Advanced calculus for applications
by Francis Begnaud Hildebrand · first published 1948
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…huge, old field, and there is some question about how much of that deserves study now. Do notice that for systems of ordinary differential equations, get to apply some linear algebra in cute ways. For advanced calculus for applications, there is the old MIT Hildebrand -- he knows what he is talking about, is easy enough to read, and a good place to go if need one of his topics. In recent decades, the pure math departments wanted to…
on “Math Basics for Computer Science and Machine Learning [pdf]” ↗…book, Coddington and Levinson is much more advanced) -- now can do basic AC circuit theory like eating ice cream. Advanced calculus from one or several more traditional books, e.g., the old MIT favorite Hildebrand, Advanced Calculus for Applications, Fleming, Functions of Several Variables, Buck, Advanced Calculus -- can now look at Maxwell's equations and understand at least the math. And can work with the gradient for steepest descent in the maximum…
on “Ask HN: How or where to begin learning mathematics from first principles?” ↗…longer really "modern"! Get a used copy; that's what I did. You don't want a newer edition! But with that out of the way, might take a fast pass through an old MIT standard Francis B.\ Hildebrand, {\it Advanced Calculus for Applications,\/} Prentice-Hall, Englewood Cliffs, NJ, 1962.\ \ There's a lot of fun stuff in there, but it's TOO short on proofs. So, I'd pass it up and return later when know enough real analysis to guess or understand…
on “Ask HN: Resources to learn real analysis?” ↗…result of Caratheodory, but in general could lose a lot of sleep working through that! I had a course from a Ph.D. from MIT from the book, apparently long a standard at MIT, Francis B.\ Hildebrand, {\it Advanced Calculus for Applications,\/} Prentice-Hall, Englewood Cliffs, NJ, 1962.\ \ So, yes, can find out about solutions via infinite series and boundary value problems. The book was very short on proofs, and to take such material…
on “A First Course in Differential Equations for Scientists and Engineers” ↗…avoided Buck, Fleming, Spivak, and of course also, now in English, Henri Cartan, 'Differential Forms'. I even avoided the classic applied advanced calculus text, long used at MIT, Francis B. Hildebrand, 'Advanced Calculus for Applications'. For Loomis and Sternberg, I agree with you, and have both the hard copy and the PDF. Since I've mentioned such advanced calculus, I will try to save many students: Students, there's a secret. The…
on “Ask HN: Learn Math the Hard Way” ↗…to formulate those two. Writing clearly, briefly, and precisely about big subjects is not always easy! The time I encountered Strum-Louville theory was a course from the fairly well known Hildebrand, Advanced Calculus for Applications from MIT and by a professor with a recent MIT Ph.D. By the way, that book is available in PDF on the Internet for free. To me the topic looked like the math of vibrating strings, etc., but the course…
on “The Two Cultures of Mathematics (2000) [pdf]” ↗…derivative, with some TeX notation f'(x) = d/dx f(x) = lim_{h --> 0} (f(x + h) - f(x))/h and I was in. I did well, made As both semesters. Went on to advanced calculus, ordinary differential equations, advanced calculus for applications, real analysis, functional analysis, real applications, peer-reviewed publications, teaching calculus, etc. E.g., for an application I derived and used y'(t) = k y(t) (b - y(t)) to please the BoD…
on “The Calculus Trap (2005)” ↗…that is differentiable but whose Riemann integral does not exist. But, still, it is amazing how easy it is to get 36 decimal digits of e, and 500 if want. I've been through calculus, advanced calculus, advanced calculus for applications, differential equations, local series solutions to the Navier-Stokes equations, exterior algebra, real analysis, measure theory, and more, have taught calculus in college, applied it in US national security…
on “Ask HN: What interesting problems are you working on?” ↗…Much Calculus Not for me! Heck, I never took freshman calculus or pre-calculus and, instead read a book and started on sophomore calculus then continued with, right, ordinary differential equations, advanced calculus for applications, and advanced calculus, topology, modern analysis, measure theory, functional analysis, exterior algebra, etc. Not enough calculus for me! Strang, of course, is emphasizing linear algebra. Great!…
on “Too Much Calculus – Gilbert Strang (2001) [pdf]” ↗