Explain MATLAB terms and differentiate operators and evaluate MATLAB expressions.

Step 1: Explain MATLAB terms.

• a) The Command Window is the primary interface in MATLAB where users type commands and view immediate results.
• b) The Workspace is a panel that displays all variables created during a MATLAB session, along with their values and data types.
• c) The Command History logs all commands executed in the Command Window, allowing users to recall and reuse previous commands.
• d) The Current Folder panel shows the contents of the directory MATLAB is currently working in, including scripts, functions, and data files.

Step 2: Differentiate operators and evaluate expressions.

• a) Unary operators operate on a single operand (e.g., negation -x). Binary operators operate on two operands (e.g., addition x + y).
• b)
  • >> 12 -5 2 This creates a row vector. $$\text{ans} = \begin{bmatrix} 12 & -5 & 2 \end{bmatrix}$$
  • >> 10-6*2 Following order of operations (multiplication before subtraction): $$10 - (6 \times 2) = 10 - 12 = -2$$ $$\text{ans} = -2$$
  • >> 5^1/2*3 Following order of operations (exponentiation, then division and multiplication from left to right): $$(5^1) / 2 \times 3 = 5 / 2 \times 3 = 2.5 \times 3 = 7.5$$ $$\text{ans} = 7.5$$

Step 3: Evaluate MATLAB vector operations.

• >>pvec = 3:2:10 Creates a vector starting at 3, incrementing by 2, up to 10. $$\text{pvec} = \begin{bmatrix} 3 & 5 & 7 & 9 \end{bmatrix}$$
• >>pvec(2) = 15 Changes the second element of pvec. $$\text{pvec} = \begin{bmatrix} 3 & 15 & 7 & 9 \end{bmatrix}$$
• >>pvec(7) = 33 Extends pvec to 7 elements, filling intermediate elements with zeros. $$\text{pvec} = \begin{bmatrix} 3 & 15 & 7 & 9 & 0 & 0 & 33 \end{bmatrix}$$
• >>pvec([2 4]) Displays elements at indices 2 and 4 of the current pvec. $$\text{ans} = \begin{bmatrix} 15 & 9 \end{bmatrix}$$
• >>linspace(5,11,3) Generates 3 linearly spaced points between 5 and 11. $$\text{ans} = \begin{bmatrix} 5 & 8 & 11 \end{bmatrix}$$
• >>logspace(2,4,3) Generates 3 logarithmically spaced points between $10^2$ and $10^4$. $$\text{ans} = \begin{bmatrix} 100 & 1000 & 10000 \end{bmatrix}$$

Step 4: Evaluate MATLAB matrix operations.

• >>mat = [1:3; 44 9 2; 5 -1 3] Creates a 3x3 matrix. $$\text{mat} = \begin{bmatrix} 1 & 2 & 3 \\ 44 & 9 & 2 \\ 5 & -1 & 3 \end{bmatrix}$$
• >>mat(3,2) Accesses the element in the 3rd row, 2nd column. $$\text{ans} = -1$$
• >>mat(2,:) Accesses all elements in the 2nd row. $$\text{ans} = \begin{bmatrix} 44 & 9 & 2 \end{bmatrix}$$
• >>size(mat) Returns the dimensions of mat. $$\text{ans} = \begin{bmatrix} 3 & 3 \end{bmatrix}$$
• >>mat(:,4) = [8;11;33] Adds a new 4th column to mat. $$\text{mat} = \begin{bmatrix} 1 & 2 & 3 & 8 \\ 44 & 9 & 2 & 11 \\ 5 & -1 & 3 & 33 \end{bmatrix}$$
• >>numel(mat) Returns the total number of elements in mat (3 rows $\times$ 4 columns = 12 elements). $$\text{ans} = 12$$
• >>v = mat(3,:) Assigns the 3rd row of mat to vector v. $$\text{v} = \begin{bmatrix} 5 & -1 & 3 & 33 \end{bmatrix}$$
• >>v(2) Accesses the second element of v. $$\text{ans} = -1$$
• >>x = [1 1] Creates a row vector x. $$\text{x} = \begin{bmatrix} 1 & 1 \end{bmatrix}$$
• >>reshape(mat,2,6) Reshapes mat into a 2x6 matrix, filling elements column-wise from the original mat. $$\text{ans} = \begin{bmatrix} 1 & 5 & 9 & 3 & 3 & 11 \\ 44 & 2 & -1 & 2 & 8 & 33 \end{bmatrix}$$

Step 5: Write a MATLAB script to plot $\sin(x)$ and $\cos(x)$.

% MATLAB script to plot sin(x) and cos(x)
x = linspace(0, 2*pi, 100); % Generate 100 points from 0 to 2*pi
y_sin = sin(x);             % Calculate sin(x)
y_cos = cos(x);             % Calculate cos(x)

plot(x, y_sin, 'b-', x, y_cos, 'r--'); % Plot sin(x) in blue solid, cos(x) in red dashed
xlabel('x');                        % Label for x-axis
ylabel('y');                        % Label for y-axis
title('Plot of sin(x) and cos(x)'); % Title of the plot
legend('sin(x)', 'cos(x)');         % Legend for the plots
grid on;                            % Display grid

The script will produce a plot with two lines: a blue solid line for $\sin(x)$ and a red dashed line for $\cos(x)$ over the specified range.

Step 6: Write a MATLAB function for trapezium area.

• a) MATLAB function TrapArea:

  function area = TrapArea(a, b, h)
  % TRAPAREA Calculates the area of a trapezium.
  %   area = TRAPAREA(a, b, h
  

  Copy