Engineering foundation course at NUST.

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

2. Mathematics can not be learnt like other subjects
MATHISNOTDIFFICULTBUTDIFFERENT
This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

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

4. TOUGH
TEACHERS
WEAK
FOUNDATION
DIFFERENT
SUBJECT
LIMITED
TIME
DIFFERENT
SKILLS
This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

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

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

7. 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

8. YOU CAN’T
H AT E M AT H E M AT I C S
&
UNDERSTAND IT
AT THE SAME TIMEThis Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

9. 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

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

11. 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

12. AESTHETICS
FUN
POWER
LEAD
NEED
This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

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

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

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

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

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

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

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

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

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

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

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

24. KNOWN
UNKNOWN
This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

25. A LT E R N AT E
ANY SIMILAR TOOLS
I D E N T I F I C AT I O N
WHAT IS THIS
WHY IT WAS MADE
P U R P O S E
H I S TO RY
WHO MADE IT
P R O F E S S I O N WHO ARE THE USERS
P R A C T I C E
HOW TO USE THIS
This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

26. MATHEMATICS
IS LIKE AN
“INTELLECTUAL TOOL
BOX”
ENGINEERS NORMALLY USE THIS TO
COMPUTE
CALCULATE
ESTIMATE
PREDICT
ANALYZE
FIND
DETERMINE ETC
CALCULUS
This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

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

28. PURPOSE
CUTTING
JOINING
This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

29. REAL LIFE
UNKNOWNS
ACTUALWORLD
INPUTS
FIND THESE
UNKNOWNS
MINDWORLD
OUTPUTS
This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

30. C O M M U N I C AT I O N
This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

31. 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

32. A S A L A N G U A G E
HIGHLY
OBJECTIVE
This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

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

34. 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

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

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

37. 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

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

39. 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 TO D E S C E N D TO
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

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

41. M U C HM A N Y
This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

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

43. 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

44. 0 10 20
MINS
1
2
FLOWRATE
2.5
This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

45. 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

46. 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 ANALYZING
GROUPS, ITEMS, PARTS DERIVE UNKNOWNS FROM
KNOWNS
KIND, MANNER, RATE
ETC
PATTERN,
OCCURRENCES
CRITERION, PURPOSE FORMULAS HELP MORE VISUAL REPRESENTATION
HELPS MORE
VISUAL
REPRESENTATION
HELPS MORE
NUMBERS,
FRACTIONS, SETS
FORMULAS, EQUATIONS FUNCTIONS TABULATED DATA
AIRTHMETICS
GEOMETRY
ALGEBRA
TRIGNOMETRY
CALCULUS
LINEAR ALGEBRA STATISTICSThis Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

47. MATHEMATICS
IMAGINATION
VISUALIZATION
THINKING
MATCHING
COMPARING
REPRESENTATION ETC
REUSEABLE
FORMULAS
DISCOVERIES
This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

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

49. 1 2 3 4 5 6 7
1 2 3 4 5 6 7
ODD
&
EVEN
This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

50. MUSCLE
POWER
C O N C R E T E
U N D E R S TA N D I N G PURPOSE
This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

51. PURPOSE
𝒆 𝒙
= 𝟏 +
𝒙
𝟏!
+
𝒙 𝟐
𝟐!
+
This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

52. DOES THIS MAKE SENSE ?
This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

53. WHAT ABOUT THIS?
This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar

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

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

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

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

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

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

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

61. 61
Q&A
This Work is the Property of Engr Dr Qaiser Hameed Malik and Engr Naveed Zafar