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Differential equations I
Given a function handle |f| an initial condition |y0| and a final time |tf|, solve numerically the differential equation dy...
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Monte-Carlo integration
Write a function that estimates a d-dimensional integral to at least 1% relative precision. Inputs: * d: positive integer....
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Simpson's Paradox - Calculate correlation coefficients for groups of data
Simpson's Paradox is a statistical phenomenon where groups of data can have a characteristic while the whole data set together h...
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Determine if x is a combination of m and n
Given positive integers x, m, and n, determine if x can be written as x = am + bn for any (non-negative) integers a and b. Your ...
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Plot Line Specifications
Create a line plot for function cos(x) where x is a vector of linearly spaced values going from 0 to input N with an increment o...
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Determine the number of odd integers in a vector
Determine the number of unique odd integers in a vector. Examples: Input x = [2 5 8 3 7 1]; Output y = 4; Inp...
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Insert zeros into vector
Insert zeros after each elements in the vector. Number of zeros is specified as the input parameter. For example: x = [1 ...
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Create an n-by-n null matrix and fill with ones certain positions
The positions will be indicated by a z-by-2 matrix. Each row in this z-by-2 matrix will have the row and column in which a 1 has...
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Change the sign of even index entries of the reversed vector
change the signs of the even index entries of the reversed vector example 1 vec = [4 -1 -2 9] ans = [9 2 -1 -4] example2...
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Create a vector whose elements depend on the previous element
The idea is to create a vector A whose elements depend on the previous element : *A(i+1) = 2*A(i)+1* *2 Inputs*: - A : The...
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We love vectorized solutions. Problem 1 : remove the row average.
Given a 2-d matrix, remove the row average from each row. Your solution MUST be vectorized. The solution will be tested for ac...
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How many Fibonacci numbers?
Find the number of unique Fibonacci numbers (don't count repeats) in a vector of positive integers. Example: x = [1 2 3 4...
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Fibonacci Decomposition
Every positive integer has a unique decomposition into nonconsecutive Fibonacci numbers f1+f2+ ... Given a positive integer n, r...
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Characterize fluid flow in a pipe as to laminar or turbulent
In fluid mechanics, characterizing the flow in a pipe is essential to predicting its behavior. The flow pattern can either be la...
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Count the number of folds needed to pack a large sheet
In a certain paper factory, large sheets of paper are being made every day. Before sending the sheets for shipment, they have to...
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Number of paths on a grid
Consider a grid formed by n vertices vertically down, and m vertices horizontally right. Your starting point is at the top lef...
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Path of least resistance
Find the length of the shortest path through the matrix from the top left to bottom right corner. You may move right, down, or d...
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Under the sea: Snell's law & total internal reflection
<https://en.wikipedia.org/wiki/Snell's_law> When a light travels from one medium to another medium, depending on the refracti...
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Reindex a vector
You are given two vectors of equal length. Vector N has numeric values (no Inf or NaN) while vector IDX has integers. Place th...
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Wind Chill Computation
On a windy day, a temperature of 15 degrees may feel colder, perhaps 7 degrees. The formula below calculates the "wind chill," i...
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Alternative Dimensions
Given a multidimensional matrix, transform the matrix so the dimensions are in the order given by variable ord. For example, giv...
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Weighted Convolution
Given two input vectors x = [x_1, x_2, ..., x_K] and y = [y_1, y_2, ..., y_K] of equal length, compute the weighted convolution ...
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Convert decimal to binary and then generate the minimum binary it can with jumbling
input is 10 --> 1010 output should be 3 --> 0011 input 23 --> 10111 output should be 15 --> 01111
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Test if two numbers have the same digits
Given two integers _x1_ and _x2_, return |true| if the numbers written with no leading zeros contain the same digits. That is, t...
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Binary Inversion
Given the unsigned 8-bit integer x, return the number y which is the binary inversion of x. For example if x is 5, y should b...
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Return fibonacci sequence do not use loop and condition
Calculate the nth Fibonacci number. Given n, return f where f = fib(n) and f(1) = 1, f(2) = 1, f(3) = 2, ... Examples: ...
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Compute the drag on a moving vehicle
We assume no rolling resistance, and the simple rule for Drag : , where is the density of the fluid (assumed at 1.2 ), is the ...
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Calculating Student Grades
The matrix grades contains raw grades for 7 students who took your course. Each row represents a different student. The first 7 ...
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