Calculus courses are the most fundamental and essential building blocks of higher mathematical learning. However, they require a great deal of mastery and background information of middle and high school classes, especially algebra.
This article will dissect the difficulty of various calculus courses and try to give you an idea of what to expect from them. Calculus is not the most difficult form of math but it’s not the easiest either.
Is Calculus Hard?
Calculus is hard because it is one of the most difficult and advanced forms of mathematics that most STEM majors encounter. Both high school and college calculus are a huge jump in terms of difficulty when compared to the math courses students have previously taken.
Typically there are two courses featuring calculus in high school; pre-calculus and calculus. Pre-calculus includes topics such as series, sequences, probability, limits, statistics, and derivatives. You will build on these concepts in high school calculus which has a strong emphasis on differentiation and integration.
Think of differentiation as the process of finding the gradient of equations instead of two points. In simple terms, integration is the reverse process of differentiation and a helpful technique to find the area under any particular equation.
Several students struggle with these high school calculus classes but many other students manage to do alright. High school calculus is largely computational and does not require an in-depth understanding of the material.
In college, your calculus classes become significantly harder to cope with. Colleges generally offer Calculus I, Calculus II, Calculus III (multivariable calculus), and at times Calculus IV.
The calculus courses in college require good critical thinking skills and a thorough understanding of the underlying concepts. These factors together explain why students find calculus courses challenging.
How Hard is Calculus?
Calculus is the bridge between high school math and advanced math courses in college. For most students, calculus is an extremely hard and challenging course of study. For math majors, it is the introduction to higher-level mathematics.
If you are planning to pursue a math degree then calculus will be one of the easier courses that you take during your freshman and sophomore years. Calculus will adequately prepare you for the more advanced math classes such as real analysis, abstract algebra, complex analysis, topology, differential geometry.
On the other hand, students taking on non-stem majors such as psychology or art may find calculus I to be the most difficult course of their academic career especially if they struggle with math. So if you are being offered a calculus class as a general component you know what to do!
Some humanities majors such as business, finance, and economics may require you to take introductory calculus courses. More often than not these courses are toned down versions of the classes STEM majors are taking. If you are good with arithmetic and algebra then these beginner-friendly calculus courses should not be too much of a hurdle.
Finally, STEM majors such as engineering, computer science, physics, and chemistry require different levels of calculus depending on the major. Top tier universities may require chemistry students to take a full year of calculus whereas others may only require a semester. Higher ranked universities are known for making their calculus courses more proof heavy which drastically increases the difficulty of the class.
Is Calculus Easier Than Algebra?
Calculus is not easier than algebra. Algebra is usually introduced in middle school. Calculus is considered much more difficult than algebra; hence it is not even a requirement for students graduating from high school unless they are planning on pursuing a career in STEM fields.
Is Calculus Harder Than Trigonometry?
Calculus is harder than trigonometry because it is much more complex, detailed, and abstract. Trigonometry is the study of the relationship between side lengths and angles of triangles. On the flip side calculus is the study of mathematics that deals with derivatives and integral functions.
Why is Calculus So Hard?
Calculus is so hard because it requires a lot of hard work, mastery over algebra, is more conceptual than basic math courses, and has several highly abstract ideas. Students find calculus difficult because it is not always intuitive and requires tremendous background information.
People are used to thinking concretely. Calculus calls for abstract thinking. Changing the way of thinking is not something most people can do instantaneously. This adds to the challenge of studying calculus. Rote memorization has little to no place in calculus courses.
Professors often say that students do not fail calculus but fail the algebra in their calculus classes. During your algebra courses, a decent understanding of algebra will get you through. However, calculus is one course where you will need complete mastery over algebra to be successful.
Any weakness in understanding algebra will be exposed during your calculus lessons. Moreover, you will also need to have a strong grasp of trigonometry, pre-calculus, arithmetic, and geometry to do well in your calculus classes.
Calculus is a very broad subject. The material taught in calculus classes is useful in a vast number of fields such as advanced mathematics, physics, engineering, economics, finance, and chemistry.
Furthermore, calculus requires immense practice and dedication. Unlike other subjects where reading the textbook and attending lectures is sufficient; calculus entails completing numerous practice sets and improve your understanding of the underlying principles.
The calculus syllabus is quite exhaustive. You will learn limits, derivatives, integrals, exponentials, logarithms, Taylor series, approximations, and these very topics in three dimensions during more advanced calculus courses.
High school calculus is mostly computation. College calculus particularly in STEM majors and top tier universities is very proof oriented. Instead of simply solving the questions you must illustrate your understanding of the underlying concepts through the use of proofs.
Why is Calculus 2 So Hard?
Calculus 2 is so hard because it requires a lot of critical thinking, has more abstract concepts, tougher problem sets, strong focus on integration, and it is a huge overall jump from calculus 1 in terms of difficulty.
Most differentiation problems (calculus 1) are quite easy to solve. Integration questions (calculus 2) require more sophistication and there are a lot more formulas to learn.
Many times integration questions cannot be directly solved using the formulas available. In such cases, you will need to restructure and adjust the question in a manner so that the formula can be applied.
Do you have to be smart to do Calculus?
Most people doing calculus are smart individuals. You do not have to be smart to do calculus but students of average intellect should be prepared to put in a tremendous amount of effort. This is due to the abstract reasoning and overall difficulty of calculus courses.
More often than not students pursuing degrees requiring advanced forms of calculus are smart students. Physics, engineering, math, computer science, and other science majors are often some of the brightest students in their classes. The average IQ of such students is definitely above the norm.
However, several average students manage to do well in STEM majors requiring calculus by working hard and being disciplined. Some of the most important qualities required to succeed in tough majors are stick-to-itiveness and grit.
What is the Hardest thing in Calculus?
The hardest thing about calculus is understanding the logic behind The hardest thing about calculus is understanding the logic behind epsilon-delta limits and formulating adequate proofs for epsilon-delta limits. Students find epsilon-delta proofs difficult especially because many calculus courses start it.
Students who go on to take more advanced calculus courses find the integration in calculus II and three-dimension based questions in calculus III particularly difficult.
Almost all students struggle with algebra in calculus to some extent or the other. Any weakness in algebra will be exposed in your calculus courses. Hence it is a great idea to practice your algebraic skills before enrolling in a calculus lecture.
Is Calculus the Hardest Type of Math?
Calculus is not the hardest type of math. While calculus may be the hardest type of math offered in high school and most college programs; it is far from being the hardest when compared to all the types of math available. Courses such as analysis, topology, and differential geometry are all harder than calculus.
At the undergraduate level courses such as calculus III and calculus IV have a reputation of being hard but are still not the most difficult courses a math major would encounter.
Beyond the undergraduate level, there are far more difficult classes than calculus being offered to students who want to study advanced mathematics.
For the overwhelming majority of people, calculus would be the most difficult math course that they have encountered. The hardest high school math course is calculus. Similarly, the hardest math course for most non-STEM and STEM majors would also be calculus.
This explains why calculus is dubbed the hardest type of mathematics whereas in reality there are much more advanced and challenging forms of mathematics available.
Is Calculus 2 Harder than Calculus 1?
Calculus 2 is definitely harder than calculus 1. The questions in calculus 1 are easier to solve as the concepts are easier and there is little critical thinking involved. On the flip side calculus, 2 demands strong analytical skills and an in-depth understanding of the subject content.
Is Calculus 2 harder than Calculus 3?
Calculus 2 is not harder than calculus 3. Calculus 2 requires you to learn several integration techniques and series. Calculus 3 is essentially calculus 1 in three dimensions and it heavily uses vector equations. Calculus 3 is more difficult since it is more abstract and has harder concepts to understand.
Conclusion
Calculus is the basis of higher-level mathematics. For most students, it is the most advanced form of mathematics that they have encountered to date. This explains why calculus has a notorious reputation of being extremely difficult.
In reality, there are more difficult and advanced forms of mathematics offered but they are unknown to the masses.
Calculus is certainly hard but if you have a strong understanding of pre-calculus, algebra, geometry, and trigonometry and are willing to put in the hard work necessary then calculus should not be too much of a challenge.
