenclature was and each was all. It burned going in, burned coming out, and in between did enough chromosome damage that one temporarily qualified as a protected wetland species, genetically, before corrective nucleases had worked the necessary extra shifts to put your phenome back on the sapien branch. X-Men, indeed.
But I digress.
Our course textbook was all Hilbert space this and self-adjoint that, and I guess they do that sort of thing but it did not serve us well, "us" here being the unmutated who view mathematics as a tool and not a status club (in either sense of the word).
The net effect was all tree and no forest. Perhaps that has something to do with the net effect. We happy few, donning jorts and field glasses, stood nose-to-bark for the better part of a year while the professor regaled us with tales of the vascular cambiumand periderm, the various coverings, spices, flavorings, tannins, resin, latex, medicines, and most of all poisons it offered. Textures and colorings, description and decortications.
Meanwhile the rich PDE landscape spread around us unseen, vistas and dells not visited nor even divulged. The kingdom of the father spread upon the earth and men do not see it; Thomas an engineering student at heart.
As such, were I today to encounter a PDE in the wild, my solution would consist of panic and pee. Sure, I can throw it on the computerzoid and do the finite elements maybe, but I sing here of analytics -- the cozy comfort of a pen and paper solution, wherein nature and nature's god are made to squeal using tools known to any post-Newtonian primitive. These lay beyond my ken and grasp where PDE are involved.
Until recently, that is. Enter Stanley Farlow.
Farlow's book was first published in 1982 and I don't know how it eluded me until now. Perhaps prior trauma gifted me a kind of hysterical PDE blindness, like Blythe collapsing in a Carentan alley.
Partial Differential Equations for Scientists and Engineers, with the title on the cover in bold Cabin in the Woods font, is a welcome relief to the dirge of Well Respected (tm) brutal PDE textbooks.
Farlow organizes his presentation into 47 bite-sized "lessons," each opening with a boxed motivation, then: material, solved problems, exercises (with solutions), and a short list of recommended go-next references. Globally the topics build upon what came before, as they should: the parabolic leads to the hyperbolic leads to the elliptic (yes, Farlow, too, focuses on the heat equation, wave equation, and Poisson's equation -- PDEs are the math equivalent of a cover band: You study equations other people have solved because there aren't any other kinds). Here we tour all of the great PDE vistas: separation of variables, superposition, characteristics, transform solutions, Duhamel's principle, spherical harmonics. Take a picture, it will last longer.
The fourth and final section is a quick recapitulation vis-a-vis numerical methods, wherein we arrive at my only complaint: no finite element, even though Farlow ends on variational techniques (dude, FE was RIGHT THERE). But 'tis but a small offense.
An appendix even includes a PDE crossword puzzle (suck it, NYT).
The presentation is breezy enough that the big picture emerges rapidly (you could read the whole thing in two weeks of evenings if you skim occasionally) and the big picture is the point. I dare say the read is enjoyable, believe it or not, especially if Farlow is playing the Robin Williams to your Matt Damon, someone at last explaining a borked PDE psyche is Not Your Fault.
Full digestion of this topic, of course, takes longer (approximately: the lifetime of the reader), but arriving at the end of Farlow brings a calmness, a relaxing of the shoulders, an easing of a furrowed brow. Partial differential equations will always be unpleasant, always formidable, mean and strong like the people of South Alabama, but by Farlow made less a horror and more mere horror-show.
Buy Farlow on Amazon.
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