Calculus is by far one of the most overwhelming subjects you can face as a student. It stands in a corner looking menacing without even having to do anything just because of the various numbers and symbols that float around it. It is also one of the more complex branches of math often taught to students at higher grade levels.
Due to the complexity and level of difficulty of this subject, most students dread this subject and have trouble dealing with it. However, calculus is just like any other subject in a sense that you can get better at it with hard work and determination. This article will walk you through what calculus is, what it includes, and how to get better at it. So if you want to improve your grades in this specific subject, then continue reading to find out how.
Calculus is a branch of mathematics that deals with the calculation of integrals and differential equations. This subject often includes more than the standard constants and x and y variables. It also includes symbols such as log, sin, cos, tan, csc, ln, e, cot, and dx which are commonly never used by the regular student for everyday calculations.
These symbols are often found in most scientific calculators but are rarely ever used. However, in the subject of calculus you will learn how to use and solve equations using these symbols.
Higher calculus is often taught in college when a student pursues a course which needs him/her to learn differentials and integrals. However, there are simplified versions taught in high schools as well in order for the students to be introduced to the subject before they go into college and find themselves lost in the subject.
The curriculum may change from school to school, but calculus is generally taught in the span of a year or two and includes 3 major topics which you should master which are:
Derivatives are the slope of a line that lies tangent to a curve at the specific point. This may sound confusing at first but try to imagine a derivative as placing a flat piece of wood on the slope of a hill. Then cut a cross section of that hill and they become a curve and a derivative in a Cartesian coordinate plane.
The hill represents the curve while the piece of wood represents its derivative. You can move the piece of wood at any point of the slope of the hill and it will become that point’s derivative. It becomes more complex as you go on and solve equations but this is the general premise of what derivatives are.
Integrals on the other hand, are kind of like the opposite of the derivative in a sense that it is often called the anti-derivative. Integrals and derivative are known as the fundamental objects of calculus.
An integral refers to a generalization of an area. Think of that cross section of that hill again and imagine drawing a vertical line in the middle of the hill. Now color the right side of that hill and label it as “s”. since we can never calculate the exact area of “s”, we use the integral to give us a rough estimate of the area inside that portion of the curve. That is the general idea behind the integral, or anti-derivative, or primitive, or whatever you want to call it.
Limits are often taught early on in the curriculum as it is simpler than the other 2 previously mentioned but it still takes up a portion of the calculus course. Limits are, as the name suggests, the limit of a function. Plain and easy to understand, right?
In calculus, you will be taught how to calculate for the limits of a function and to determine whether it exists or not. This will be important as functions whose limits do not exist will be found in different areas in the Cartesian coordinate plane and will not make that hill shape which is necessary for you to learn the next topics.
Now that you know what you will be dealing with when you take on calculus, it is now time to discuss how to you can get better at the subject to improve your grades.
The first step to improve your scores and grades in calculus is to understand the basics first. Calculus, like any other branch of mathematics, follows the basic principles of mathematics. PEMDAS is still relevant even in calculus. Basics arithmetic processes and the rule of integers are still relevant even if calculus includes more complex and abstract topics.
It is important to have a proper grasp of the basics and principles of mathematics so that you will have little to worry about when you will solve for problems in calculus. You will have fewer errors when solving problems for calculus as you can focus all of your attention on the new theorems and principles when solving for these problems.
The second thing you should do is listen to the lectures of your teachers when they are discussing calculus and take notes so that you will not forget them. it is important to listen first as most teachers will provide an example about how to solve a problem first before giving you any seatwork or homework. This will allow you to get a general idea of how to solve these kinds of equations and problems.
You can then use your notes to review what the teacher discussed when you have forgotten it. You will also have a written record of how your teacher did the example given so that you will always have something to look back on when you find difficulties solving calculations.
If you feel like your notes are not enough and want a more detailed explanation on the topics at hand, then you can always grab a textbook from your local library or borrow one from someone you know. A textbook will have more examples and a more detailed way of explanation of the topics to make you understand the topics better.
Calculus will introduce you to new theorems which are unique and necessary to solve problems regarding calculus. When solving for limits, you will be introduced to new theorems needed to solve for the limits of an equation. When you will solve for differentials and integrals, different sets of theorems will also be introduced in order for you to arrive at the desired and correct answer.
These theorems will serve as the light that will guide your path towards the correct answer. Without these theorems to guide you, you would be wandering aimlessly without a clear vision of what is the correct answer. It is important to know and master these theorems in order for you to be able to get better at calculus.
Nothing in this world is gained without putting in any effort. This applies for getting better at calculus as well. Without exerting effort and practicing your calculus skills, you will see no significant improvement in your performance and grades.
It is also important to know that it takes a lot of time and effort to improve on something. So, while you are constantly practicing your calculus skills, work on your patience as well. You should understand that practicing vigorously over a short period of time will only tire you out and may cause burnout. You should schedule your review sections in between intervals to make sure you will be able to store what you have learned in your long-term memory.
The people who designed curriculum that you are currently experiencing were working under the presumption that you are a straight A student. Which is why it can often be easy to fall behind in lectures in calculus as it would seem too fast paced for the regular student.
However, you should always try to avoid falling behind from the rest of your class as this will greatly hinder your progress in getting better at calculus. The more time you spend stuck up on a certain topic, the less time you will have to learn the other topics included in the curriculum. This would mean that you would have to put in twice as much effort as before in order for you to catch up and that can be a pretty tiring thing to do.
If you have any queries about any part of the discussion, do not be afraid to ask your professor or teacher about it after class. The teaching staff will be more than happy to explain the bits that you did not understand and will be greatly excited to see a young individual taking his/her studies seriously.
You should not be afraid to approach your professors or teachers as it is their job to teach you and make you understand the topic they teach. You can also learn a few tips from your teachers on how to solve problems quickly which can be really useful during tests.
If you feel like professional help is too much for you to take, then you can consider joining a study group to help you get better at calculus even more. A study group consisting of 3-4 members will make the task of understanding various topics easier as you can assign each person a different topic and they will share what they have learned to the group. This is a great way to juggle both socializing and studying at the same time.
If you prefer someone to help you study that is not your teacher but also want to be taught on a one-on-one basis, then you might want to consider hiring your own private tutor. A private tutor will be able to guide you through the nitty-gritty parts of calculus just as well as a professional teacher while offering their sole attention on you.
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