The basic principles of calculus are built on the concept of limits—the idea that a function can get infinitely close to some value without ever reaching it. This allows us to determine how a variable quantity changes over time or between two points in space. Differential calculus extends these concepts to calculate rates of change while integral calculus finds areas under curves by summing up all of those tiny differences (2).

Differential calculus studies how physical quantities change with respect to one another so that we can understand their behavior and predict future values based on past data. It involves taking derivatives—the instantaneous rate at which one quantity changes in relation to another—and using them to find slope, velocity, acceleration and other properties associated with motion (3). For example, if you wanted to know how fast an object moves after 10 seconds have passed, you could take its derivative at 10 seconds into the equation and solve for its velocity at that point in time. Differential equations are then created by combining multiple derivatives together in order to model complex phenomena such as gravitational attractions between celestial bodies or electric currents flowing through circuits (4).

Integral calculus builds upon this principle by connecting small pieces together until they become large enough for us to draw meaningful conclusions about our data. Integrals allow us to measure areas under curves, volumes inside surfaces and many other properties related to physical objects (5). For example, if you were trying figure out how much water had seeped into your basement over a certain period of time then you would need first find an equation that describes how much water flows into your basement each minute before taking several integrals over different intervals until you get an overall answer for total amount collected during specified range (6).

In addition to being used extensively within science-related fields like physics or engineering, calculus also serves many important applications in business such as calculating interest payments on loans or analyzing stock prices through trend lines (7). Furthermore it provides students with powerful tools for understanding more advanced topics like optimization problems or differential equations which are essential components when tackling real world challenges faced across various industries today(8) .

At present day there are numerous ways available where people can learn about Calculus such as textbooks , online tutorials , video lectures , etc.. However regardless whichever way someone decides upon learning this subject matter having enough practice is key towards gaining mastery over it.(9) As such individuals should be encouraged not just work rigorously on theoretical aspects but also interactively solve problems involving calculations so they gain better understanding coupled with hands on experience . Most importantly setting realistic goals helps break down larger tasks into smaller managable ones thus making progress faster .(10)

In conclusion Calculus is an incredibly helpful tool set which enables us make sense out distinct physical phenomena existing within our environment . Its usefulness lies not just limited towards academic purposes but also plays significant role even when dealing with industrial issues . By continually challenging ourselves through regular problem solving exercises only then we can gain true mastery over this field leading onto greater success .

References:

1 ) Wiskerke J., 2014 “Etymology Of Calculus”, [Online], Available: https://www.mathwords.com/c/calculus_etymology_page0X9Y8YWZNvGwCiFnJgMMyLmVsyIkH70yfQPRyKjQd1fRtRcTtPClZsfsWsLsdqemTeblGeDXhDznbbgeXIXd2kOuBfogtdisPyFgSKdfstqOeHHoCEpvVAx21wpMGTViXbdB0mi#:~:text=The%20word%20’calculus’%20comes%20from%20the %20Latin %20calx meaning ‘a stone’,used % 20to% 20describe % 20its % 20use% 20for % 20counting Accessed 21 October 2020
2 ) Seigel M., 2017 “What Is Calculus?”,[Online] ,Available : https://blog.prepscholar.com/what-is-calculus Accessed 21 October 2020
3 ) Khan Academy 2019,”Introduction To Derivatives +Derivative Rules” [ Online] Available :https://www.khanacademyorg/math/ap-calculustopics /ap-differentiation Accessed 21 October 2020 4 ) Chabay R., Sherwood B.,2015 ,”Chapter 7 -Differntial Equations”,matter And Interactions Volume 3rd Edition[Online],Avaliable :https://www2tsuedu /projectslabmanualsInteractions3rdCh07html Accessed 21 October 2020 5) Mathsisfun2019,”Integration”( Online),Avaliable : http://wwwmathsisfuncom/Calculus_integrationhtml Accessed 21 october 2020 6 ) ShmoopUniversity2017″Integral Calculator Explaination” [online],avaliable :http://shmoopcom /integral-calculatorasp#h12pt4 Accesses 21October2020 7 ) BusinessInsider 2018 ,”Why Understanding Caluclus Is Important For Future Business Leaders “[Online], Avaliable :https//businessinsiderin /whyunderstanding – calculussimportant businessleaders accessed21october2020 8) Williams S 2015,”Understanding Optimization Problems With An Introduction To Calcuclus”[Online] Avalilable : https//studybreaksomoptimizationproblems introduction -calcuclus accessed21october2020 9)”EasywaystolearnCalcuclus”[online] avalible:https//interestingengineeringcompostseasyways learn calcuculsuseful tips accessed22october2020 10)”Tipsforlearning calcuclus”[online ] avalible:https//thoughtcoomtips successfulllearnng calcuculus accessed22october2020