Is calculus hard to learn?
Understanding the concept helps any worried student who wonders, ‘Is calculus hard?’
Is calculus hard? Yes, and no. This branch of mathematics, discovered in the 17th century, was developed out of a need to understand continuously changing quantities.
Many mathematicians both love and hate calculus. They say calculus demonstrates the beauty of math, but also the agony of math education. Most lessons, they argue, feature contrived examples, arcane proofs, and memorization that body slam the student’s intuition and enthusiasm – in the same way that requiring young children to learn art by studying paint chemistry, the physics of light, and the anatomy of the eye.
Sir Isaac Newton, one of the two discoverers of calculus, was trying to understand the effect of gravity that causes falling objects to constantly accelerate. The speed of an object increases constantly every split second as it falls. For example, how can we calculate the speed of a falling object at a frozen instant in time, such as its speed when it strikes the ground?
Is calculus hard? Here’s a calculus meaning
But what is calculus? A calculus definition holds that it’s the branch of mathematics that deals with the finding and properties of derivatives and integrals of functions, by methods originally based on the summation of infinitesimal differences. The two main types are differential calculus and integral calculus.
Differential calculus is concerned with continuous change and its applications. This allows us to optimize functions, which means to find their maximum or minimum values, as well as to determine other valuable qualities describing functions.
Integral calculus is a process that resembles the reverse of differentiation. This means efficiently adding many infinitely small numbers. This allows us, in theory, to find the area of any planar geometric shape, or the volume of any geometric solid.
To put it in a simpler way, however: Calculus does to algebra what algebra does to arithmetic. Arithmetic is about manipulating numbers via addition, multiplication, and so on.
Algebra finds patterns between numbers, such as a^2 + b^2 = c^2, a famous relationship describing the sides of a right triangle. Calculus finds patterns between equations: you can see how one equation (circumference = 2 * pi * r) relates to a similar one (area = pi * r^2).
Calculus allows us to answer questions such as:
- How does an equation grow and shrink? Accumulate over time?
- When does it reach its highest/lowest point?
- How do we use variables, such as heat, motion, or populations, that are constantly changing?
Like evolution, calculus expands our understanding of how nature works – which relates back to Newton’s discovery of this mathematical endeavor as he studied the physical properties of the world around him.
Is calculus hard? The key to learning calculus
The first thing to know about calculus, and generally all branched of mathematics, is that their reputation for difficulty always makes students believe they’re harder to learn than they really are. It’s critical to think of calculus as just another subject you’re about to study.
Classes in calculus, like all technical subjects, generally have a basic structure. In every class, the instructor presents a series of concepts. For each concept, the professor will derive the result from concepts students already know, and/or provide an example of the concept in practice.
Students usually copy these concepts down, take them home, memorize them and then find they don’t understand them and can’t apply them to solve hard calculus problems.
Mastering calculus, however, requires that instead of simply writing down and memorizing concepts, a student must develop a deep insight into the meaning of the concept, so that a mental picture can be formed of what it means.
Gaining insight into every single concept taught in a calculus course is considered the only way to master it. Developing insight is what’s difficult about calculus, though like anything else it gets easier with practice.
That’s why students who have completed calculus courses advise that students:
- Do assigned problems the same day or day after the class, while the material is fresh.
- Be prepared to spend an extra 8-10 hours per week outside of class studying and gaining insight into the concepts.
- Read ahead in the textbook so the material isn’t completely new when the instructor delivers it.
- Do as many practice problems as possible.
To succeed in learning calculus, students should already have a strong foundation in algebra (elementary and intermediate) and pre-calculus. Pre-calculus introduces students to functions and the graphing of functions. It covers topics such as linear and polynomial functions, inverse functions, exponential functions, logarithmic functions, trigonometric functions and inverses.
Regardless of your comfort with calculus, it can still present challenges at any time. When an instructor isn’t available to answer questions and help you get past a roadblock, the Calculus Experts on JustAnswer are available at any time, day or night, and all you need is an Internet connection.