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., M.CSs.budidarma@ub.ac.id

WIBISONO SUKMO WARDHONO, ST, MTwibiwardhono@ub.ac.id

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

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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