1. Dr. Jie Zou PHY 33201 Welcome to PHY 3320 Computational Methods in Physics and Engineering

2. Dr. Jie Zou PHY 33202 Introduction to MATLAB: Fundamentals 1 Outline The MATLAB environment Assignment Mathematical operations Use of built-in functions Graphics 1 Applied Numerical Methods with MATLAB for Engineers and Scientists, 2 nd ed., Steven C. Chapra, McGraw Hill, 2008, Ch. 2.

3. Dr. Jie Zou PHY 33203 The MATLAB environment Start MATLAB, command window, command prompt >> You can type in commands line by line after >>; for each command, you get a result. Example: Type in the following and hit return >> 55 - 16  MATLAB will display ans = 39 MATLAB assigns the result to ans whenever you do not explicitly assign the calculation to a variable of your own choosing. Now, type in >> ans + 11  What do you think MATLAB will display?

4. Dr. Jie Zou PHY 33204 Assignment Assign values to variable names: scalars, arrays, vectors, and matrices. Scalars: A scalar is a single value. EnterThen enter >> a = 4  >> a = 4, A = 6;  a = 4 4 Notice Echo Printing if “,” is used; echo printing is suppressed when “;” is used. EnterThen enter >> a  >> A  Note that names are Case-Sensitive in MATLAB.

5. Dr. Jie Zou PHY 33205 Assignment (cont.) Arrays: An array is a collection of values that are represented by a single variable name; Vectors: 1D arrays; Matrices: 2D arrays. Examples: Create a row vector and a column vector EnterThen enter >> a = [ 1 2 3 ]  >> b = [ 2; 4; 6]  a = or>> b = [2 4 6]’  1 2 3b = 2 4 6 Also note that this current assignment of a Overrides the previous assignment of a = 4.

6. Dr. Jie Zou PHY 33206 Assignment (cont.) Example: Create a matrix >> A = [1 2 3; 4 5 6; 7 8 9]  A = 1 2 3 4 5 6 7 8 9 Example: Access an individual element of an array >> b (2)  >> A (2, 3)  ans = 46 MATLAB built-in functions: ones (m, n), zeros (m, n), and size () >> E = zeros(2, 3)  >> u = ones (1, 3)  >> size (A) 

7. Dr. Jie Zou PHY 33207 Assignment (cont.) The colon “:” operator Examples >> t = 1: 5  >> t = 1: 0.5: 3  t = 1 2 3 4 5 1.0 1.5 2.0 2.5 3.0 >> t = 10: -1: 5>> A (2, :)  t =ans = 10 9 8 7 6 54 5 6 Note that when a colon “:” is used in place of a specific subscript, the colon represents the entire row or column. Now try >> t (2: 4)  What do you think the result will be? The linspace function: linspace(x1, x2, n). Try >> linspace (0,1,6) and >> linspace(0,1)

8. Dr. Jie Zou PHY 33208 Mathematical operations and built-in functions Common operators: ^, -, * /, + - Examples: >> 2 * pi  >> y = - 4^2  ans =y = 6.2832 -16 Example: Vector-matrix calculations >> A.^2  What is the result? Built-in functions: log, exp, abs, sin, cos, sqrt, sum, min, max, mean, sort, length, etc. The Built-in functions operate directly on vector and matrix quantities. Example: >> log (A)  What is the result? For a list of all built-in elementary functions, type >> help elfun For how to use a specific built-in function, for example, sum, type >> help sum

9. Dr. Jie Zou PHY 33209 Graphics 2D plots: plot (x, y); 3D plots: plot3 (x, y, z); Note: x, y, and z are vectors of the same length. Example: The velocity of a falling bungee jumper:. Plot v from t = 0-20 s. Step 1: >> g = 9.81; m = 68.1; cd= 0.25; Step 2: >> t = [0:2:20]’; >> v = sqrt (g*m/cd)*tanh(sqrt(g*cd/m)*t); Step 3: >> plot (t, v) % try plot (t, v, t, v, ‘o’) Step 4: >> title (‘Plot of v versus t’) >> xlabel (‘Values of t’) >> ylabel (‘Values of v’) >> grid Also, check hold on; hold off; and specifiers for colors, symbols, and line types (see Table 2.2 on the hand out).  McGraw-Hill Companies

10. Dr. Jie Zou PHY 332010 Plot of v versus t After Step 3: plot After Step 4: title, xlabel, ylabel, and grid