QueensCollege, CUNY
Don't use plagiarized sources. Get Your Custom Essay on
matlab for physics
Just from $13/Page
Physics Department
Physics 275/661 – Scientific Computing
Spring 2020 – Dr. David Goldberg
Page 1/5
HOMEWORK ASSIGNMENT 1
Vectors and Matrices – Back to Basics
MATLAB has many ways to deal with vectors and matrices very efficiently. However, in order to practice
foundational skills, you will write your own script to accomplish some of these basic tasks.
Vector Algebra
Due Monday, 2/3/2020, before 4PM
Magnitude of an n-Dimensional Vector
Given an n-dimensional vector:
�⃗�? = [??1,??2,??3, … ,????−1,????]
The magnitude is defined as:
|�⃗�?| = �??12 + ??22 + ??33 +⋯+ ????−12 + ????2
Write a script that defines a 1 × ?? vector, and computes its magnitude. The framework of the script can be as
follows:
1 clear
2
3 % define vector
4 v = [1, 2, 3, 4, 5];
5
6 fill in code here that computes the magnitude
7
8 % display result
9 disp([‘Magnitude of v, |v| = ‘, num2str(magV)])
Note that the code you write in after line 4 should automatically adjust for vectors of different dimension. If
you were to add an additional element to the vector in line 4, the rest of the script should not need any
modification in order to run properly. Test your script for different vectors and with other dimensions.
Scalar Product of n-Dimensional Vectors
Given two n-dimensional vectors, �⃗�?, and ??�⃗ , where:
�⃗�? = [??1,??2, … , ????]
?? = [??1,??2, … , ????]
The scalar product, �⃗�? ⋅ ??�⃗ is defined as:
�⃗�? ⋅ ??�⃗ = ??1??1 + ??2??2 + ⋯+ ????????
Write a script that computes the scalar product of two vectors. The outline can be as follows:
Physics 275/661
Spring 2020
Dr. David Goldberg
david.goldberg@qc.cuny.edu
Page 2/5
1 clear
2
3 % define vectors
4 a = [1, 2, 3, 4, 5];
5 b = [6, 7, 8, 9, 10];
6
7 fill in code here that computes the scalar product
8
9 % display result
10 disp([‘Scalar product a.b = ‘, num2str(sProd)])
Again, note that the code you write in after line 5 should automatically adjust for vectors of different
dimension. If you were to add an additional element to the vector in line 4 & 5, the rest of the script should
not need any modification in order to run properly. Test your script for different vectors and of other
dimensions.
Matrix Algebra
Due Wednesday, 2/5/2020, before 4PM
Part I: y = Ax
Suppose vector ?? is of dimension ?? × 1 and matrix ?? is of dimension ?? × ??:
?? = �
??1
??2
⋮
??
??
� ; ?? = �
??11 ⋯ ??1??
⋮ ⋱ ⋮
????1 ⋯ ??????
�
The product of ?? and ?? is defined as:
?? = ???? = �
??11 ⋯ ??1??
⋮ ⋱ ⋮
????1 ⋯ ??????
� �
??1
⋮
????
� = �
??11??1 + ??12??2 + ⋯+ ??1??????
⋮
????1??1 + ????2??2 +⋯+ ??????????
� = �
??1
⋮
????
�
Where ?? is of dimension ?? × 1. A generic element in ?? is defined by:
???? = �??????????
??
??=1
for ?? = 1, 2, . . . ,??
Write a script where given ?? and ??, computes ??.
Part II: ?? = ?? × ??
Suppose matrix ?? is of dimension ?? × ?? and matrix ?? is of dimension ?? × ??. The product of A and B, ?? × ?? is
defined as:
?? = ?? × ?? = �
??11 ⋯ ??1
??
⋮ ⋱ ⋮
????1 ⋯ ??????
� �
??11 ⋯ ??1??
⋮ ⋱ ⋮
????1 ⋯ ??????
� =
⎣
⎢
⎢
⎢
⎢
⎢
⎡�??1??????1
??
??=1
⋯ �??1????????
??
??=1
⋮ ⋱ ⋮
�??????????1
??
??=1
⋯ �????????????
??
??=1 ⎦
⎥
⎥
⎥
⎥
⎥
⎤
= �
??11 ⋯ ??1??
⋮ ⋱ ⋮
????1 ⋯ ??????
�
mailto:david.goldberg@qc.cuny.edu
Physics 275/661
Spring 2020
Dr. David Goldberg
david.goldberg@qc.cuny.edu
Page 3/5
Where ?? is of dimension ?? × 1. A generic element in ?? is defined by:
?????? = �????????????
??
??=1
for ?? = 1, 2, . . . ,???? = 1, 2, . . . ,??
Write a script where given ?? and ??, computes ??.
Rolling Dice – Winner Winner, Chicken Dinner
Rolling a Single Dice
Due: Monday, 2/3/2020, before 4PM
In a game of standard six-sided dice, the sides are labeled 1, 2…,6. Modified the script we wrote in class for
the fair two-sided coin so that it simulates a fair six-sided dice. Below is an example of what the output
should look like:
How many rolls are needed until the distributions begins to consistently look uniform? 10, 102, 103, or more?
Rolling Two Dice
Due: Wednesday, 2/5/2020, before 4PM
Suppose you roll two fair dice at the same time. The list of possible outcomes on a single roll of two dice is
shown below where, (??, ??) denotes ??, on dice 1, and ??, on dice 2:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
Table 1: All possible outcomes of a two-dice roll. The highlighted diagonals show pairs of the same sum.
mailto:david.goldberg@qc.cuny.edu
Physics 275/661
Spring 2020
Dr. David Goldberg
david.goldberg@qc.cuny.edu
Page 4/5
Part 1
• You are to write a MATLAB script that rolls two dice, and computes the sum of the numbers that
appear on the top-face of the dice.
• Repeat this for ?? rolls and plot in bar plot the frequency of each sum, for:
?? = 10, 50, 100, 1000, 104, 105, 106. If you are confident to try ?? = 107 and beyond, you may but
it will take a time to run depending of the efficiency of the code and the speed of your computer.
• Make sure your graphs are properly annotated with meaningful titles and labels.
Your results should be similar to those shown in the graphs below. The solid circles represent the “expected
outcome” based on probability. The circles were added by using the “hold on” command after plotting the
bar graph. Don’t forget to use the “hold off” command after you’re finished adding the plot.
Part 2
Explore how the statistics change if:
• One of the dice is unfair.
• Both dice are unfair, but not necessarily weighted to the same side.
What changes do you observe for these scenarios?
mailto:david.goldberg@qc.cuny.edu
Physics 275/661
Spring 2020
Dr. David Goldberg
david.goldberg@qc.cuny.edu
Page 5/5
mailto:david.goldberg@qc.cuny.edu
Vectors and Matrices – Back to Basics
Vector Algebra Due Monday, 2/3/2020, before 4PM
Magnitude of an n-Dimensional Vector
Scalar Product of n-Dimensional Vectors
Matrix Algebra Due Wednesday, 2/5/2020, before 4PM
Part I: y=Ax
Part II: ?=?×?
Rolling Dice – Winner Winner, Chicken Dinner
Rolling a Single Dice Due: Monday, 2/3/2020, before 4PM
Rolling Two Dice Due: Wednesday, 2/5/2020, before 4PM
Part 1
Part 2
