 By Klaus Jänich

Das Buch "Mathematik 1/Geschrieben f?r Physiker " zusammen mit dem im Fr?hjahr 2002 erschienenen Band 2 verfolgt eine neuartige Strategie f?r die mathematische Ausbildung der Physikstudenten im ersten Studienjahr. Radikale "Rechtzeitigkeit" des Stoffes (Differentialgleichungen ab der zweiten Unterrichtswoche usw.) und physikbezogene neben rein mathematischen ?bungsaufgaben gehen Hand in Hand mit der Vermittlung des tieferen mathematischen Verst?ndnisses. Dieses ungew?hnliche Konzept erfordert viel erl?uternden textual content, wobei die aus anderen Lehrb?chern des Autors bekannte erkl?rende und ?berzeugende paintings zu schreiben voll zum Einsatz kommt. Viele Abbildungen veranschaulichen die Begriffe und Zusammenh?nge. Als vorlesungsbegleitendes Lehrbuch und auch zum Selbststudium bestens geeignet.

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Extra resources for Mathematik 1, geschrieben fuer Physiker

Example text

Proof of Theorem 5 Applying well-known results in the theory of parabolic equations, we infer that there exists a unique solution to ut + Au = R, u(0) = 0, (40) with u € W1,oo(0, +oo; H) n H^Q, +co; V) D L°°(0, +oo; F 2 (fi)). (41) Note that (41) entails u S ^(Qoo). (42) Hence, we choose the constant M in (38) to be M = exp(\\u\\LOO(Qoo)+u*), where u* = max{|KH L o o ( n ) ,log6» c + ||5|| L oo Woo) }. (43) Let us now take the difference of (22) and (40), test it by (u — u*)+, where (•) + stands for the positive part and u := u — u.

E. in Q\. Subsequently, from (44) we deduce \ ||(S-u')+(i)|& + \\y(u-u*)\\lHo,t]H) < 0. e. e. in Qt. e. in Qoo, and the proof is complete. For the sake of completeness, let us recall the following proposition (for the proof refer to ) from which uniqueness of the solution follows. e. e. e. in x i < X2, (51) QT- It is worth to note that the above result can be applied to prove uniqueness of the solution on the whole interval (0,+oo). Moreover, the property of the solutions stated by Theorem 9 is interesting from a thermomechanical point of view.

Aiki, Phase field model including a hysteresis operator. To appear in: Proceedings of the WCNA 2004.  T. Aiki, A model of 3D shape memory alloy materials. J. Math. Soc. Japan 57, 903-933 (2005).  T. -H. Hoffmann and T. Okazaki, Wellposedness for a new mathematical model for magnetostrictive thin film multilayers. Adv. Math. Sci. Appl. 14, 417-442 (2004).  T. Aiki, A. Kadoya and S. Yoshikawa, One-dimensional shape memory alloy problem with small viscosity. To appear in: Mathematical Approach to Nonlinear Phenomena; Modelling, Analysis and Simulations, Gakkotosho, Tokyo.