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7982022 No.7982022 [Reply] [Original]

Trying to teach myself multivariable calculus and differential equations. What are some /sci/ recommended sources?

>> No.7982037

>>7982022
Hubbard and Hubbard's Vector Calculus, Linear Algebra and Differential Forms: A Unified Approach

Simmons' Differential Equations with Applications and Historical Notes

>> No.7982665

A Synopsis of Elementary Results in Pure and Applied Matematics Volume 2

>> No.7982769

>>7982022

http://17calculus.com/ - Parametrics to Vector Fields

http://17calculus.com/differential-equations/ - Ordinary DE

>> No.7982803

>>7982022
Feynman Lectures

>> No.7984117

>>7982037
>Hubbard and Hubbard
I haven't used this myself, but the sort of approach that stresses these connections and cookbook/intuitive presentation with an eye towards building rigor are good things. It's generally well-recommended.

Colley's vector calc book does the latter well, though there's not much material on DE/LA and the chapter on forms, manifolds, and stokes' is fairly lacking (though likely the best you can hope for at this level.)

The old standby is Apostol vol 2, which is a rigorous and proof based (not cookbook) yet appropriately "first course" text that develops LA theory alongside multivariable functions and has good material on the application s of both to DE. It can be dry and it's hard to find a decent scan.

Arnold's ODE book is interesting geometric approach to the theory and worth reading on a rainy day. It's at an "advanced calculus" level and quite removed from the usual engineer's course on differential equations.

For the fully rigorous treatment, your options are Munkres' analysis on manifolds, Spivak's calculus on manifolds, and Do Carno's differential forms. There's a lot of fluff in the early chapters of the first which could conceivably substitute for a cookbook calc 3 course and is approachable without a prior analysis course. Do Carno is very short, somewhat minimalist and very to the point.