数学分析讲义 - nju.edu.cn

1 C 2006-2010 | i Newton Leibniz 15 16 19 19 Cauchy , Riemann Weierstrass 20 Grassmann Poincar e Cartan Stokes

2 Newton-Leibniz Taylor Riemann Riemann Riemann Kummer Euler-Maclaurin Stirling Fourier Fourier ii Parseval Lagrange Jacobian Riemann Green Gauss Stokes

3 Riemann- stieltjes Riemann- stieltjes Riemann Green Gauss Stokes Gamma Stirling Fourier Plancherel Fourier i.

4 : ..19 .. Cauchy .. Stolz ..56 .. ( ) ..109iiiiv ..156 Taylor .. L H opital .. Taylor .. Taylor ..202 Riemann Riemann ..242 ..262 ..272 ..307 .. Taylor ..349 Fourier Fourier .. Fourier .. Parseval .. Fourier .. Fourier .. Fourier .. Fourier ..384vi ..408 .. Taylor.

5 Lagrange ..451 Riemann ..490 ..509 .. Green .. Gauss .. Stokes .. : Riemann- stieltjes .. Riemann- stieltjes ..543 .. Stokes ..579 .. Beta .. Gamma .. Stirling .. Fourier ..617 635 637viii.

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10 Q n 1 , n 1 , n .. ( ) , p1 2, p2, p3, , pk. n 1`p1p2 pk. n pip1 i kq, n . pi, pi n. n , . , . A,B . px,yq, x A ,y B . , A B , A B, A B tpx,yq|xPA, yPBu. A B ,A B . A t1,2,3u,B t4,5u, A B tp1,4q,p1,5q,p2,4q,p2,5q,p3,4q,p3,5qu,A B 6 . , , A,B m,n , A B mn . A,B , A B .. A,B , A ta1, a2, , ai, u, B tb1, b2, , bj, u. A B A B tpai,bjq|i,j 1,2, u.