Many students view calculus nervously – worried that somehow it will be tougher than any math class they have taken yet. In reality, the basic material in calculus is not that difficult, and many things that helped you understand math before will still help you at this level. The list below has been made from years of observing what successful students do differently in calculus courses. Whether you are in calculus now or taking it next semester you are likely to find some good ideas below:
1. Check your algebra skills
To be able to DO calculus you need to really understand algebra – really really understand it. Details that may have been possible to overlook now matter bigtime! Can you take a really large fraction with algebraic expressions in the numerator and denominator and simplfy it? Do you remember how to multiply polynomials? Actually just about everything you learned in algebra will come up at some point. If you are already taking calculus or will be soon, it would be helpful to pick up an algebra book for when you get stuck. Something like Schaum’s outline which gives the step by step instructions without any of the extras (plus its only $13!). There are also plenty of free resources such as purple math and our very own algebra review articles.
2. Get up to speed on your graphing calculator
If you haven’t used a graphing calculator much yet, you will find it amazing how much actually seeing the functions help you understand what is going on. If you are working on a problem and really stuck, sometimes taking a look at the graph helps you find your mistakes. If at all possible get comfortable with the calculator BEFOREHAND! It is a lot more difficult to learn a new calculator along with a lot of new math ideas.
3. Don’t just memorize – learn WHY
Algebra is very step by step and in some ways you can solve problems without ever really thinking about what you are doing. If you learn the steps you can get an answer. You could probably do the same with calculus but just as in algebra there is a major problem with this style of learning: If you run into any trouble at all you will be done! If you don’t understand why then how will you work your way out of a jam? With the more open ended problems this can be a real issue. So, when you read examples or try problems, pay attention to why each step is done. Once you see this you may start finding shortcuts and realizing that you really don’t have to memorize as much as you thought.
4. Pay attention to notation
It may seem silly, but the little details of the correct notation are important. This is the language of calculus and if you are using it incorrectly, how can you expect to truly understand anything? If someone had problems with reading comprehension as far as recognizing questions and then you noticed he was using question marks incorrectly in his own writing, wouldn’t you think that was part of the issue? When you forget a “dx” or to get rid of the integral symbol after you have taken the integral you are making it impossible to go back and truly read your work. How will you review what you did? Will you be able to follow it?
5. Actually learn the formulas
Ok earlier, I said “don’t just memorize”. This is true. BUT – you will have to memorize some things. There is simply no way around this whatsoever, so just make it happen. You MUST memorize the rules for differentiation and integration for instance. The best way to achieve this is by working problem after problem after problem until they are second nature. You know how if I ask you name, you dont have to write it first or even think? You just KNOW. That’s how it should be with the formulas/rules in calculus.