One topic that students have a love/hate connection with is calculus. Calculus represents both the beauty and the sorrow of mathematicians, showing them on opposite sides of this argument.
But because calculus is a crucial subject and can boost grades, students must strive to master it. Although the principles of calculus can be described as brain, students should be required to find out ways to work on this challenging topic, understand it, and perform well on exams.
Read on to find out the best ways to learn calculus
What Is Calculus, And Why Should You Learn It?
Calculus is simply the study of how things change. Calculus provides a framework for modeling scenarios in which change exists and a way to figure out the predictions of these models (Source: Massachusetts Institute of Technology, Department of Mathematics)
We lose motivation since the majority of us at the school level do not grasp how to use calculus in practical settings. In order to comprehend why we study a subject that is so challenging to understand, it is crucial to realize how frequently calculus is used in practical settings.
In fact, learning calculus equips all students with the knowledge and skills required to recognize how a subject or system of study is affected by a changing environment.
Calculus is a subject that has been extensively studied, and it can even be used to program a machine to follow your commands.
By understanding calculus, you can learn how to control the system and make it do what you want it to. In other words, calculus gives you extraordinary power over the material world.
Here are a few applications of calculus in the real world:
|Autonomous driving of cars
|World of Warcraft
|Optical character recognition
Best Way to Learn Calculus
The area of mathematics known as calculus deals with derivatives, limits, functions, and integrals. We can absolutely say that it is difficult to deal with as a result.
It is undeniable that calculus is a significant component of mathematics and that many students find it to be the most challenging component as well, making it difficult for most students to deal with and comprehend.
Calculus, however, can be simplified if the pupils know how to get around it. The actions that, if correctly taken, can assist students in completing calculus and achieving high marks in it are listed below:
1- Start with Fundamental Mathematical Concepts
Calculus may be considered a branch of mathematics that is further connected to a number of other mathematical concepts that students must master before attempting to understand calculus. These constituent pieces are:
- Algebra: Learn all the algebraic principles and gain a solid grasp of sets and groups in algebra.
- Arithmetic: Before attempting to grasp calculus, you should be proficient in fundamental arithmetic and be able to do all operations.
- Geometry: Learn everything about shapes along with their properties.
- Trigonometry: Understand the relationships between side lengths and angles triangles.
2- Understanding the Calculus Concepts
Recognize that the study of calculus consists of two parts: differential calculus and integral calculus. Calculus can be defined as the study of change, accumulation, and rate of change. The rate of change can be seen as a derivative, whereas accumulation can be seen as an integral.
You should practice learning about time vs. velocity, rate of change, time vs. distance, etc., because the rate is a key concept in calculus.
The most important thing to know about solving calculus problems is that there are three main segments of calculus:
3- Understand Calculus Formulas
Before beginning to solve calculus problems, try to understand some basic formulas relating to the derivatives and integrals that make up the subject.
You should work on comprehending the formulae by reading the proof used to arrive at the formula. Instead of attempting to remember the formula, try to understand it by reading the proof.
4- Understand the Idea of Limits
In Mathematics, a limit is described as a value that a function takes as that function’s inputs get closer and closer to some given number. Limits are essential in calculus and are used to define integrals, derivatives, and continuity.
It’s important to use limites to decompose a complex function into manageable components before evaluating it.
The complex function must first have all of its problems fixed before being added together. This is how a difficult problem could be made simple. The significance of boundaries in this context makes it essential to understand them.
5- Recognize the Fundamental Theorem Of Calculus
The fundamental theorem of calculus is very important in calculus as it links the concept of integration and the concept of differentiation of a function.
There is no way to avoid learning the fundamental theorem associated with calculus when it comes to comprehending it. Students are able to comprehend integration and differentiation with the aid of the fundamental theorem.
The fundamental theorem of calculus aids in understanding how differentiation and integration frequently operate in opposition to one another.
6- Use a Graphic Calculator
Without visual aids, calculus can be challenging to comprehend. With the aid of graphing calculators, you may better understand the equations you are creating and manipulating by having functions visualized for you.
Limits are frequently shown on the screen, and derivatives and functions are frequently calculated automatically.
If you don’t want to purchase a full calculator, many tablets and smartphones now provide affordable but functional graphing software.
If you want to purchase a graphic calculator, I wrote a whole article about the 5 Best Graphing Calculators and how to pick the best one.
7- Increase your Calculus Problem-Solving Practice
It’s time to start practicing the problem after you’ve finished comprehending the formulas and the theorem. You might start with the derivatives puzzles to get some practice. You can advance to integral problems after gaining practical experience with these difficulties.
It’s important to practice as many questions as you can in a day if you genuinely want to become proficient in calculus. It’s crucial to keep some practice questions on hand daily so you can stay engaged with the material.
Even if you are stuck on a problem, talk to your teachers or your classmates about it to find the solution so that you can go on.
8- Examine your Doubts
It is far too typical to have questions about calculus formulas, theorems, or problems during the learning process. Don’t be afraid to ask your teachers questions about it. The learning process also includes asking questions to clarify any confusion you may have about a topic.
Your teachers are always available to answer your queries and are more than glad to do so.
9- Review your Concepts
Even after you have finished understanding the basics of calculus, it is crucial to leave room for improvement. You can think about verifying your understanding of your notions to see if you actually do so.
It is fantastic if you comprehend the ideas and difficulties, but if not, always discuss your concerns with your lecturers to receive clarification.
Having your questions answered will improve your understanding of the material, which will improve your command of calculus.
What to read next:
- Is Calculus Harder Than Algebra? (Here’s the definite answer!)
- Is A Level Maths Worth It? (Yes! and here’s why)
- Introduction to Logarithmic Functions.
Calculus can be regarded as one of the most important areas of mathematics, despite its degree of difficulty. If you are having trouble with calculus, keep putting yourself in the appropriate direction to get the desired outcomes.
If you do this, you will undoubtedly be able to comprehend theorems associated with calculus in a better light.
Where to start? Check out this course from MIT: Calculus for Beginners and Artists.