The term Calculus as we know it today has its origin in the Latin term ‘calculus’ which literally translates to ‘small pebbles’ that were used for calculations and counting, for example on the Abacus.
A crucial part of Mathematics, it is basically the study of constant changes, just like geometry is the study of size and shapes, and algebra is the study of mathematical applications.
Table of Contents
Genesis/Origin:
In the 17th century, two of the brightest minds in the field of mathematics developed this branch of mathematics, which is today used in a number of fields including engineering, science, economics, etc.
These two geniuses were – Isaac Newton, someone who needs no further introduction, and Gottfried Wilhelm Leibniz, the famous German polymath of the time.
Today, Calculus has become a part and parcel of any Mathematical endeavor, and many consider it to be the gateway to more advanced courses in the field of Mathematics.
What are the branches of Calculus?
Calculus as a subject is broadly divided into two sub-categories. One, being differential calculus, which includes the instantaneous rates of change and slopes of curves. The process is commonly referred to as Differentiation.
The other one is integral calculus which includes accumulating quantities and areas under and between the curves. This process is commonly referred to as Integration.
It is interesting to notice that both of these branches are connected to each other by a common thread – the fundamentals of Calculus.
Moreover, both of them use the fundamentals of the meeting of infinite series and sequence to a well-defined limit.
Never the less, there are differences between the two branches!
Stuck on Assignments?
click here for your solution
What is the difference between differential and integral Calculus?
To put it in layman’s term the difference between these branches of Calculus can be very much compared to the difference between squaring a number and finding the square root of a number.
When we square a number and then find the square root of the squared number, then the positive integer of the square root is the value of the squared number.
Similarly, when you integrate the result which you obtained by differentiating a continuous function, it automatically leads to the original function.
Moreover, differentiation calculates the slope while integration calculates the area under the curve.
Therefore, in simple terms differentiation is the opposite process of integration and vice versa!
But there is always the possibility of students of not being able to understand the differences properly. Then you can always use the help of portals like MyMathLab Answers.
What are the applications of Calculus?
There is hardly any branch of physical sciences that does not involve the usage of Calculus.
Here are some of them:
• Computer science
• Engineering
• Economics
• Business
• Actuarial science
• Medicine; and even in demographical calculations.
The main reason for this vast base of applicability of Calculus is for the simple fact that it helps in getting exact answers.
Just check out the sheer number of questions that get posted on online tools like MyMathlab Answer and you will get a clear idea!
How is calculus related to physics?
The most apparent use of Calculus can be seen in Physics where all the concepts of electromagnetism and classical mechanics are connected through Calculus.
Concepts like moment of inertia, mass of an object f fixed density, total energy within a conservative field can all be understood with the use of Calculus.
Differential Calculus can also be found in Newton’s Second Law of Motion, and even Einstein’s Theory of Relativity can be explained with the help of Calculus.
You’d be fascinated to know that it is even used…
In the realm of Chemistry it is considered for determining radioactive decay and in Biology, for figuring out the population dynamics.
It is even used in the field of economics where it allows the figuring out of maximal gain by providing a viable way to calculate the maximal cost and revenue.
It has even found its way of application the vast field of medicine where it can be used for finding the optimal branching angle of blood vessels so that blood can flow unhindered.
It is therefore imperative for students of Mathematics to clearly understand the concepts of Calculus, even if it includes spending on an online tool like MyMathLab Answer.
How can Calculus help you while calculating slopes and velocities?
The revolutionary Italian thinker, Galileo Galilei, took the world by storm when he came up with his investigations of motion, so as to find the velocity of any particular moving particle which is in motion under some law.
And, ever since then the ghost of finding tangents to curves has been haunting scientists from all over the world.
Galileo revolutionized ‘motion’ by figuring out that in t seconds a freely falling body falls a distance of gt2/2 (where g is the gravitational law, as it later came to be known).
Therefore, from here the average velocity from time t to t+h can be deduced to be [g (t+h)2- gt2/2]/h, which in turn simplifies to gt+gh/2 which is a quotient of the function gt2/2.
It was from here that Galileo was able to interpret instantaneous velocity, for as h becomes 0 the formula changes to gt.
This formula again is closely related to the one used for finding slope of the tangent for a parabola f (t) =y=gt2/2.
From a geometric point of view, gt +gh/2 is the slope of a secant line connecting (t, f (t)) to f (t+h)).
Thus, it was Calculus which was ultimately able to create this unique connection between geometry and physics, transforming both of them in the process.
And, you would wonder why so many people take the assistance of portals like take my online class to better understand the complex concepts of Calculus!
But how exactly can a tool like MyMathLab Answer help?
Calculus, an important branch of applied mathematics, although a simple topic to understand for many students, can be a nightmare for other students to fully comprehend the concepts.
And then there is the pressure of finishing assignments on time and passing examinations.
All of this can be intimidating for any student, except for the fact that you are an Einstien or a John Nash!
But how exactly can a tool like MyMathLab Answer help?
Calculus, an important branch of applied mathematics, although a simple topic to understand for many students, can be a nightmare for other students to fully comprehend the concepts.
And then there is the pressure of finishing assignments on time and passing examinations.
All of this can be intimidating for any student, except for the fact that you are an Einstien or a John Nash!
It is here…
…that a tool like MyMathLab Answer helps the student by providing them help with their assignments so that it gets completed on time.
It also helps students to get answers for their quizzes and doubts and helps students with their Calculus homework as well.
Similarly, tools like pay someone to take my online class has come as a blessing to students all over the world as it helps students to cope with the pressure of their syllabus.
However, for the moment let us focus on the proper usage of MyMathLab answer!
Stuck on Assignments?
click here for your solution
Here’s how to use this tool in an efficient way:
• Never delay or postpone your work.
• Complete one assignment before moving on to another one.
• Try referring to different resources.
• Motivate yourself and try to look for real life applications for subjects like Calculus (discussed above).
• Manage to use each second in an efficient way.
• Work only when you feel the desire to do so.
A unique feature of this tool is that it can personalize projects based on a student’s performance.
This helps students to realize their weak spots and guides them to work harder on those specified areas.
What are the benefits of using mymathlab answer?
• Gives students the confidence to do homework and answer quizzes correctly.
• Helps them in getting their desired grades.
• Provides the option of availing the services of others to take tests on their behalf.
• Get correct answers to every question.
Thus if you are having issues understanding Calculus, then MyMathLab Answer is the best possible tool there is that can help you out.
In conclusion…
It needs to be mentioned that although tools like the ones mentioned above can help students to better comprehend a complicated subject like Calculus, it ultimately depends on the students whether he/she has the requisite patience and perseverance to hang on.
But for those who are ultimately able to grasp Calculus has a bright future ahead, as they can apply for a number of different jobs with attractive salary packages.
- Expert Guide On How To Cheat On IXL - September 18, 2024
- 7 Tricks On How To Cheat On A Proctored Exam And Test - September 16, 2024
- How To Get Edmentum Answer Key? - September 9, 2024