This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

Mathematics can not be learnt like other subjects

MA

TH

IS N

OT

DIFFIC

ULT

BU

T D

IFFER

EN

T

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

TOUGHTEACHERS

WEAKFOUNDATION

DIFFERENTSUBJECT

LIMITEDTIME

DIFFERENT SKILLS

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

MATH IS NOT FOR ME

I AM NOT FOR MATH

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

YOU CAN’T

H AT E M AT H E M AT I C S&

U N D E R S TA N D I T AT THE SAME TIMEThis Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

6 0 , 0 0 0 / 7 0 0 0 Y E A R S

Almost true …

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

ARITHMATIC ALGEBRA

CALCULATIONSCOMPUTING

MEASUREMENT

ANALYSIS

COUNTING

CALCULUS STATISTICS

S O C I A L D E V E L O P M E N T

NUMBERS

P R E H I S T O R I C I N F O R M A T I O NA G R I C U L T U R A L I N D U S T R I A L

GEO SPACE, SHAPES

LIVING HUNTING TRADING GOVERNANCE EMPIRESTRAVELLING RELIGION WAR INDUSTRY INFORMATION

FREQUENCY RATEANGLE CHANGEREPRESENTATION

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

AESTHETICSFUN

POWER LEAD

NEED

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

KNOWN

UNKNOWN

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

A LT E R N AT E

A N Y S I M I L A R T O O L S

I D E N T I F I C AT I O N

W H AT I S T H I S

W H Y I T W A S M A D E

P U R P O S E

H I S T O R Y

W H O M A D E I TP R O F E S S I O N W H O A R E T H E U S E R S

P R A C T I C E

H O W T O U S E T H I S

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

MATHEMATICS IS LIKE AN

“INTELLECTUAL TOOL BOX”

ENGINEERS NORMALLY USE THIS TO COMPUTECALCULATEESTIMATEPREDICTANALYZEFINDDETERMINE ETC

CALCULUS

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

PURPOSE

CUTTING

JOINING

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

REAL LIFE UNKNOWNS

AC

TU

AL W

OR

LD

INPUTS

FIND THESEUNKNOWNS

MIN

D W

OR

LD

OUTPUTS

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

C O M M U N I C A T I O N

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

O P I N I O N I S

A D D E D

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

A S A L A N G U A G EHIGHLY

OBJECTIVE

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

THIS SYMBOL ONLY REPRESENTS

HAPPENING OF SOMETHING“VERY RAPIDLY”

X

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

ex

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

M U C H

W I L LW A S

M A N Y

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

SEE THROUGH MATH

F O R B E T T E R U N D E R S TA N D I N G O N E H A S T O D E S C E N D T O

T H E A P P R O P R I AT E L AY E R

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

M U C HM A N Y

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

M U C H

W I L L

M A Y

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

0 10 20

MINS

1

2

FLOW

RA

TE

2.5

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

M U C H

W I L LW A S

M A N Y

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

MANY MUCH WILL WAS

( THOUGH IN-SEPERABLE)MANY- MUCH- WILL – WAS

KINDS, TYPES, COST, TIME, CAPACITY, DEPRECIATION ETC

GROW, BEHAVE, PERFORM, EMERGE, RESPOND, ENTAIL ETC

PERFORMANCE,CONFORMANCE ETC

ITEM (ENTITY)NOUN

VALUE (RELATION) PARAMETER (CHANGE)PROCESS

DATA (OCCURRED)

PRESENT PRESENT FUTURE PAST

IDENTIFICATION CALCULATION PREDICTIONS ANALYSIS

LANGUAGE, CONFLICT AVOIDANCE MECHANISM

ESTIMATING, CALCULATING FOR CONFLICT AVOIDANCE

ESTIMATING ,JUDGING, ASSESSING, PLANNING, KNOWING

JUDGING, FORECASTING

COUNTING COMPUTING DETERMINING ANALYZINGGROUPS, ITEMS, PARTS DERIVE UNKNOWNS FROM

KNOWNSKIND, MANNER, RATE

ETCPATTERN,

OCCURRENCES

CRITERION, PURPOSE FORMULAS HELP MORE VISUAL REPRESENTATION HELPS MORE

VISUALREPRESENTATION

HELPS MORE

NUMBERS, FRACTIONS, SETS

FORMULAS, EQUATIONS FUNCTIONS TABULATED DATA

AIRTHMETICSGEOMETRY

ALGEBRATRIGNOMETRY

CALCULUSLINEAR ALGEBRA

PROBABILITYSTATISTICSThis Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

MATHEMATICS

IMAGINATIONVISUALIZATION

THINKINGMATCHING

COMPARINGREPRESENTATION ETC

REUSEABLEFORMULAS

DISCOVERIES

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

1 2 3 4 5 6 7

1 2 3 4 5 6 7

O D D &

E V E N

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

MUSCLE POWER

C O N C R E T E U N D E R S T A N D I N G PURPOSE

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

PURPOSE

𝒆𝒙 = 𝟏 +𝒙

𝟏!+𝒙𝟐

𝟐!+

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

DOES THIS MAKE SENSE ?

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

WHAT ABOUT THIS?

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

60This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

61

Q&A

This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar