When you start higher education, your maths classes are going to be different. You will have new topics, a new maths syllabus, more rigorous than the last one you did, and basically more advanced, one of those A level maths is solving calculus.
Calculus is a branch of mathematics that deals with the study of continuous change, it was first conceived of around the mid-17th century by Isaac Newton and Gottfried Leibniz.
In A-level maths, calculus is a fundamental topic that made its way into almost everything. It is divided into two main parts, one known as differential calculus and the other known as integral calculus.
Different methods are used to solve differentiation and integration but they are a part of the same whole, calculus. You may or not come across differentiation and integration in your secondary school, but you will definitely have to take their courses at the university.
All Nigerian universities and higher institutions of learning teach differentiation as part of the maths curriculum. You will most likely be required to study it especially if you want a degree or diploma in a technical course such as engineering or telecommunications.
Both differentiation and integration are used to calculate and solve many maths dilemmas. Like the trajectory of a rocket, or the number of materials needed to build something. Calculus made its way into many fields of sciences and tech, you can find it in school subjects such as physics. It is a crucial component in calculations involving rates of change and infinitesimal numbers.
To solve calculus what you need is a good background in algebra and solid backing from a maths tutor who knows the topic very well.
With the right maths tutor, you can learn A level maths at a speedy rate than most of your course mates, and develop your maths skills in no time. Although if you are feeling bookish you can always go to the library.
Get some textbooks to practice and solve maths. Books on differentiation and integration are always available, for both regular maths and/or A level maths.
A Quick Introduction To Differentiation And Integration
These two mathematical concepts exhibit the power to solve mathematical problems of different types. Since their introduction into our world, differentiation and integration have been of tremendous service to humanity.
Can you imagine what life in Nigeria would look like without the knowledge of these concepts and how to solve them? We will not have the means of building skyscrapers gracing our capital city.
Or the means to build the nice-looking Nnamdi Azikiwe International airport, or to solve any engineering issue for that matter. It would have totally been the dark age.
No one would be able to enjoy the advancements of modern technology without calculus lending its hand to help us accomplish these amazing feats. Our advancement in the computing industry and great achievements in space travel were made possible thanks to solving differentiation and integration theorems.
What Is Differentiation?
Differentiation deals with the rates of change with respect to time or some other value, and when you are calculating it on a graph, you will be calculating the curves and slopes of the graph.
You know how a graph has values on the left hand side in a vertical climb upwards, as you go upwards the numbers climb too. And at the bottom of the graph, you will see a horizontal line with another set of values, from left to right, the numbers increase as you go from left to right.
If the equation of the graph has a negative value, then the graph would have another line running from the zero point from right to left on the horizontal axis, and another one from top to bottom on the vertical axis, dissecting the horizontal axis forming a perfect cross.
When you input the values of the equation of the graph and it forms a curve, then, you can use differentiation to calculate for any point on that curve, to extract an equation that you can solve.
Differentiation has some rules that you can use to solve it. Some questions that have a standard format or that have some characteristics such as ‘raised to a power of’ or exponents have rules that govern them.
For instance, if you have an x3 then there is a simple rule of differentiation that is used to determine its derivative.
What Is Integration?
Integration is used to calculate areas and volumes and many other things, in small proportions that add up to the actual size or value of the shape.
For instance, if you are given a task to calculate the area of a certain map, and the map is separated into grids, about a centimeter square each, it would be much easier if you simply count the grids and add them up to find the whole area of the map, right? That is roughly what integration does.
If we switch to graphs, then integration is used to calculate the spaces under a curve. To find what is known as the integral. That integral is the total opposite of a derivative. So integration is basically the opposite of differentiation.
Numbers in large proportions or ones in small increments that need to be sorted out can be found or calculated with the help of integration.
Interesting Things About Calculus
Just knowing that calculus has something to do with the magnificence of our famous Abuja international airport, that alone should make it really interesting.
So many things rely on the accuracy and powers of calculus, it is amazing that a couple of maths theorems run our economy and finances, tackle our engineering and construction problems, allows us to know the exact point in time something is going to be before it even begins to move.
That is velocity and acceleration. And we can solve complex maths equations and convert them into simple forms, ones we can digest readily and calculate accurately, thanks to differentiation and integration.
Calculus is linked to so many things in our modern world, it is almost in every industry, such as in the aviation industry where calculus has a lot to do with the manufacture of the plane parts.
The complex business of building an aircraft needs calculus to bring together all of the various equations and formulas for lift, pressure on parts, curves and so on before it comes to life.
Calculus in Nigeria serves us well in commerce, we are adept at calculating our revenues, it helps us to have an idea of whether it is going to be a harsh year in the market or a profitable one. If you read the newspapers you will find these types of information all the time, accurately represented.
Isn’t it interesting to know that this is a function of calculus? That it is both directly and indirectly involved in our economics.
Even though in most cases it’s actually a software that runs the equations behind the scenes, now that we have powerful computers. You just input the figures and the values, it does the main solving for you. But still, it is intriguing to know what happens behind the machine.
One of the most interesting things about solving calculus is in calculating things that are not so obvious to us. We all know that when you have four apples and have one more to add to them you will have five apples.
This is obvious, it is easy to visualize and conceptualize an algebraic-type formula for this equation. But calculus allows us to see more, we can calculate the speed and point at which any of the apples would be if it were to fall from a fruit basket.
It is absolutely mind-blowing the things we can do with differentiation and integration, so far, there is no limit to what we can achieve using calculus.
Solving Maths With A Maths Tutor in Nigeria
During your maths A level course in Nigeria, you will study extended versions of topics you knew in maths and learn new ones, you can quickly become overwhelmed by the amount of knowledge you are expected to consume all at once and may need help if you want to pass your courses and Maths A level exams.
Maths A level will push you to the limit, it is better to come prepared.
You can find a maths tutor in Lagos, in Abuja or anywhere else you live within Nigeria if you want extra maths tuition. One of the great things with having a maths tutor is you get to choose your teacher, and you don’t necessarily need someone with a degree and years of experience teaching A level maths before you can start your tuition.
Students in your school of study can help you out, it could be those with a better grasp of the subject among your peers or with the seniors above your level, they can become your A level maths tutors.
Some students relate more with someone their age, so understanding the theorems of calculus won’t be a bother. Although depending on why you need a tutor, you may feel the need to study with someone who has lots of experience, they are more specialized.
Your maths tutor can be of very good use to you by assisting you with your homework, practicing more, and revising for exams. This way, you can reduce the risk of failure and increase your odds of passing your A level maths exams.
Learn the three most important rules of logarithm, and refresh your knowledge on the subject.