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New head garb has been ordered

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Presentation on theme: "New head garb has been ordered"— Presentation transcript:

1 New head garb has been ordered

2 INTRODUCTION, APPROXIMATION AND ERRORS

3 This rapper’s name is Tauheed Epps 2 Chainz Tity Boi Kendrick Lamar

4 01.01 INTRODUCTION

5 To find velocity from location vs time data of the body, the mathematical procedure used is
Differentiation Integration

6 The form of the exact solution to
is

7 Given the f (x) vs x curve, and the magnitude of the areas as shown, the value of
y x a 5 7 2 b c -2 2 12 Cannot be determined

8 A steel cylindrical shaft at room temperature is immersed in a dry-ice/alcohol bath. A layman estimates the reduction in diameter by using Less More Same while using the value of the thermal expansion coefficient at -108oF. Seeing the graph below, the magnitude of contraction you as a USF educated engineer would calculate would be ______________than the layman’s estimate.

9 END

10 01.02 MEASURING ERRORS

11 The number of significant digits in 2350 is
4 5 3 or 4

12 The absolute relative approximate error in an iterative process at the end of the tenth iteration is 0.007%. The least number of significant digits correct in the answer is 2 3 4 5

13 Three significant digits are expected to be correct after an iterative process. The pre-specified tolerance in this case needs to be less than or equal to 0.5% 0.05% 0.005% 0.0005%

14 01.03 SOURCES OF ERROR

15 Round-off error Truncation error
The error caused by representing numbers such as 1/3 approximately is called Round-off error Truncation error

16 The number 6.749832 with 3 significant digits with rounding is
6.75 6.749 6.750

17 Truncation Error Round off Error
The error caused by using only a few terms of the Maclaurin series to calculate ex results mostly in Truncation Error Round off Error

18 The number 6.749832 with 3 significant digits with chopping is
6.75 6.749 6.750

19 END

20 01.04 BINARY REPRESENTATION

21 (8)10=(?)2 1110 1011 0100 1000

22 (01011)2 =(?)10 7 11 15 22

23 01.05 FLOATING POINT REPRESENTATION

24 Relative absolute true error
Using fixed point representation in a computer puts a upper bound on the ________________ in representing a number. Absolute true error Relative absolute true error

25 Relative absolute true error
Using floating point representation in a computer puts a upper bound on the ________________ in representing a number. Absolute true error Relative absolute true error

26 2-bits used for exponent
The absolute relative true error in a floating point representation using chopping for a number is less than Machine epsilon 2-bits used for exponent

27 add 7 subtract 7 add 15 subtract 15
Five bits are used for the biased exponent. To convert a biased exponent to an unbiased exponent, you would add 7 subtract 7 add 15 subtract 15

28 END


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