Vector Manipulation - Circles and Ellipses - Mathematics Assignment Help

Vector Manipulation Mathematics Assignment Help

Assignment Task: Basic vector manipulation: Generate 3 vectors A, B and C of 10 elements each with the following properties: Elements of A are equally spaced between 0 and 3. Elements of B are randomly chosen in the range 0 and 1. Elements of C are randomly chosen in the range 1 and 5. Generate a vector D that contains the sum of the vectors A and B. Generate another E vector that contains the element-by-element product of vectors A and C. Drawing Circles and Ellipses Create a subplot with two figures one on the top of the other. On the first figure, draw a circle of radius 5 units centered at (2 , 1). Hints: You need to generate points along the circle and then use the plot command; the circle may be parameterized as x = r cos ()+ xo, y = r sin() + yo  for 0???2? where (xo , yo ) are the coordinates of the center of the circle, r is the radius of the circle; use axis('equal') to get the same scaling on both the vertical and horizontal axes. On the second figure, draw an ellipse with semi-major and semi-minor axes of lengths a = 3 and b = 1 respectively. The ellipse is oriented along the cartesian axes. Hint: The ellipse may be parameterized as x= acos(), y = b sin(). Do not forget to label axes and two give titles to each figure. Absolute Error Write a program to evaluate e using the series (with x=1): ex=n=0xnn! Test your program as you increase the number of terms in the series. Find the relation between the absolute error and the number of terms in the series. Determine how many significant digits of precision that you obtain in your answer as a function of the number of terms in the series. How many terms are necessary to reach machine precision (~10-16)? Taylor series approximations Consider the function fx=11+x2 in the interval - 1< x < 1. Plot the function f(x) in this interval On the same figure plot the linear Taylor’s expansion around x = 0.1 On the same figure, plot the quadratic Taylor’s expansion around x = 0.1. Comment. Note: Draw the plots in different colors, insert x-label, y-label, title and a legend for the figure. Functions in Matlab: Write a function mysum with the following header: function S = mysum(v) that takes a vector as an input and returns the sum of all the elements in the vector as an output. Test the function on few sample examples of your choice. Compare your results with the built-in function sum(). Write a MATLAB function: function [E, F, b] = DecimalToBinary(d, k) which takes as input a non-zero decimal number d (both integral and fractional parts) and a positive integer k and converts d to a binary number b up to k fractional digits. Your function should output the 2 vectors E and F that represent respectively the integral and fractional parts of b, and the binary number b displayed with its sign, its integral and fractional parts. Write a MATLAB function: function [d] = AnyBaseto10(I, F, B) which takes as input two vectors I and F that represent respectively the integral and fractional parts of a number in base B, converts them to base 10 and outputs the results as the corresponding decimal number d which is displayed with its sign and its integral and fractional parts. Write a MATLAB function: function [t e f d ] = GetVectorD(v) which takes as input a octal vector v of 16 components representing a machine number in IEEE - double precision, changes it to binary and then extracts the values of the sign (t), the exponent (e) , the fractional part of the mantissa (f) and the calculates the decimal representation of the number (d). Hint: you can use the functions created earlier to convert from 8 to 10, then from 10 to 2.

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