Calculus is one of the branches of Mathematics that contains derivatives, limits, functions, and integrals.
It is a very important part of Mathematics, and for many students, it is quite hard to master.
However, there are certain study practices you can adopt that will help you get a better grasp of this complicated subject.
The tips given below will help you formulate a better approach to mastering calculus.
1. Learn (or revise) basic mathematic principles.
Calculus is related to other parts of Mathematics, so learning such things as arithmetic, trigonometry, algebra, and geometry will help you understand calculus better.
It is recommended to start with basic arithmetic and try to understand all arithmetic operations at first.
In algebra, you have to learn about the word problems, be able to understand basic properties as well as the basics of sets.
2. Learn (or revise) basic formulas.
Integrals and derivatives have some underlying formulas which you need to understand. In addition, each formula in calculus has its own proof.
You need to understand the formula and understand the proof as well. Do not just try to blindly memorize the formula without realizing how it can be applied.
3. Be patient. Mastering calculus takes time.
Everybody is capable of learning calculus, but some students fail to do it because they are unwilling to spend enough time on it.
The time that is required to master calculus depends on the grade you want to get in the end, how smart you are, and on how difficult the course is.
If you want to earn grade A, you have to put in at least 2 hours every weeknight and approximately 6 hours over the course of the weekend.
If you cannot devote more than 10 hours a week to calculus outside of your classroom, you shouldn't expect to get stellar results.
4. Whatever you do, do not fall behind.
If you get behind on your classwork or homework, it will be hard for you to catch up with your classmates.
The people who designed the calculus course operated under the assumption that the students who are going to attend the course are quite smart, and they have been successful in all of their previous mathematical studies.
For this reason, the pace of the course is quite brisk, and you need to put in the effort to keep up.
It is recommended to work as hard as you can for the first month, and at the end of it, look back at your achievements and evaluate the situation.
5. Do not skip any classes.
A good calculus teacher in Maths will explain all the necessary techniques and make sure that the ideas are clear. If you miss even one class, it will be hard for you to gain that knowledge somewhere else.
The teacher explains how ideas in mathematics are strung together, and enables you to reach logical conclusions; the teacher does all of that by using the calculus vocabulary, which is essential for you to hear. Even if you are behind on your homework, come to class anyway.
If you cannot catch up with your peers on your own, ask your teacher (or your classmates) about tutoring or counseling. Alternatively, you can ask one of your smarter classmates to help you out after school.
6. It is better to do your homework in a study group.
In order to comprehend the ideas better and be motivated to do your homework, you can form a small study group with your classmates.
According to one study, those students who form study groups and do their homework together are much less likely to drop out of calculus class and much more likely to get A or B.
Ideally the group will consist of 3 to 5 students, and you can meet up with your group two or three times a week for a few hours.
When you are in your study group, use mathematical language, trade tips, and you can also cram for the upcoming test.
7. An effective way to use mathematics textbooks.
Good textbooks should help you understand techniques and concepts, gain an understanding of the material to help you develop your techniques, and give you the opportunity to review the previous material.
The first phase of working with the book is called the exploratory phase.
Try not to underline anything or highlight anything at this stage as you don't yet understand the difference between vital information and minor detail.
Just read a section and see what problems are discussed.
Examine the pictures, read the definitions of the problems. If something looks interesting to you, follow the explanation, but if something looks too complicated, you can skip it for now.
8. Mastering Calculus
The next stage is the so-called mastery stage. During this stage, you must go through the section in detail.
Read the introduction, all of the examples, explanations, theorems as well as proofs. If you come across an example or the explanation that you do not understand, you can put a question mark next to it and move on to the next one, come back to it later when you have more knowledge and confidence.
Once you have understood the bulk of the textbook, go back to the questions you have marked and try to solve the problems.
If you still do not understand how the problem should be solved, you can ask your teacher, your tutor, or one of your classmates for help. As for the nature of the problems, some of them will require you to remember all concepts. Others will require you to combine old concepts with the new ones.
Practice makes perfect, so if you're constantly trying to solve new problems in calculus, you are getting closer and closer to mastering it.