By Wilfred Kaplan
The Kaplan e-book is direct, concise, and well-organized. quite often, I loved it.
However, a few of Kaplan's motives have been a section TOO concise. In these circumstances, i discovered myself going again to Multivariable Calculus (Stewart's Calculus sequence) -- i.e., the second one half Stewart's substantial calculus booklet, released individually so you do not get a hernia from sporting it round. should you snatch some extent quick, Kaplan is healthier; if you want extra aid, Stewart is better.
One grievance: The Kaplan booklet is particularly affordably certain. by way of the tip of the semester, my replica was once falling aside.
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Extra info for Advanced Calculus (4th Edition)
I(O) sont transversaies pres d'un point (xo,eo) de leur intersection. On suppose en outre que, pres de ce point, la restriction de dpm it. A est non degeneree, ce qui entraine que Ie champ hamiltonien de Pm est transverse it. A pres de (xo, On not era I la bicaracteristique passant par ce point. eo). 38 Soit R un operateur 2-microdifferentiel de biordre (m, -1), dont Ie symbole appartient a 8';-1,0 + 8';,-2 2-microlocalement pres des points x Xo, ~ = €o, (ox,o€) = ±H",,(xo,€o) (ou ce dernier vecteur vit dans Ie quotient de T(T*Rn) par T(A».
II se trouve qu'il est utile d'adjoindre aux Conf(k, Y, r), qui sont les espaces de 'sandwiches' de symboles confines pour les calculs de Weyl successifs, les symboles negligeables des calculs anterieurs ; c'est Ie sens de la partie (c) de Ia definition. Comme pour la premiere microlocalisation, Ie resultat essentiel sera un theoreme de biconfinement pour les elements de <:foiif( k, Y, r) X <:foiif( k, Z, r). II faut auparavant definir par recurrence la fonction qui contrOlera la petitesse de ces elements lorsque Y est loin de Z.
Sci. Ec. Norm. Sup. (4· serie) 21 (1988) 91-132 [4J M. Beals. Self-spreading and strength of singularities for solutions to semi-linear wave equations Ann. of Math. 118 (1983) 187-214 [5J M. Beals. Propagation of smoothness for nonlinear second order strictly hyperbolic equations Proc. of Symposia in Pure Math. 43 (1985) 21-45 [6J M. Beals et G. Metivier. Progressing wave solutions to certain nonlinear mixed problems. Duke Math. Jour. 53 (1986) 125-137 [7J M. Beals et G. Metivier. Reflection of transversal progressing waves in nonlinear strictly hyperbolic mixed problems.