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Integral Lintasan Kompleks

Integral Lintasan Kompleks. By : Dewi Octariana (0802101010 49 ) Lukman Jakfar S. (0802101010 50 ) Yunika Dewi W. (0802101010 51 ) Dina Frensista (08021010105 2 ) D wi S ilvia (08021010105 3 ). Integral Lintasan Kompleks. Integral lintasan fungsi sepanjang C ditulis.

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Integral Lintasan Kompleks

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  1. Integral LintasanKompleks

  2. By : DewiOctariana (080210101049) LukmanJakfar S. (080210101050) YunikaDewi W. (080210101051) Dina Frensista (080210101052) DwiSilvia(080210101053) IntegralLintasanKompleks

  3. Integral lintasanfungsisepanjang C ditulis • Integral tertentudari f(z) dari a ke b sepanjangkura C dapatditulis

  4. Untuk z pada C makadapatditulis • dengan a ≤ t ≤ b sehingga

  5. Sifat-sifat

  6. Jika f(z) = u(x,y) + iv(x,y) = u + iv, makadengan integral gariskompleksdapatdinyatakandalamsuku-suku integral garis real sebagai :

  7. Contoh 4.3.1 Hitung Jika f (z) = y – x + 6 i x2danterdiriatas 2 penggalgarisdari z = 0 sampai z = idandari z = isampai z = 1 + i

  8. Teorema 4.3.1 Jika f kontinuepadalintasan

  9. Contoh 4.3.2 Jika C lintasantertutupsegitigadengansudut -3 , 0 dan 4i

  10. Teorema 4.3.2 (Teorema Cauchy) • Fungsianalitikdanfungsikontinuedalam integral tutup C, • Contoh 4.3.3 • C kuvatertutupsederhana

  11. Contoh 4.3.4 Jika C lingkaran |z| = 1

  12. Teorema 4.3.3 Teorema Cauchy – Gausar Fungsianalitikdidalamdanpadalintasantertutup C

  13. Buktikanjika C lintasantertutupsepanjangsisi-sisibujursangkardantitik-titiksudut 1+i, -1+i, -1+(-i), 1-i denganarahpositif, maka CONTOH

  14. Thank You

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