Why Is Calculus Considered The Hardest Class In College? - Salarship

While studying mathematics, I heard horror stories about failed calculus exams.

In my experience, calculus is challenging because it deals with nonintuitive concepts related to limits and infinity that require a high level of conceptual thinking.

College professors are also fussier about the accuracy of proofs, so students can no longer get away with approximate “high school-like” calculus proofs.

Let me explain why first-year college students find college calculus courses so difficult.

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3 Reasons Why Calculus Is Considered The Hardest Class In College

Calculus is often regarded as one of the most challenging subjects in college for several reasons.

1. High Failure Rates

Many students fear calculus because it has a high failure rate.

Depending on the college, the failure rate for Calculus 1 can be anywhere between 25% and 65%.

More generally, more students tend to fail Calculus exams than Statistics or Linear Algebra exams.

2. The “College Factor”

Then, due to the “college factor” (being away from home, no policing, partying, etc.), many students will not put in the sufficient amount of time required to learn calculus, and thus many will fail.

Some might find it difficult because they may have reached their ability (ceiling) to do the math, or they might find that the sheer amount of work is overburdening.

Another remark I have often heard is that calculus professors are bad at teaching compared to high school teachers.

3. Calculus is a Broad Topic

One aspect (the objective aspect) of calculus that many students may find difficult is that calculus is a broad topic with many rules and formulas.

These rules and formulas are put forward to be memorized, including derivative formulas, the product rule, the chain rule, implicit differentiation, the fact that integrals and derivatives are opposite, and the Taylor series.

As such, calculus can get very confusing very quickly.

Let’s discuss some of the actual course topics and math that you will encounter in calculus to determine how difficult the material actually is (the objective factors).

Complex Topics That You Will Encounter During Calculus Classes

Let’s discuss the core sections of calculus courses to give you a better understanding of how complex calculus actually is.

Calculus 1

Calculus 1 typically has you start by learning single-variable differential calculus. This means you will learn to find the limits of algebraic functions.

Take into consideration that for both the derivative and integrals (which we will explain), working out the approximation will lead you to the approaching number (the slope or the area), which is called the “limit.”

Due to the fact that limits are key in calculating the derivative and the integral, you will typically start off by learning limits first in calculus.

Typical topics in Calc 1 are:

• Definition of derivative
• Techniques and applications of derivative (trigonometric and exponential functions)
• Introductions to anti-differentiation
• Definitions of “epsilon-delta” limits
• L’Hôpital’s rule

Calculus 2

Calculus 2 (integral calculus) might have you start with FTC (the Fundamental Theorem of Calculus) and then work through integration techniques.

Here you will learn how to calculate the area under a curve and between two curves.

Depending on your curriculum’s structure, much of your standard calculus will be spent calculating derivatives and integrals.

You’ll most likely start with the essential functions that include:

• Polynomials
• Trigonometric functions
• Exponential functions
• Logarithmic functions

Thus, depending on your curriculum’s structure, derivatives and integrals may be combined in calculus 1 and calculus 2.

You will also learn more complex functions by adding, subtracting, multiplying, and dividing these functions together. You will even start to combine functions together using function composition.

Other topics that you might encounter in calculus 2 are;

• Sequences and series
• Partial fraction decomposition
• U-substitution
• Polar coordinates

Calculus 3

Calculus 3 is multivariable calculus.

When you start learning calculus, you will initially learn basic functions. This means functions that have one input and one output. However, we live in a three-dimensional world (four if you include space-time).

In a three-dimensional space, you will not have a slope but rather a plane. To compute this, you will calculate the derivative both in the x-direction and in the y-direction.

These are called partial derivatives. These two partial derivatives are needed to express the tangent plane.

More topics that you will come across in Calculus 3 will include;

• Higher-order derivatives
• Scalar fields
• Vector fields
• Taylor series

The Bottom Line

One of the reasons many students find it difficult is because of the fact that it is the first higher maths course they will take at college, and due to many subjective and environmental factors.

Many first-year students find calculus difficult when, in fact, if you ask most fourth-year math majors about it, they would probably say it’s pretty easy.

However, always remember that every person is unique, and their capabilities may not lie in understanding higher mathematics.

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