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# BAB I Matematika I

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Fungsi dan berbagai sistem koordinatLimitDiferensial total dan parsialMaximasi dan MinimasiIntegralVektor Matrik Matematika I Matematika untuk teknik : Kastroud (Erwin Sucipto)  FUNGSI DAN SISTEM KOORDINAT Pendahuluan.Beberapa pengertian :Variabel dan Konstanta.Variabel : harganya setiap saat dapat berubah.Konstanta : harganya tetap. CONTOH :y = 15 x + 10y = mx + cKonstanta : m dan cVariabel : x dan yTujuan : Untuk memperoleh hubungan antara dua variabel yang harga-harganya diperoleh dari suatu percobaan atau hasil pengamatan.  SISTEM KOORDINAT Koordinat Cartesius : dibagi 4 daerah : kuadran I, II, III dan IVTitik P dinyatakan oleh sepasang bilangan (a, b) -4-3-2-101234-4 -3 -2 -1 0 1 2 3 4 Q (2, -3)P(a,b)yx ▪   IVIIIIII  |y 1  – y 2 ||x 1  – x 2 |Q(x 2 , y 2 )yxR(x 2 , y 1 )P(x 1 , y 1 ) Teorema Pythagoras : a 2 + b 2 = c 2 Panjang PR = |x 2  – x 1 |dan RQ = |y 2  – y 1 |Maka jarak (tak berarah) antaraP dan Q = d  (P, Q)= √( x 2  – x 1 ) 2 + (y 2  – y 1 ) 2 Carilah jarak P(-2, 3) dan Q(4,-1) d  (P, Q) = √(4 – (-2)) 2 + (-1  – 3) 2 = √36 + 16 = 7,21
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