A brief introduction to MATLAB for students of Science, Engineering and Mathematics Jorge Lemagne Bindura University

Summary IntroductionGetting started with MATLABIllustration in Math courses 2

What is MATLAB? MATLAB is a high-level language and interactive environment for numerical computation, visualization, and programming (MathWorks, 2013). 3

Some applications of MATLAB Signal processing and communicationsImage and video processingControl systemsTest and measurementComputational financeComputational biology 4

Widely used More than a million engineers and scientists in industry and academy use MATLAB, a language of technical computing. 5

Also an aid for mathematics students Moreover, MATLAB is a teaching and learning aid for mathematics students. It has been integrated as a supplement to the traditional classroom teaching and learning. For example, at University of Ha'il, Saudi Arabia, a study was made on engineering mathematics students. 6

Benefits The use of the software has enhanced students' conceptual understanding despite their weak mathematical skills. It has been noticed that students' attitudes have been positive and their performance in the course has improved 7

For mathematics courses Students taking some mathematics courses are expected to acquire a basic working knowledge of MATLAB (University of Utah). MATLAB may be used to help complete some of the homework assignments. Also for the completion of designated computer assignments (University of Utah). 8

Some requirements Students need to have access to a computer with MATLAB installed (Massachusetts Institute of Technology, 2015). They should have a way to access their files whenever they start working. In particular, they need to have access to MATLAB outside of class hours. 9

A two hours introduction In the bibliography there exist several good tutorials on MATLAB. However, a student would need considerable time to assimilate any of them, and so would a lecturer for the explanation. The brief introduction that is presented in this contribution can be explained in two hours and has been exposed as a lecture by the author at Bindura University. 10

In a computer laboratory Preferably, this lecture should be given in a computer laboratory so that the students can verify in practice all explanations. After learning this brief introduction the students will be able to solve simple problems, or to study a tutorial or to pass a course on MATLAB more easily. 11

Summary (2)  Introduction  Getting started with MATLAB Illustration in Math courses 12

GETTING STARTED WITH MATLAB The name MATLAB stands for MATrix LABoratory. The basic data element in MATLAB is an array that does not require dimensioning. 13

Much faster This allows you to solve many technical computing problems, especially those with matrix and vector formulations, in a fraction of the time it would take to write a program in a scalar non-interactive language such as C or FORTRAN. 14

Starting MATLAB On Windows platforms, to start MATLAB, double click the MATLAB shortcut icon on your Windows desktop. After a short lapse, you will see something like this: 15

Command Window For the time being we only need this window, the Command Window. If there are others open, we can close them. 16

Vectors Let us start to use the Command Window, manipulating some vectors (i.e. arrays of one dimension). 17

You can work with entire arrays Where other programming languages work with numbers one at a time, MATLAB allows you to work with entire arrays quickly and easily. 18

To enter arrays We can enter arrays into MATLAB in several different ways. an explicit list of elements One of them is by entering an explicit list of elements. 19

Entering vectors: Example At the command line, after MATLAB prompt “>>”, type this statement: >> a = [ ]; >> This instruction or statement assigns the vector [ ] to the variable “a”. 20

An assignment operator >> a = [ ]; “=” does not have the same meaning as in Mathematics. an assignment operator In this case, it is not a relational operator but an assignment operator. 21

Workspace Workspace Once you have entered the array, it is automatically remembered in the MATLAB Workspace: You can refer to the array, simply by its name, in this case “a”. 22

The Colon Operator The colon “:” is one of the most important MATLAB operators. It occurs in several different forms: The expression 1:7 is a row vector containing the integers from 1 to

For non-unit spacing Specify an increment. >> 0:pi/4:pi ans = ans Note: When you do not specify an output variable, MATLAB uses the variable “ans”, short for answer, to store the results of your calculation. 24

The Colon Operator: Another example 25

Sin function between 0 and 2π and step 0.1 (1) 26

Hundreds of available functions MATLAB has hundreds of available functions. To display documentation of one, for example, sin, type >> doc sin 27

M files M files M files are text files containing MATLAB code. To create an M file we can use the MATLAB Editor or another text editor. 28

MATLAB Editor (1) 29

The same statements The M file will contain the same statements you would type at the MATLAB command line. Save the file under a name that ends in “.m”. 30

MATLAB Editor (Rev) 31

Plotting “sin” with specified step 32

Content of M file % This very simple program plots sin(x) for % different values between 0 and 2*pi. Answer = inputdlg(‘Step size=‘); Step = str2double(Answer); x = 0:Step:2*pi; y = sin(x); plot(x,y,'*') 33

Input dialog box 34

Content of M file (Rev) % This very simple program plots sin(x) for % different values between 0 and 2*pi. Answer = inputdlg(‘Step size=‘); Step = str2double(Answer); x = 0:Step:2*pi; y = sin(x); plot(x,y,'*') 35

Sin function between 0 and 2π and step 0.1 (Rev) 36

Script script The M file corresponding to the preceding program is called script. Scripts are the simplest kind of M files because they have no input or output arguments. 37

Matrices and Subscripts Let us create the matrix >> A = [ ]; >> Dürer's magic square This table is known as Dürer's magic square. 38

Dürer Albrecht Dürer (1471–1528) was a painter, printmaker and theorist of the German Renaissance. Dürer’s Self-Portrait at 28 (a), Melencolia I (b) and Detail of Melencolia I (c) 39

Dürer's magic square [ ] Sum is 34 Sum is 34 by: Rows Columns Diagonals Quadrants In the center four squares In the corner squares etc. 40

Sums by columns A = [ ] Let us verify a few of these features. The first instruction to try is >> sum(A) ans = by columns These are the sums by columns. 41

Sums by rows A = [ ] by rows To obtain the sums by rows, we consider first A’, the conjugate transpose of A. Then, we type: >> sum(A')' ans = 34 42

Sum on the main diagonal A = [ ] on the main diagonal The sum of the elements on the main diagonal is obtained with “sum” and “diag” functions: >> sum(diag(A)) ans = 34 43

Subscripts with colons Subscript expressions involving colons refer to portions of a matrix. For example, sum(A(:, 4)) computes the sum of the elements in the fourth column of A: >> sum(A(:, 4)) ans = 34 44

Another way for creating matrices On the example of order-4 magic square, we created a matrix by entering an explicit list of elements. A = [ ]; Another way is by “load” command. See paper. 45

Summary (3)  Introduction  Getting started with MATLAB  Illustration in Math courses 46

ILLUSTRATION IN MATH COURSES The author of this paper is introducing MATLAB in his courses. Here are two examples: 47

Multivariate Methods The following table shows the heights (in inches) and the weights (in pounds) for 10 employees of a firm (Taken from Makridakis & Wheelwright (1983)) Examine the extent of the relationship between the two measures. 48

To solve Height_Weight problem (1) Create Create an M file with the preceding table Save Save it as Height_Weight.m (for example). In the Command Window, type: >> load Height_Weight.m >> mean(Height_Weight) ans = >> % These are the corresponding means. 49

To solve Height_Weight problem (2) >> cov(Height_Weight) ans = >> % This is the covariance matrix. 50

To solve Height_Weight problem (3) >> corrcoef(Height_Weight) ans = >> % This is the correlation coefficient matrix. >> The sample is not large, but we might say there is quite a strong relationship between the two variables. “mean”, “cov” and “corrcoef” are only three of the many functions that can be used in MATLAB. 51

Optimization 52

Graphical solution of Optimization problem Therefore, the solution is z=8. 53

REFERENCES (1) Majid, M.A., Huneiti, Z.A., Al-Naafa, M.A. & Balachandran, W., (2012), A study of the effects of using MATLAB as a pedagogical tool for engineering mathematics students, Interactive Collaborative Learning (ICL) 15th International Conference on,

REFERENCES (2) Makridakis, S., & Wheelwright, S (1983), Forecasting methods and Applications, 2nd edition, New York Wiley Massachusetts Institute of Technology (2015), Syllabus, MIT OpenCourseWare, s997-introduction-to-matlab-programming- fall-2011/Syllabus/ s997-introduction-to-matlab-programming- fall-2011/Syllabus/ 55

REFERENCES (3) MathWorks, The, Inc., MATLAB R2013a University of Utah, The, Department of Mathematics, (n. d.), MATLAB Information,

REFERENCES (4) Wikimedia Foundation, Inc., (2015), Magic square, Wikipedia, Wikimedia Foundation, Inc. York University (n. d.), MATLAB LESSON 1,