College students would believe that they are used to difficult core classes in their time. But the difficulty is subjective and may creep up on someone without notice if they aren’t wary enough. This is especially true for multivariable calculus, a high-level mathematics course that a college student must encounter in some part of their curriculum.
How hard is multivariable calculus? How hard is it compared to other math classes? And what can you do to make it easier? This article will answer these questions and more.
What is Multivariable Calculus?
Students will start taking much more challenging classes in high school and college. This includes mathematics, where they will deal with equations and questions that require them to understand the subject enough to find the best answer. And these questions won’t have simple integers or even single variables, but sometimes more than one type of variable simultaneously.
Multivariable calculus is a form of calculus that deals with functions of several variables, as well as concepts such as continuity, differentiation, and integration. Multivariable calculus can be easily considered an extension of regular calculus and shows how adding more than one variable can make a subject that much more difficult.
It is not the place or time to get into the nitty-gritty of how exactly multivariable calculus works—that is up to you when you finally get to Calculus II or Advanced Calculus. However, we want to give a clear idea of what multivariable calculus is: if single-variable calculus is working with 2D axes, or simply X and Y, then multivariable calculus is working with 3D axes, or X, Y, and Z. While there is an extra dimension to worry about, you know how to deal with dimensions, making things a whole lot easier.
But you are not here to know what multivariable calculus is: you are here to know how hard it is. Like all subjects, especially mathematics, it is up to the individual. But it wouldn’t be “advanced” calculus if it didn’t come with difficulties. How exactly difficult is multivariable calculus? Could it be considered the hardest math class?
Is Multivariable Calculus the Hardest Math Class?
Is multivariable calculus the hardest math class you can find? Multivariable calculus is not a class that high school students would take: at least not those in the regular classes, but the Advanced Placement and Honors classes. High school students barely perform single variable calculus in high school, as their mathematics curriculum is focused more on algebra and geometry. Calculus is a regular study for college students, however, and they should expect to see it come up in their time regardless of their major.
But does that make multivariable calculus the hardest math class? Not necessarily. What makes the hardest mathematics class is up to the individual. Some may find statistics, a subject that deals with concepts like probability, standard deviation, analysis, and modality, would be more difficult. Others say that advanced levels of physics, which interestingly use similar but more practice concepts as multivariable calculus, like differential forms. However, multivariable calculus is a part of advanced calculus, which is no slouch in the difficulty department. Advanced calculus is the highest level of mathematics for every student but the math majors.
But just how hard is multivariable calculus to learn on its own? What are a student’s chances of acing the class if they have always struggled with math?
How Hard is it to Learn Multivariable Calculus?
Multivariable calculus is a difficult class to learn. As the name implies, it’s a step above single-variable calculus. Now you have to worry about multiple variables, which throws a wrench in figuring out how to solve functions or make them work. Multivariable calculus starts to involve continuity, slopes, rates of change, long division, and summations—exponentially increasing the difficulty of the subject. Multivariable calculus also involves derivatives, the idea of a function’s rate of change in response to another variable.
The difficulty of multivariable calculus largely lies in how many different concepts one has to learn to tackle even a single function while asking that the student juggles multiple functions at once.
It is very easy to say that multivariable calculus is hard. But how hard is it when compared to other math classes? For example, the infamously challenging linear algebra?
Is Multivariable Calculus Harder Than Linear Algebra?
One math class infamous for its difficulty is linear algebra, which deals with vectors, linear transformations, etc. Linear algebra is a well-defined and understood field—except for college students, who struggle with them mightily. Is multivariable calculus harder than linear algebra?
One significant difference between multivariable and linear algebra is that many colleges require the latter and essential calculus to take the former. Meanwhile, linear algebra has no requirements besides an understanding of algebra. In many respects, this would make linear algebra the easier of the two.
Additionally, linear algebra is understood in mathematics, leaving little room for new theorems or unsolved problems. It’s an evergreen subject, while other subjects like multivariable calculus are less straightforward. It is sufficient to say that multivariable calculus is harder than linear algebra.
But enough about how difficult the class is. How does a student make it less difficult? What can they do to start properly learning multivariable calculus?
3 Tips for Learning Multivariable Calculus Include Specific Tips
We have explained much of what makes multivariable calculus hard. If you are not already scared off from taking the subject, then don’t worry any further because we have three valuable tips that you can utilize to make learning multivariable calculus easier. These are particular to multivariable calculus, but these tips are generally good for getting through any college subject.
Get a Refresher on Mathematics
The first thing any student should do if they are worried about taking multivariable calculus is get refreshed on mathematics. They should remind themselves of what they learned in algebra, calculus, geometry, and every off-shoot related to them.
These concepts are all critical to understanding multivariable calculus. A refresher can make it easier to understand ideas in the subject better than if you took on the class fresh. Most multivariable calculus classes will remind students of some ideas, but in the interest of moving ahead, they will assume that the student remembers and knows enough. But more than remembering ideas, students should also get used to practicing examples to understand multivariable calculus practically.
Practice the Practice Questions
A mistake that many students trying to learn make is that they dumb down their studying and learning into simply reading and understanding the concepts. While that is crucially important when it comes to studying, it will all go to waste when you are confronted with a real problem you need to solve. Multivariable Calculus, 7E by James Stewart is a great textbook to start with if you haven’t already.
Practice examples and questions. Repeat derivatives and learn the process of differentiation. You should not only understand what the right or wrong answer is but understand how to get there. Practice dozens of different forms of questions a day to beat them into your head. If you are wrong, it is a practice question and not the end of the world. Address your mistake and compensate for it the next time you practice. It would help to also take notes to document exactly what you are doing right and wrong. Speaking of which…
Take Strong Notes
A key part of learning multivariable calculus is taking notes on what you have learned. Keep in mind that mere memorization will not help you learn when you need it the most. When it comes to high-stress situations like tests or exams, what you remember will fall right out of your head, and you’ll spend more time remembering what to do than being able to do it.
Taking notes is about charting your progress and mistakes from your refreshers and practices. Ideally, you would break down the lessons and concepts into something easily digestible that sits in your subconscious instead of your conscious. When you have done that, then multivariable calculus will be as easy as muscle memory on top of what you learned and practiced.
Wrapping Things Up: How Hard is Multivariable Calculus?
How hard is multivariable calculus? While it is not the most challenging math course, you should never underestimate its difficulty. For students who are not math majors, it may be the most difficult course they will encounter. Indeed, other math classes are required to take this one. But in spite of its difficulty, multivariable calculus can be conquered like any other, so long as a student dedicates themselves to reminders, practice, and good note-taking!