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all numbers have a pattern. all patterns contain a message. all messages reveal a destiny. (number 23 movies). TIF 4102. calculus. any question?. Lecturer. BUDI DARMA SETIAWAN , S.Kom., M.CS s.budidarma @ub.ac.id WIBISONO SUKMO WARDHONO , ST, MT wibiwardhono @ub.ac.id. WIBI. - PowerPoint PPT Presentation
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Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
all numbers have a pattern
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
all patterns contain a message
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
all messages reveal a destiny (number23 movies)
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
calculus
TIF4102
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
any question?
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
BUDI DARMA SETIAWAN, S.Kom., [email protected]
WIBISONO SUKMO WARDHONO, ST, [email protected]
Lecturer
BISONWIBI
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Purcell, E.J. & D. Valberg, Calculus with Analytic Geometry
Anton, H., Calculus with Analytic Geometry, 5th ed. John Wiley & Sons
Varberg, Dale; Edwin J. Purcell; Steven E. Rigdon. Calculus, 8th Edition, Prentice Hall Inc, 2000
Refference
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Complex NumberTrigonometri
VectorSingle variable function
LimitSingle variable
differentialSingle variable integral
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
1
First sight ...Calculus Introduction
Complex NumberTrigonometri-1
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
2
Trigonometri-2QUIZ-1
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Concept of Number1, 2, 3, 4, 5,
6, ...naturalnumberRound
edRational
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Integer
..., -3, -2, -1, 0, 1, 2, 3, ... roundednum
berHow about the precision?
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Real Number
3/4, -7/8, 21/5, 19/-2, 16/2, -17/1
rational
Every number formed by m/nHow about 5/0 or -9/0 ?
34
UNDEFINED
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Real Number
3/4, -7/8, 21/5, 19/-2, 16/2, -17/1
rational
Every number formed by m/n
for n ¹ 0
34
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Real Number
Ö2, Ö5, 3Ö7, pirrational3
4
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
x2 – 6x + 9
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
x2 + 2x - 15
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
a
cabbxx
.2
..4,
2
21
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
x2 + 2x + 5
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
f
f
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
x = 4 + j6
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
x = 3 – j8x = -5x = - 6 – j10x = j12
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
x = a + jb
θ
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
x = 3 – j8
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
x1 = a + jbx2 = c + jdx1+x2=(a+c)
+j(b+d)
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
(x-a)(x-b)(x-c) ... (x-z)
= ?dsds(x-d)(x-e)(x-f) ... (x-y)(x-x)0
0