Matti Lehtinen: Matematiikan historian luentoja
Matti Lehtinen: Matematiikan historian luentoja
Matti Lehtinen: Matematiikan historian luentoja
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7 Differentiaali- ja integraalilaskennan esivaiheet......................................................... 45<br />
7.1 Stevin, Kepler ja Galilei...................................................................................... 45<br />
7.2 Cavalierin integroinnit ........................................................................................ 46<br />
7.3 Descartes, Fermat ja analyyttinen geometria ...................................................... 48<br />
7.4 uusia integrointimenetelmiä ................................................................................ 49<br />
7.5 Tangenttikonstruktioita ....................................................................................... 52<br />
8 Newton ja Leibniz....................................................................................................... 55<br />
8.1 Binomisarja ......................................................................................................... 55<br />
8.2 Newtonin differentiaali- ja integraalilaskenta..................................................... 55<br />
8.3 Leibniz................................................................................................................. 57<br />
9 Analyysin nopea kehitys 1700-luvulla........................................................................ 60<br />
9.1 Bernoullin veljekset ............................................................................................ 60<br />
9.2 Englannin matematiikkaa 1700-luvulla ............................................................. 62<br />
9.3 Euler .................................................................................................................... 63<br />
9.4 Ranskan valistusajan matemaatikkoja ................................................................ 66<br />
9.5 Lagrange.............................................................................................................. 67<br />
10 Ranskan vallankumouksen ajan matematiikkaa ....................................................... 69<br />
10.1 Monge ja École Polytechnique.......................................................................... 69<br />
10.2 Fourier ............................................................................................................... 69<br />
10.3 Laplace ja Legendre .......................................................................................... 70<br />
10.4 Gauss................................................................................................................. 72<br />
11 Analyysin täsmällistymisen vuosisata ...................................................................... 74<br />
11.1 Cauchy............................................................................................................... 74<br />
11.2 Abel, Jacobi, Dirichlet....................................................................................... 76<br />
11.3 Riemann ............................................................................................................ 77<br />
11.4 Weierstrass ........................................................................................................ 78<br />
11.5 Irrationaalilukujen luokat ja reaalilukujen täsmällinen määrittely.................... 79<br />
12 Geometria 1600−1800-luvuilla................................................................................. 81<br />
12.1 Projektiivisen geometrian alkuvaiheet .............................................................. 81<br />
12.2 Synteettinen ja analyyttinen geometria ............................................................. 81<br />
12.3 Epäeuklidisen geometrian synty........................................................................ 82<br />
12.4 Euklidisen geometrian perusteet ....................................................................... 84<br />
12.5 Klein ja Erlangenin ohjelma.............................................................................. 85<br />
13 Algebran kehitysvaiheita .......................................................................................... 86<br />
13.1 Polynomiyhtälön algebrallinen ratkaisu............................................................ 86<br />
13.2 Algebran vapautuminen .................................................................................... 86<br />
13.3 Hamilton ja epäkommutatiivisuus..................................................................... 87<br />
13.4 Matriisit............................................................................................................. 88<br />
13.5 Algebralliset struktuurit .................................................................................... 89<br />
14 Matemaattinen logiikka ja joukko-oppi.................................................................... 90<br />
14.1 Matemaattisen logiikan synty............................................................................ 90<br />
14.2 <strong>Matematiikan</strong> perusteet ..................................................................................... 90<br />
14.3 Cantor ja joukko-oppi ....................................................................................... 91<br />
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