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MFIN704W21 binary

创建日期：2024-04-03 15:00:37

所属分类：数学mathematics

标签： MFIN704W21

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MFIN704W21
The following are some practice questions to help you prepare for the midterm.
1) Convert 625.875 into binary.
2) Convert -27.5625 into binary. Calculate the machine epsilon assuming 64-bit floating points
numbers.
3) Use the Newton-Raphson Method to find the root of () = − − with an initial guess of x=0
4) Let () = ln⁡(). Approximate using Second-Order Taylor approximation at = 2 with a step
size of ℎ = 0.5
5) Find the first order Taylor Approximation of () = −0.14 − 0.153 − 0.52 − 0.25 + 1.2 at
= 0.5 with a step size of ℎ = {1, 0.5, 0.25}.
6) Consider Function 3 − 2 + 4, at x=0 find the forward, backward, center difference with
h=0.25
7) Perform LU decomposition, and verify LU=A by hand on (normalization/scaling not required)
[
8 2 1
3 7 2
2 3 9
]
8) Using backward difference formula, find the missing values
() ′()
0.5 1.9
0.6 2.2

9) Explicit (by hand)
a. = [0,10], Δ = 2, Δ = 0.1
b. Boundary and Initial conditions
i. All interior points zero ( = 2,4,6,8, = 0) = 0
ii. Edge points ( = 0, ) = 100, ( = 10, ) = 50 ∀
c. Solve for unknowns at t=0.1 and t=0.2
10) Implicit (by hand)
a. Write out a row or two for the matrix that is the system of equations for the Black-
Scholes Model
11) Write-out pseudo code for the bisection method
12) Name and describe three (3) sources of error we covered in class.
13) Represent 25.375 in binary (in form 11111111.1111)
14) Find the internal rate of return (IRR) of the following cash flows using Newton’s Method with an
initial guess of r=0.325. Verify your result, should be within +/- $1 after one iteration, stop if it is.
= −$500 +
$300
1 +
+
$450
(1 + )2

15) Find the center difference approximation of the derivative for () = 2 − 2 + 1 at = 2 for
ℎ = 1
16) Using the result from Question 4 for the first derivative, find the first order Taylor
Approximation at = 2 with ℎ = 2. If (4) = 9, what is the relative error?
17) Find the L and U matrix for the following:
[
2 4
1 8
]

MFIN704W21 Midterm Prep M. Milewski
18) Solve for the unknown using the explicit method for PDE
= 0 = 0.5
+1 = 11 9 10
= 10 5
−1 = 9 4 5

19) Answer the following questions based on this code snippet:
A = [];
n=1000;
for i =1:n
A(i) = 2^i;
end
mean = 0
for j = n:-1:1 % going backwards through the array
mean = mean + A(j);
end
mean = mean/n;
B = [];
for k = 1:n
B(k) = A(i) – mean
end
a. What does the code do?
b. What numerical issues can be encountered? Be specific.

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关键词一关键词二关键词三关键词四关键词五和法规和的发更好的风格和 ECON 615 FINC 612 CSC148 COMP 639 ACCT 203 ACCT 211 PSYC 101 MTH2009 COMP52315 PSYCO 432 statistics MATH4063 11 xxx 1 MA1MSP MAST30028 MATH3888 CS341 EEE30002 ES2F5 MCD4160 CC0933 ECON 1101 MCHM3001 CHEM3118 COMMGMT 2511 COMP41280 STAT 631 24T1 IRE379 SENG365 ECON433 FIT3139 MATH4602 LING5621M FINS5516 ECON3208 MN2177 L2 SM EEET1415 Finance DS4023 COMP3004 7CCSMRTS K1S5B6 Stat230 CSCI4211 CSI2132 ECON30130 MAS6100 ENVS222 COM2107 INFO1112 STAT 4004 FIT2100 comp2022 COMP4691 Physics 307 Econ 659 probability CSCI316 fir29 CSCI203 COMP3160 COMP6714 INFO1113 Physics 7B Physics Photonics S203031 STAT2005 COMP90015 CSCI 2110 CSCC46 Information CSC477 COMP4650 Statistical COMP 346 COMP1017 ELEC340 MATH1007 Programming function STAT 244 CS 134 Java cse13s Math 108A FW20 ECON3389 CSE 130 Science 331 COMP9020 engineering COSC 445 CSE 5523 GAME2012 visualization MATH 235 Math 370 CSC343 COGS 108 EE524 COMP10200 STAT 416 3FK4 MSCI 311 ECON6113 ACC40700 EMESTER1 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COMP532 MAS275 COMP5318 COMP4002 FIT5086 MAST20004 FIT3152 FIT5129 CIS2380 CS521 COMP 1005 EECMS CITS5501 ECE 462 ECON 6002 ENG 4051 CSC 648 CMT654 MECHENG 713 PHYS1002 AMME 2000 FP0060 DDES3200 MECHENG 743 BINF90002 FIT2081 ISYS90081 ELECTENG 722 BUS 360 ECOS3010 BUS2810 ETF2100 ENG2048 STAT5002 COMP2017 CEME 2003 MATS3004 COMP9319 PHYS1001 COMP5349 AMME2261 COMP-381 FIT3173 COSC2757 ENG4025 QBUS2820 COMP9414 MATH2021 EOSC118 MFIN6690 PMATH 321 CSE-141L MATH575A COMPSCI5002 COMP1511 management comp2123 FINS3616 COMP 3331 COMS30034 DTSC 71 AcF 702 AcF702 DTSC71 MAT021 ELE8083 ACFI213 EG-127J 127J FIT5163 FIT2001 ELE00113M CMT310 CS 245 ENGL 1101 MTH6115 EE497 CS 325 Math 124A MTH5130 MBA502 MGT 5380 ARCH 1261 F033800 20LLP109 ELE4009 FINANCIAL COMP3331 Computer ECE4179 20T3 COMP9311 COMP9311 UNSW MFIN6210 ACCT 5930 EE590 ENG2029 ECO100 SIT315 ACCT3610 COMP3600 STK2100 FIT2004 COMP30020 ACTL1101 Stat 101B BANA 200 COSC2473 ENGG1400 AI COMP90043 MMF 1914H PHYS 127 CS584 CIVL2010 ECMT2150 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