How to study engineering when it's all problem sets and formulas

If you're trying to figure out how to study engineering, the first thing worth knowing is that you don't learn it by reading. You learn it by solving. In Calculus, Linear Algebra, Physics, Statics or Circuits, the exam almost never asks you to describe a topic. It hands you a problem you haven't seen, asks you to get to the answer with your work shown, and gives you less time than feels fair.

What works is easy to say and hard to do: work problems without looking at the solution, understand where each formula comes from instead of memorizing it on its own, and practice on past exams early in the term, not the week before the final.

This one actually is my field. I'm in my final year of computer engineering, and I went through the same math and physics core that nearly every engineering major shares. What follows is what I learned there, combined with what we know about how people learn, applied to how engineering courses test you.

Engineering isn't hard because the lectures are confusing

In the first couple of years (Calculus I to III, Linear Algebra, Differential Equations, Physics, Chemistry, Statics) something happens that throws a lot of people off: the lecture makes sense. The professor works a problem on the board, every step follows, and you walk out feeling like you've got it. Then you sit down alone with a similar problem and have no idea where to start.

The hard parts tend to be:

• Choosing the approach. In lecture, someone already decided which tool to use. On the exam that decision is yours, and it's most of what's being tested.
• The sheer amount of practice. One physics topic can show up in twenty variations that each need a different setup. Doing two of them isn't enough.
• Courses that stack. If Calculus is shaky, Physics II and Thermodynamics get twice as hard, because they use its tools without reteaching them.
• The clock. Being able to solve a problem in forty minutes doesn't help when the midterm gives you fifteen per question.

That's why rereading your notes or flipping through worked examples gives the same false comfort as highlighting. Everything looks familiar, but recognizing someone else's path isn't the same as finding it yourself.

Work the problem without the solution next to you

The most common trap in engineering is studying with the solution manual open. You read the problem, try for two minutes, get stuck, peek at the next line, think "oh, right," and keep going. By the end of the night you've gone through fifteen problems and solved none of them.

A method that works better:

1. Actually try. Ten or fifteen minutes with nothing open, even if all you manage is listing the givens, drawing a diagram and writing the equation you think applies.
2. If you're stuck, take one hint. The first step of the solution, nothing more. Cover the rest with a sheet of paper.
3. Finish on your own. With that hint, keep going without looking until you reach the answer.
4. Redo it from scratch the next day. Without looking at your own work. If you get it, you've learned it; if not, back to step one.

This is active recall applied to problem sets: what you struggle to pull out of your head is what sticks. Spreading the attempts across different days adds the spacing effect, where material you revisit with gaps in between is remembered better than material you drilled ten times in a row.

Theory still matters (you just study it differently)

Some people get through engineering courses with only the problem sets and skip the theory. That works right up until the exam includes a problem that doesn't look like anything from the homework. At that point the only way out is understanding what each formula says and when you're allowed to use it.

For every important formula, it helps to know three things:

• What it calculates and what each term means. Not "the energy equation," but what every symbol stands for and in which units.
• Where it comes from. You don't need to derive it from scratch, but you should know which principle it's built on. A formula you understand is one you can rebuild if you blank.
• When it doesn't apply. The conditions: closed system, constant acceleration, a continuous function. A lot of exam mistakes are the right equation used in the wrong situation.

A quick test is the Feynman technique: explain a theorem or a law out loud, in plain words, as if you were telling a first-year student. Wherever your explanation stalls is what you don't understand yet.

Past exams are the map

Engineering exams resemble each other far more than exams in most other majors. Every course has its problem types, its way of setting them up and the topics that show up every single time. Working through old exams shows you all of that at once.

How to use them without wasting them:

• Start mid-semester, not at the end. If you save past papers for finals week, you find out too late what gets tested the most.
• Time yourself. Set a timer for the real exam length. Speed is a skill you can train.
• Keep a list of problem types. One per course: which types appear, which ones always show up and which ones you keep missing.
• Check against the official solutions if they exist. If they don't, compare with classmates or bring it to office hours.

I went into more detail in the post on how to use past papers, and in engineering it's probably the best return on your study time.

Lecture slides full of equations

Part of the theory arrives as the professor's lecture slides: pages packed with equations, plots and diagrams with almost no text explaining them. In class, the professor talks through them. When you open them alone two weeks later, it's hard to reconstruct what each one was supposed to say.

For those slides I use Filmina, a web app that explains each slide out loud and points at the part it's talking about. It also looks at every slide as an image, so it explains plots and diagrams along with the text, and it reads formulas the way you'd say them ("the derivative of f with respect to x"), along with what each term calculates. There's more on how it explains each slide. Then you can ask Mina about the whole lecture and practice with questions. Two limits: it needs an internet connection, and it can't read a scanned PDF. It also won't do your problem set for you. It helps you understand the theory so the problems start working out for you.

Tools that actually help in engineering

Beyond the slides, a few tools make a real difference if you use them right:

• To check, not to solve. Wolfram Alpha, Desmos, GeoGebra or a CAS calculator tell you whether your answer is right. Use them after you've solved the problem, never before, because you won't have them on the exam.
• Your exam calculator. Practice with the exact one you'll bring. Hunting for a function during a midterm is time you don't get back.
• Code to understand. In courses like Numerical Methods or Signals and Systems, writing the algorithm in Python or MATLAB forces you to understand every step.
• Your own formula sheet. Many engineering exams let you bring one, and even when they don't, building it forces you to organize the course. Write it by hand, with each formula's conditions next to it.
• Office hours. That's what TAs and professors hold them for. Bringing a problem you attempted and the exact step where you got stuck gets you far more than asking "how do you do number 7?"

Study groups help too, with one rule: everyone solves alone first, then you compare. Watching someone else solve it is just the group version of peeking at the solution.

A week you can keep up with

With several problem-heavy courses at once, the risk is that problem sets pile up and you walk into the exam with half of them untouched. A realistic rhythm:

1. Lecture day: a pass through the theory or the slides, plus one or two problems on that topic while it's fresh.
2. During the week: the problem set for that topic, without the solution, a few at a time across several days.
3. Weekend: redo from scratch the problems that gave you trouble.
4. From mid-semester on: one past exam per week, timed.
5. Before the exam: your list of problem types, one of each, without looking.

A few problems solved on your own beat many you only watched, and that's most of what studying engineering comes down to.

Frequently asked questions

How do you study for an engineering exam?

Work problems without looking at the solution and practice on past exams under the real time limit. Study the theory so you know when each formula applies, not so you can recite it.

How many practice problems should I do for an engineering class?

There's no number that works for everyone, and it depends on the course. What matters is having solved, on your own, at least one problem of every type that usually shows up on the exam, and redoing the ones you missed on different days.

Do you need to memorize formulas in engineering?

The core ones, yes, but it pays to understand where they come from and when they hold, because then you can rebuild them if you forget. Writing your own formula sheet by hand, with the conditions for each one, helps lock them in even if you can't bring it to the exam.

Is it normal to understand the lecture but not be able to solve the problems?

Yes, and it's the most common thing in the first years of engineering. Following a problem someone else solves isn't the same as finding the path yourself. The fix is to attempt first, take just one hint when you're stuck and redo the problem later.