Lectures On the Calculus of Variations
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In our eReader you can find the full English version of the book. Read Lectures On the Calculus of Variations Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Lectures On the Calculus of Variations
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Is a continuous closed curve without mul- tiple points (a so-called ''^Jordan-curve''') . It divides, there- fore, ^ the oc, ?/-plane into an interior and an exterior. According to a theorem due to Schoenfliess" the set of points §>j. Is identical ivitli the interior of 2' together witli the houndarji 2'.
2. Let /q, iy be two values of / satisfying the inequality and let @o denote the arc of the curve (10) corresponding to the interval (/o, ti). Since the line: 0.^:0^, to^t^t^ lies in the inter...ior of iSj^. , its image @o li^s in the interior of ^^. And has, therefore, no point in common with the boundary 2'. The two curves ®o ^^^^ ^' being continuous, it follows, '" therefore, that a neighborhood (/o) of the arc @o c^in he con- structed which is entirely contained in ^f..
3. Since A(/, Oo)=t=0 in {TqTi) and A(/, a) is continuous in iSfc, it follows from the theorem on uniform continuity* that k can he taken so smcdl that 1 Compare J. I, No. 102. The interior as well as the exterior is a " continuum.
What to read after Lectures On the Calculus of Variations?
You can find similar books in the "Read Also" column, or choose other free books by O Oskar Bolza to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Is a continuous closed curve without mul- tiple points (a so-called ''^Jordan-curve''') . It divides, there- fore, ^ the oc, ?/-plane into an interior and an exterior. According to a theorem due to Schoenfliess" the set of points §>j. Is identical ivitli the interior of 2' together witli the houndarji 2'.
2. Let /q, iy be two values of / satisfying the inequality and let @o denote the arc of the curve (10) corresponding to the interval (/o, ti). Since the line: 0.^:0^, to^t^t^ lies in the inter...ior of iSj^. , its image @o li^s in the interior of ^^. And has, therefore, no point in common with the boundary 2'. The two curves ®o ^^^^ ^' being continuous, it follows, '" therefore, that a neighborhood (/o) of the arc @o c^in he con- structed which is entirely contained in ^f..
3. Since A(/, Oo)=t=0 in {TqTi) and A(/, a) is continuous in iSfc, it follows from the theorem on uniform continuity* that k can he taken so smcdl that 1 Compare J. I, No. 102. The interior as well as the exterior is a " continuum.
What to read after Lectures On the Calculus of Variations?
You can find similar books in the "Read Also" column, or choose other free books by O Oskar Bolza to read onlineMoreLess
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