11 Common MATLAB Keywords and Syntax for Engineers

I am writing a guide that highlights the most commonly used MATLAB keywords and their associated syntax, with practical examples, for my classmates to help with tasks like working with polynomials, Laplace transforms, plotting, solving equations, basic circuit analysis like mesh analysis, as well as differentiation, integration, and partial fractions. 1. Basic MATLAB Syntax and Keywords These are foundational commands that manage the environment and display results. Example: You’re starting a new script and want to clean the workspace. clc % Clears the command window clear % Clears all variables close all % Closes all figure windows Use these at the start of every script to avoid clutter and ensure a clean slate. 2. Variables and Operators In MATLAB Example: You want to compute the value of a quadratic expression ( y = x^2 + 2x + 1 ) for ( x = 3 ). x = 3; y = x^2 + 2x + 1; % y = 16 You can also create a vector and apply the same formula element-wise: x = 0:1:5; y = x.^2 + 2.x + 1; % Use element-wise operations for vectors 3. Control Structures In MATLAB Example: You want to classify a number based on its sign: x = -5; if x > 0 disp('Positive') elif x

Mar 31, 2025 - 13:50

11 Common MATLAB Keywords and Syntax for Engineers

I am writing a guide that highlights the most commonly used MATLAB keywords and their associated syntax, with practical examples, for my classmates to help with tasks like working with polynomials, Laplace transforms, plotting, solving equations, basic circuit analysis like mesh analysis, as well as differentiation, integration, and partial fractions.

1. Basic MATLAB Syntax and Keywords

These are foundational commands that manage the environment and display results.

Example: You’re starting a new script and want to clean the workspace.

clc        % Clears the command window
clear      % Clears all variables
close all  % Closes all figure windows

Use these at the start of every script to avoid clutter and ensure a clean slate.

2. Variables and Operators In MATLAB

Example: You want to compute the value of a quadratic expression ( y = x^2 + 2x + 1 ) for ( x = 3 ).

x = 3;
y = x^2 + 2*x + 1;  % y = 16

You can also create a vector and apply the same formula element-wise:

x = 0:1:5;
y = x.^2 + 2.*x + 1;  % Use element-wise operations for vectors

3. Control Structures In MATLAB

Example: You want to classify a number based on its sign:

x = -5;
if x > 0
    disp('Positive')
elif x < 0
    disp('Negative')
else
    disp('Zero')
end

Exam Tip: Expect questions that ask you to loop through values or make decisions based on conditions.

4. Working with Polynomials In MATLAB

Polynomials are stored as vectors of coefficients starting from the highest degree.

Example 1: Represent ( x^3 - 6x^2 + 11x - 6 ):

p = [1 -6 11 -6];

Find roots:

r = roots(p);  % Returns [3; 2; 1]

Evaluate polynomial at x = 2:

y = polyval(p, 2);  % Returns 0

Multiply polynomials ( (x+2)(x+3) ):

conv([1 2], [1 3])  % Returns [1 5 6]

Divide polynomials ( (x^2 + 5x + 6) / (x + 2) ):

[q, r] = deconv([1 5 6], [1 2]);  % Quotient and remainder

5. Laplace and Inverse Laplace Transforms In MATLAB

Used to convert time-domain functions into the s-domain.

Example: Find Laplace of ( e^{-2t} ):

syms t s
f = exp(-2*t);
F = laplace(f)  % Returns 1/(s + 2)

Inverse Laplace:

ilaplace(1/(s + 2))  % Returns exp(-2*t)

Exam Tip: You may be asked to transform simple time-domain signals to the s-domain.

6. Solving Equations In MATLAB

Example 1: Solve quadratic equation ( x^2 - 5x + 6 = 0 ):

syms x
solve(x^2 - 5*x + 6 == 0, x)  % Returns 2 and 3

Example 2: Solve differential equation ( dy/dt = -2y ), with ( y(0) = 1 ):

syms y(t)
dsolve(diff(y,t) == -2*y, y(0) == 1)  % Returns exp(-2*t)

7. Differentiation and Integration In MATLAB

Differentiate: ( f(x) = x^3 + 2x^2 + x )

syms x
f = x^3 + 2*x^2 + x;
df = diff(f)  % Returns 3*x^2 + 4*x + 1

Integrate: ( f(x) = x^2 )

int(x^2)  % Returns x^3/3
int(x^2, x, 0, 2)  % Returns 8/3 (definite integral)

Exam Tip: Know how to perform both definite and indefinite integrals symbolically.

8. Partial Fraction Decomposition In MATLAB

Partial fractions are used to simplify rational expressions—especially for Laplace transforms.

Example 1:

syms s
expr = (s + 5)/(s^2 + 3*s + 2);
partfrac(expr)

Explanation: MATLAB factors the denominator as (s + 1)(s + 2) and returns:

3/(s + 1) + 2/(s + 2)

Example 2: More complex case:

expr2 = (s^2 + 5*s + 6) / ((s + 1)*(s + 2)*(s + 3));
partfrac(expr2)

9. Plotting and Visualization In MATLAB

Example: Plot sine and cosine functions:

x = 0:0.1:2*pi;
plot(x, sin(x))
hold on
plot(x, cos(x))
title('Sine and Cosine')
xlabel('x')
ylabel('Function value')
legend('sin(x)', 'cos(x)')

Exam Tip: You may be asked to visualize signals or plot mathematical functions.

10. Matrix Operations In MATLAB

Example: Solve system of equations using matrices:
[
\begin{cases}
x + 2y = 5 \
3x + 4y = 6
\end{cases}
]

A = [1 2; 3 4];
B = [5; 6];
X = A\B;  % Solves AX = B

Other operations:

det(A)     % Determinant
inv(A)     % Inverse
rank(A)    % Rank of matrix
eig(A)     % Eigenvalues and eigenvectors

11. Solving Circuit Problems In MATLAB: Mesh Analysis Example

Example: Solve mesh currents in a 2-mesh circuit:
[
\text{Mesh 1: } 10 = 2I_1 + 4(I_1 - I_2) \
\text{Mesh 2: } 0 = 3I_2 + 4(I_2 - I_1)
]

A = [6 -4; -4 7];
B = [10; 0];
I = A\B;
I1 = I(1);
I2 = I(2);
disp(['I1 = ', num2str(I1), ' A'])
disp(['I2 = ', num2str(I2), ' A'])

Explanation: Use matrix equations for circuit analysis. This example solves for currents using mesh analysis.