Matematika Teknik

Kode mata Kuliah MKK3102

Mata Kuliah Matematika Teknik

SKS 2

Semester 3

Hari/Jam Selasa / 19.30 - 21.00

Ruang B-02

Dosen Muhamad Iqbal ST

Email iqbal@cloud-indonesia.com/claudluciffer@gmail.com

Phone 08986452813

Riwayat Kerja

Periode Perusahaan JabatanFebruary 2000 – December 2002

CV. Wahana Karya Komputer, Engineer Staff

Technical engineer staff

September 2003 – August 2008 P.T. Byma Arsihas IT administrator staffFebruary 2011 – February 2012

PT. Firstmedia TBK. New Roll Out (NRO) Senior Project monitoring And Controlling

February 2013 – Now PT Wisnu Rahadian Jaya

Business Development

Riwayat Pendidikan

Riwayat pendidikan

S1 graduated from Electro Telecommunication at Mercubuana University jakarta

S2 Telecommunication Management at Mercubuana University

Referensi

Buku 1. Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons Inc, 2011, 10th edition

2. Stroud, KA, Engineering Mathematics, Industrial Press, 5 th edition

3. Dale Varberg, Edwin Purcell and Steve Rigdon, Calculus, Prentice Hall, 2007, 9th ed.

Penilaian

Nilai Angka Nilai Keterangan

>85 A 4 Sangat Baik

71-85 B 3 Baik

51-70 C 2 Cukup

45-50 D 1 Kurang

<45 E 0 Ulang Lagi Ya

Bobot Penilaian

No Penilaian bobot

1 Kehadiran 10.00%

2 Tugas, Quiz, keaktifan 20.00%

4 UTS 30.00%

5 UAS 40.00%

    100.00%

SISTEM ALJABAR LINEAR DAN MATRIKS

Aljabar linear adalah bidang studi matematika yang mempelajari sistem persamaan linear dan solusinya, vektor, serta transformasi linear. Matriks dan operasinya juga merupakan hal yang berkaitan erat dengan bidang aljabar linear

Mengapa Matriks?Aljabar Linear lebih mudah di selesaikan dengan

MatriksKarakterisasi atau Pemodelan suatu sistem

Notasi Matriks

Matrix Kumulatif dan Asosiatif

Perkalian Matriks

Perkalian Matriks

Hukum Asosiatif

Hukum Distributif

Contoh AplikasiMenggambarkan Matriks

Penjualan 3 macam produk (I, II, dan III) di toko pada hari kerja (senin, selasa, rabu, kamis dst)

Contoh Aplikasi (a) Nodal Incidence Matrix. The network in Fig. 1

consists of six branches (connections) and four nodes (points where two or more branches come together). One node is the reference node (grounded node, whose voltage is zero). We number the other nodes and number and direct the branches. This we do arbitrarily. The network can now be described by a matrix A= [ajk], where

A is called the nodal incidence matrix of the network Show that for the network in Fig. 155 the matrix A has the given form.

Contoh Aplikasi

Fig I

karakterisasi koneksi dalam jaringan listrik, jaringan jalan penghubung kota-kota, proses produksi dan lain-lain

Soal

Operasi Penjumlahan dan Pengurangan MatriksJika A dan B adalah matriks yang

mempunyai ordo samaPenjumlahan dan Pengurangan dari A + B

adalah matriks hasil dari penjumlahan elemen A dan B yang seletak

Matriks yang mempunyai ordo berbeda tidak dapat dijumlahkan atau dikurangkan◦a.) A + B = B + A ◦b.) A + ( B + C ) = ( A + B ) + C ◦c.) k ( A + B ) = kA + kB = ( A + B ) k , k =

skalar

Derivation from the circuit in Fig. 159 (Optional). This is the system for the unknown currents x1 = i1, x2 = i2 x1 = i1 , x3 = i3 , in the electrical network in Fig. II. To obtain it, we label the currents as shown, choosing directions arbitrarily; if a current will come out negative, this will simply mean that the current flows against the direction of our arrow. The current entering each battery will be the same as the current leaving it. The equations for the currents result from Kirchhoff’s laws:

Kirchhoff’s Current Law (KCL). At any point of a circuit, the sum of the inflowing currents equals the sumof the outflowing currents.

Kirchhoff’s Voltage Law (KVL). In any closed loop, the sum of all voltage drops equals the impressed electromotive force.

Node P gives the first equation, node Q the second, the right loop the third, and the left loop the fourth, as indicated in the figure.

Eliminasi GaussMemahami jenis solusi sistem

persamaan linier dan dapat mendapatkannya

Eliminasi GaussContoh: Diketahui persamaan

linear

Jawab: Bentuk persamaan tersebut ke dalam matriks:

Operasikan Matriks tersebut

B2-2.B1

Eliminasi Gauss

B3-2.B1

B3-3.B2

B3/8 dan B2/-1

Eliminasi Gauss

2-4.B3

B1-3.B3

B1-2.B2 (Matriks menjadi Eselon-baris tereduksi)

Derivation from the circuit in Fig. 159 (Optional). This is the system for the unknown currents x1 = i1, x2 = i2 x1 = i1 , x3 = i3 , in the electrical network in Fig. II. To obtain it, we label the currents as shown, choosing directions arbitrarily; if a current will come out negative, this will simply mean that the current flows against the direction of our arrow. The current entering each battery will be the same as the current leaving it. The equations for the currents result from Kirchhoff’s laws:

Kirchhoff’s Current Law (KCL). At any point of a circuit, the sum of the inflowing currents equals the sumof the outflowing currents.

Kirchhoff’s Voltage Law (KVL). In any closed loop, the sum of all voltage drops equals the impressed electromotive force.

Node P gives the first equation, node Q the second, the right loop the third, and the left loop the fourth, as indicated in the figure.

Solusi

Back Substitution