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Sample Test 3

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UCF

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Sample Test 3 ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff

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Project #1 Math lab

Project #1 Math lab

You need to include an
introduction, primary discussion, and summary. Include graphs, tables, and images, as necessary,
to improve the clarity of your discussion. Your project needs to be both correct and well written.
Communication remains a critical component of our modern, technological society.
A few notes about format: you MUST use MS Word for your project and use Equation Editor for all
mathematical symbols, e.g. 𝑧(𝑡) = sin(𝑡) +
1
ln(𝑡)
. Problem 1: Consider the following Initial Value Problem (IVP) where 𝑦 is the dependent variable
and 𝑡 is the independent variable:
𝑦
′ = sin(𝑡) ∗ (1 − 𝑦) with 𝑦(0) = 𝑦0 and 𝑡 ≥ 0
Note: the analytic solution for this IVP is:
𝑦(𝑡) = 1 + (𝑦0 − 1)𝑒
cos(𝑡)−1Part 1A: Approximate the solution to the IVP using Euler’s method with the following conditions:
Initial condition 𝑦0 = −
1
2
; time step ℎ =
1
16
; and time interval 𝑡 ∈ [0,20]
+ Derive the recursive formula for Euler’s method applied to this IVP
+ Plot the Euler’s method approximation
+ Plot the absolute error between the approximation and the exact solution using a semi-log plot Part 1B: Approximate the solution to the IVP using the Improved Euler’s method with the following
conditions: Initial condition 𝑦0 = −
1
2
; time step ℎ =
1
16
; and time interval 𝑡 ∈ [0,20]
+ Derive the recursive formula for the Improved Euler’s method applied to this IVP
+ Plot the Improved Euler’s method approximation
+ Plot the absolute error between the approximation and the exact solution using a semilog plot Part 1C: Approximate the solution to the IVP using the RK4 method with the following conditions:
Initial condition 𝑦0 = −
1
2
; time step ℎ =
1
16
; and time interval 𝑡 ∈ [0,20]
+ Plot the RK4 method approximation
+ Plot the absolute error between the approximation and the exact solution using a semilog plotProblem 2: Consider the following Initial Value Problem (IVP) where 𝑦(𝑡) is the dependent
function: 𝑦
′ = 𝑦 − 𝑦
2 + 1.14 cos(𝑒
𝑡/2
) with 𝑦(0) = 𝑦0 and 𝑡 ≥ 0Part 2A: Approximate the solution to the IVP using the Improved Euler’s method with the following
conditions: Initial condition 𝑦0 = 1; time steps ℎ =
1
8
,
1
16
,
1
32
,
1
64
; and time interval 𝑡 ∈ [0,20]Plot the Improved Euler’s method approximation for all 4 time steps Discuss the results of these approximations Part 2B: Approximate the solution to the IVP using the RK4 method with the following conditions: Initial condition 𝑦0 = 1; time steps ℎ =
1
8
,
1
16
,
1
32
,
1
64
; and time interval 𝑡 ∈ [0,20]Plot the RK4 approximation for all 4 time stepsDiscuss the results of these approximations

Advanced Quantitative Method

Advanced Quantitative Method

Hello tutor,for this
assignment as I head some friend we need o use excel and I attached an
example of previous work in case you need them. I have took screenshots of the three parts and the table too.This
is a homework assignment and the good thing there is no limit for
attempting. Like in case anything not correct we can adjust it.Yet, please if you need the lecture of this class let me knowThank you and please see attached.

homework with course for computer method

homework with course for computer method

For each question, describe your methods in detail, using
equations/illustrations/graphs as needed. Each response should take
no more than two pages and should be submitted as a printed
document as well as uploaded to Blackboard as a PDF file. Don’t forget to include a new question of your own for consideration on
future HWs and class discussions.

program a given floating point binary number to its decimal

program a given floating point binary number to its decimal

There are three questions. The second question and third question must be used by Matlab. Thank you.1. (i) What is a floating point number? Why is it “floating point”? (ii) Explain the use of the mantissa and exponent for its representation on a computer. Why is it
necessary? (iii) Explain the terms “normalization”, “hidden bit” and “bias” in the context of floating point
number representation2. Write a program that converts a given floating point binary number with a 24-bit normalized
mantissa and an 8-bit exponent to its decimal (i.e. base 10) equivalent. For the mantissa, use the
representation that has a hidden bit, and for the exponent use a bias of 127 instead of a sign bit. Of
course, you need to take care of negative numbers in the mantissa also. Use your program to answer
the following questions: (a) Mantissa: 11110010 11000101 01101010, exponent: 01011000. What is the base-10 number? (b) What is the largest number (in base 10) the system can represent? (c) What is the smallest non-zero positive base-10 number the system can represent? (d) What is the smallest difference between two such numbers? Give your answer in base 10. (e) How many significant base-10 digits can we trust using such a representation? The third question was in the attachment.

MCD4140 Monash College Computing for Engineers Eulers Method Math Laboratory

MCD4140 Monash College Computing for Engineers Eulers Method Math Laboratory

Background The van der Pol equation is a 2nd‐order ODE that describes self‐sustaining oscillations in which energy is withdrawn from large oscillations and fed into the small oscillations. This equation typically models electronic circuits containing vacuum tubes. The van der Pol equation is: d𝑦 d𝑡𝜇1𝑦d𝑦 d𝑡𝑦0 where 𝑦 represents the position coordinate, 𝑡 is time, and 𝜇 is a damping coefficient.

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