Calculus is among the most daunting subjects that many high school and college students will ever face. Students who take this class typically struggle with it at one point or another, whether due to the hard-to-grasp concepts, the intimidating notation, or the difficult problems.
Challenges aside, however, calculus is undeniably one of the most important building blocks of modern science and technology.
From optimizing your budget to editing photos to calculating the growth rate of a population of bacteria, calculus plays an essential role in our lives and is worth understanding.
Here are a few tips to help you learn how to study calculus more effectively:
1. Solve Calculus Problems Strategically
The main way to improve your performance in any math subject is to keep solving problems. However, with calculus, in particular, it is imperative to understand the underlying principles in each problem solved.
As such, when you practice solving problems on homework or assessments, take the time to figure out the motivation and general problem-solving strategy.
2. Take Excellent Notes
It’s important to take notes on your learnings from classes and the problems you solve.
Unlike precalculus, which is characterized by the disjointed nature of the main topics, calculus is a subject that builds on itself. Understanding concepts as they are discussed and remembering them weeks later when they are referenced again are key to being successful in this class.
3. Go Back to Precalculus Lessons
There’s a reason precalculus is called precalculus. At many points throughout calculus, you’ll need to remember how to make graphs of rational functions or manipulate trigonometric expressions.
Be sure to keep your notes from precalculus accessible, as there will inevitably be parts of precalculus you will need to refer back to so that you can completely solve a problem.
4. Include as Many Drawings in Your Notes as Possible
Including visual components in the notes you take is an essential part of maintaining a good calculus notebook.
Many of the concepts discussed won’t make any sense until you draw them out and visualize them for yourself. It doesn’t matter whether or not you’re actually good at drawing—these drawings are for you, to help you understand how everything comes together. Regarding integration, in particular, there’s nothing like a good visualization of a Riemann sum.
5. Seek External Visualizations
Many of us are visual learners. But if you’re like me, you can’t seem to draw a straight line or a decent circle! If that’s the case, it’s imperative to have access to simple, compelling, and effective visualizations from other sources.
Fortunately, mathematicians around the world dedicate their lives to providing these visualizations. A phenomenal example is 3Blue1Brown, a YouTube channel highly revered for the quality and clarity of its computer-generated visuals.
6. Keep a Dictionary of Calculus Notations and Terms
It’s essential to keep track of all the important definitions and notations that you learn.
To the average person, a calculus problem will look incredibly daunting since there is so much notation that will seem unfamiliar. Calculus notation builds on top of the notation learned in algebra and precalculus and adds a fair share of new symbols.
The best way to keep track of all the definitions and notations for studying is to keep a dictionary of important pieces of information, either at the front or back of your notebook or somewhere else that is easy to access.
7. Think of Real-World Applications for Calculus Tools
Calculus is one of the most relevant and widely used fields in STEM, with applications ranging from economy to agriculture and pharma. However, it can be difficult to make these connections in the classroom, leading students to feel like they are spending their energy on something meaningless.
Take a look at some common applications of calculus in real life. You’ll be surprised at this subject’s breadth of applications—and hopefully inspired to keep learning more!
8. Don’t Be Afraid to Ask for Help
When you run into trouble understanding part of a problem or concept, reach out to your teacher for help. And if you could use personalized one-on-one support, consider working with a subject tutor who specializes in calculus.
Calculus, while undeniably challenging, is a beautiful subject. Even if you aren’t interested in pursuing a career in STEM, understanding calculus is an essential part of understanding how modern technology and the world as a whole work.