MATLAB appears in many Australian degrees. Engineering, maths, physics and data science units all use it. Some students start with no coding background, and week one can feel stressful. The good news is that most assignments rely on the same core topics. Learn these well and your marks can lift fast. Here are the topics that appear most often, with sample questions for each.
1. Matrix Operations and Linear Algebra
This is considered the base of MATLAB. Tasks include solving systems, finding inverses and working out eigenvalues using tools like the backslash operator and eig. If you’re looking for ready-to-use questions, here you have two:
- Solve 2x + y − z = 3, x − 3y + 2z = −4 and 3x + 2y + z = 7 using the backslash operator. Check your answer by substitution.
- Create a 4×4 matrix A. Find its determinant, inverse and eigenvalues to explain what happens when the determinant is zero.
Matrices also power the next topic, where exact answers are not always possible.
2. Numerical Methods
Some questions are too complex to have a single formula. At such times, you are expected to code root finding, integration and interpolation from scratch, or use fzero, trapz and interp1. For your assignment, you can try the following typical questions:
- Find the root of f(x) = x³ − 2x − 5 using Newton’s method. Stop when the error is below 1e-6 and report the iterations.
- Integrate sin(x) from 0 to π using the trapezoidal rule with 10, 100 and 1000 intervals, comparing each with the exact value.
3. Differential Equations
Mechanical, civil and chemical units use ODEs to model motion, heat and reactions. Assignments often use ode45 and ask you to explain the plot through the following questions:
- Use ode45 to model a damped mass on a spring. Plot displacement for 20 seconds and describe the motion.
- A tank fills at a set rate and drains through a hole. Write the ODE and find when the level reaches 2 metres.
4. Signal Processing
This MATLAB topic comes early for electrical and communications students. Tasks here include building a sine wave, adding noise and filtering it, with FFT showing the frequencies inside. Here are two examples you can build your assignment around:
- Create a 50 Hz sine wave with random noise, and then use FFT to plot the spectrum and identify the main peak.
- Design a low-pass filter to remove the noise and plot the signal before and after filtering.
Moving on, signals are just one kind of data, but we must look at pictures as well.
5. Image Processing
An image is just a matrix of numbers. You might convert a photo to greyscale, sharpen edges or count objects using imread, imshow and edge. To practise your hand, you can use the following tasks:
- Load a colour image, convert it to greyscale and show both side by side. Then apply edge detection and comment on the result.
- Write a script that counts the coins in a photo while explaining each step of your method.
Next comes a topic about systems that react to what they sense.
6. Control Systems and Simulink
Engineering units use transfer functions and step responses. You may check stability or tune a PID controller in Simulink. Two sample questions to practise here are:
- Build a second-order transfer function. Plot its step response and report the rise time and overshoot.
- Model a cruise control system in Simulink with a PID controller. Tune it until the speed settles within 2% of the target.
A finished design still needs testing against real numbers, which brings us to our next topic on data work.
7. Data Analysis and Curve Fitting
Science and business units ask you to load data, clean it and find a pattern. Here you can use some common tools like readtable, polyfit and corrcoef. Try these questions:
- Load a CSV of temperature readings, remove missing values and calculate the mean, median and standard deviation.
- Fit a line and a quadratic curve to lab data with polyfit. Compare the R-squared values and pick the better fit.
8. Optimisation
Optimisation looks for the lowest cost or highest output within set limits using fminsearch or linprog. All you have to do here is define your goal and limits before you write code. Two sample questions to work on:
- Use fminsearch to find the dimensions of a 500 mL cylindrical can that uses the least metal.
- A factory makes two products with limited labour and material. Now, to find the most profitable mix, use linprog.
9. Machine Learning Basics
Newer units ask for simple models that classify data, predict values or group points, using fitlm, fitctree and kmeans. Keep the model simple, since clear reasoning scores well. Simple questions to try your hand at are:
- Split a dataset into training and test sets to build a regression model with fitlm and report the test error.
- Use k-means to group customer data into three clusters. Plot them and describe what sets each group apart.
Questions like these show how far MATLAB can take you in one degree.
Final Thoughts
Your unit outline shows which topics you need. Pick two or three that match your course and practise one problem from each. A quick tip would be to test your code on small examples first by writing short notes on what each result means. If a tough question slows you down, online MATLAB support can help you move past it. Steady practice will build confidence quickly and will take you one step closer to your desired grade in Australian universities.
