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Bachelor in Economics (S.E): Manajemen
Course : Matematika Ekonomi (1506ME02)
online.uwin.ac.id
Session Topic : Introduction
Course: Matematika Ekonomi
By Handri Santoso, Ph.D
UWIN eLearning Program
Lecturer Profile
Handri Santoso, S.Si. M.Eng Dr.Eng
Head of Informatics Department
Surya University
Teaching Experience : Surya Univ. : Calculus, Basic Programming, Statistic & Probabilistic, Human Information Processing,
Computer Graphics
Yokogawa Indonesia Co.:Basic Control Engineering for technical training employees & costumers STKIP Surya: Introduction to Informatics, Basic Programming Univ. of Indonesia: Computer Science, Calculus State Polytechnic Jakarta: Embedded Systems
Education : S1 University of Indonesia Physics / Instrumentation
S2 Nagaoka Univ. of Technology, Japan Mechanical Systems Engineering / Information Science
and Control Engineering
gS3 Nagaoka Univ. of Technology, Japan Information Science and Control Engineering
Contact Detail
Handri Santoso
Email: [email protected]
Availability Hours
Wednesday : 21:00 21.30
By prior arrangement via e-mail
Course website
http://online.uwin.ac.id
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Content
Part 1 Penyampaian SAP dan Rencana Perkuliahan Part 2 Konsep Sistem Bilangan Part 3 Pengertian Model Matematika
Part1: Rencana Perkuliahan
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Course Structure
Lectures: 14 Weeks
Timetable: Lectures: Wednesday: 21:00 21:30;
Room Computer Center Room
Assessment: Midterm Test, 30 % of the mark (UTS)
Assignments in the class , 20 % of the mark
Final Test, 50% of the mark (UAS)
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Bahan-bahan perkuliahan
Material perkuliahan dapat diunduh dari blog
www.harukaedu.com
Persiapkan diri sebelum kelas
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Why do we need to mathematics ?
What programming does for you ?
It teaches you how modelling the natural phenomenon
in our small world, such as earthquake, optimization, ,
help you to solve the repeating problems, Even the ebb
and flow of such human activities as population
dynamics and economics are better viewed from
programming task. Including to identification yourself in
image processing,
Principal objective of programming is to help you from repeating the same tasks (jobs),
minimizing errors and speed up your jobs. Or
others boring jobs
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Study Tips
Tip 1: Do the homework exercises.
The homeworks are for your benefit, not the lecturer's. The exercises will train your mind and
sharpen your intuition. So do the work. It will pay
off in the end.
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Study Tips - Continue
Tip 2: Mathematics are meant to be practiced. You cannot just read it and expect to get any benefit out of
it at all. When you encounter a new concept in a mathematics, do not expect to understand it on the first reading, no matter how carefully you read it. You should
go trying to solve the problems.
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Study Tips Continue
Tip 3: Your greatest assets are in the class with you. Your classmates are in the same boat as you. Organize a study group.
Tip 4: In your group activity, take turns. Have one person get up and do a problem on the board,
explaining what he or she is doing as the problem unfolds. If the person at the board gets stuck, the others in the group should try to provide hints or ask the person at the board telling questions. If the person at the board is doing fine, the others in the group should challenge him or her. Make the problem-doer justify each step orally. If anybody in the group does not understand a step, the person at the board ought to be able to explain it to his or her satisfaction.
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SAP & Rencana Perkuliahan
Pembagian Kelompok
Check your email address
Powered by HarukaEdu.com - 1506ME02- Hal 15
SAP & Rencana Perkuliahan
Topik Perkuliahan
1. Pendahuluan
2. Jenis-Jenis Fungsi Linier
3. Applikasi Fungsi Linier dalam Ekonomi bag 1
4. Applikasi Fungsi Linier dalam Ekonomi bag 2
5. Fungsi Kuadrat
6. Applikasi Fungsi Kuadrat dalam Ekonomi bag 1
7. UTS
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SAP & Rencana Perkuliahan
Topik Perkuliahan
8. Applikasi Fungsi Kuadrat dalam Ekonomi bag 2
9. Karakteristik & Operasi Operasi Matriks
10.Menentukan Kofaktor, determinan & Balikan matriks
11.Penggunaan Matrik untuk mendapatkan solusi
persamaan linier & Applikasi matriks dalam masalah
bisnis
12.Pengertian & Jenis Deret serta Applikasi Deret dalam
Ekonomi (Matematika Keuangan)
13. Applikasi Matriks & Deret dalam Ekonomi
14. UAS
Part2: Sistem Bilangan
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Pembagian Jenis Bilangan
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Bilangan Asli, contoh: 1, 2, 3, 4, 5, 6...
Bilangan Bulat, contoh: -6,-5,-4,-3,-2,-1,0,1, 2, 3, 4, 5, 6...
Bilangan Rasional, contoh: ...,-3, -2, -3/2, -1, 0 , 1, 4/3, 2, 7/3, 3,...
Bilangan Irrasional, contoh:
Bilangan Riil, contoh:
Garis Bilangan Riil
..., 5, 2, 2, 3, 7,...
..., 5, 3/ 2, 2, 1,0,4 / 5, 2, 3,5 / 2,...
0 1 2 3 4 5 -5 -4 -3 -2 -1
3-5/2
Sistim Bilangan Riil
Edwin S.N. Kalkulus I September 2013 3/27
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Rasional
Bulat
Asli
Riil
Irrasional
Edwin S.N. Kalkulus I September 2013 4/27
Sistim Bilangan Riil
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Hubungan perbandingan antar bilangan
Tanda < melambangkan lebih kecil dari
Tanda > melambangkan lebih besar dari
Tanda < melambangkan lebih kecil dari atau sama dengan
Tanda > melambangkan lebih besar dari atau sama dengan
Tanda Ketidaksamaan
1. Jika a < b, maka a > -b
2. Jika a < b dan x > 0, maka x.a < x.b
3. Jika a < b dan x < 0, maka x.a > x.b
4. Jika a < b dan c < d, maka a+c < b+d
Sifat Perbandingan
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Operasi Bilangan 1. Kaidah Komutatif
a + b = b + a
a x b = b x a
2. Kaidah Asosiatif
(a + b) + c = a + (b + c)
(a x b) x c = a x (b x c)
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4. Kaidah Distributif
a (b + c) = ab + ac
5. Unsur Identitas
a + 0 = a -- Penjumlahan
a x 1 = a -- Perkalian
6. Kebalikan
Invers a = -a -- Penjumlahan
Invers a = 1/a --- Perkalian
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Operasi Tanda
Operasi Penjumlahan
a. (+ a) + (+b) = (+c)
b. (- a) + (- b) = (- c)
c. (+ a) + (- b) = (+ c) jika |a| > |b|
(+ a) + (- b) = (- d) jika |a| < |b|
d. (- a) + (+ b) = (+ c) jika |a| < |b|
(- a) + (+ b) = (- d) jika |a| > |b|
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Operasi Tanda
Operasi Pengurangan
a. (+ a) - (+ b) = (+ c) jika |a| > |b|
(+ a) - (+ b) = (- d) jika |a| < |b|
b. (- a) - (- b) = (+ c) jika |a| < |b|
(- a) - (- b) = (- d) jika |a| > |b|
c. (+ a) - (- b) = (+ c)
d. (- a) - (+ b) = (- c)
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Operasi Tanda
Operasi Perkalian
(+ a) x (+ b) = (+ c) (- a) x (- b) = (+ c)
(+ a) x (- b) = (- c) (- a) x (+ b) = (- c)
Operasi Pembagian
(+ a) : (+ b) = (+ c) (- a) : (- b) = (+ c)
(+ a) : (- b) = (- c) (- a) : (+ b) = (- c)
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Operasi Bilangan Pecahan
Operasi Pemadanan
Operasi Penjumlahan dan Pengurangan
Operasi Perkalian
Operasi Pembagian
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Operasi Pemadanan
:
:
x
x
cb
ca
b
a
cb
ca
b
a
Operasi Penjumlahan dan Pengurangan
Dua buah pecahan atau lebih, hanya dapat ditambahkan atau
dikurangkan apabila mereka memiliki suku pembagi yang sama
atau sejenis. Jika suku pembaginya belum sama, maka terlebih
dahulu harus disamakan sebelum pecahan-pecahan tersebut
ditambahkan dan dikurangkan.
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Operasi Perkalian
Operasi Pembagian
xy
ab
y
b
x
a
xb
ay
b
y
x
a
y
b
x
a:
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Latihan
7
2:
4
3)(
6
1
7
2
4
3)(
6
1
7
2
4
3)(
6
1
7
2
4
3)(
:
d
c
b
a
Selesaikan
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Pecahkan masalah berikut
?,5)(
?,243
)(
?,155)(
?438
2)(
:
2
3
xxd
yy
c
xxb
xa
Selesaikan
Powered by HarukaEdu.com - 1506ME02- Hal 32
online.uwin.ac.id
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Course : Matematika Ekonomi (1506ME02)