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ENGR 121: Week 2 Lecture Notes

by: spencer.kociba

ENGR 121: Week 2 Lecture Notes ENGR 121-B

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Summary of Lecture: how to classify, categorize, modify and conduct operations using matrices and vectors in MATLAB (which stands for Matrix Laboratory)
Computation Lab I
Class Notes
Engineering, Matlab, coding, programming
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This 3 page Class Notes was uploaded by spencer.kociba on Sunday October 2, 2016. The Class Notes belongs to ENGR 121-B at Drexel University taught by in Fall 2016. Since its upload, it has received 70 views. For similar materials see Computation Lab I in Engineering and Tech at Drexel University.


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Date Created: 10/02/16
ENGR 121 B  Lecture Notes for 9/26/2016 Spencer Kociba Summary of Lecture: how to classify, categorize, modify and conduct operations using  matrices and vectors in MATLAB (which stands for Matrix Laboratory) MATRICES ● Matrix: stores a set of values of the same type ○ every value is an element ○ Matrix = m rows, n columns ● Creating Matrices ○ Ex. >> m=[ 1,4,6; 7,8,10; 2,7,15; 3,7,8] becomes a 4x3 matrix ■ 1,4,6 = 1st row, 7,8,10 = 2nd row, etc. ■ ; indicates the end of a row ■ MATLAB will show an error if your elements and the size of the matrix don’t add up ○ >>z=10*rand(3,5) becomes a 3x5 matrix with random numbers from (0,10) ○ >>z(1,2) refers to row 1, column 2 element ○ >>z(2,:) refers to all elements in row 2 ○ >>z(:,2) refers to all elements in column 2 ○ >>z([1,3], end) refers to 1st and 3rd row elements of the last  column ● Matrix Multiplication ○ Maxtrix * Matrix = New Matrix ○ In A (n x m) and B (N x M), in order to multiply A*B, m=N. To  multiply B*A, M=n ○ >>x=A*B ○ x.^(a) raises each element in matrix x by the power of a ● Matrix functions ○ zeros(n) = nxn matrix of zeros ○ zeros(n,m) = nxm matrix of zeros ○ ones(n) =  nxn matrix of ones ○ ones(n,m) = nxm matrix of ones ○ **these functions only work for 0s and 1s (there’s no  sixes(n,m) function) VECTORS ● Row vector = 1 row, n columns (1xn) ● Column vector = 1 column, n rows(nx1) ● Generating vectors ○ “Colon operator” ■ >>x=2:1:7 generates an output [2 3 4 5 6 7] ● 2=starting number (min),  1=increment, 7=ending number (max) ○ Linspace  ■ (linearly spaced vector (similar to the colon  operator) ■ >>x=linspace(­5,1,5) ● ­5=min, 1=max, 5=number of  elements in the vector (will be equally spaced between the  range of ­5 to 1) ● Accessing and modifying vectors ○ x(2) refers to element 2 in vector x ■ ****MATLAB starts counting at 1, not 0 (different from other programming languages) ○ y(1:4) refers to elements 1,2,3 and 4 of vector y ○ z([1 3 5]) refers to elements 1,3 and 5 of vector z ○ x(1)=10 changes the first element of vector x to 10 ○ In a vector x that is 1xn… ■ x(n+1)=­1 creates an additional column and  assigns ­1 to it ■ x(n+4)=6 creates an n+4th column and assigns  6 (the columns between n and n+4 are created and are assigned 0) ○ Dot product ■ <a,b,c>  ∙ <d,e,f> = ad+be+cf ■ IF YOU ARE DOING AN ELEMENT BY  ELEMENT MULTIPLICATION… ● Z.*Y ○ The period tells  MATLAB to perform operation element by element GENERATING PLOTS ● Plots are professional looking, great for inserting into data reports, research  papers, design briefs, etc. ● Commands ○ >>x=­pi:2*pi/20:pi where the range is (­pi, pi) with increments  of 2*pi/20 ○ >>y=sin(x) ○ >>figure ←this just gives you a blank canvas for plotting (optional) ○ >>plot(x,y, ‘b+’) ←b+ means “symbols on plot are blue ‘+’s” ○ ● Plotting Multiple functions on the same plot ○ >>x=0:2*pi/128:2pi  ○ >>y=sin(x) ○ >>z=cos(x) ○ >>plot(x,y, ‘ro’) ○ >>hold on ← This holds onto the same canvas to do one plot ○ >>plot(x,z, ‘b+’) ■ Extra add ons ■ legend(‘sin’, ‘cos’)   gives plot a legend ■ xlabel(‘x’)   gives x axis label a label ■ ylabel(‘cos or sin’)   gives y axis label a label ■ title(‘_____’)    gives plot a title ○


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