Applications Of Integrals: Fill & Download for Free

If you want to learn Calculus. You should follow the order below.FunctionsLimitsContinuityDifferentiationApplication of Derivatives i.e. DifferentiationIntegrationApplication of IntegrationDifferential EquationsAnd also you should have good knowledge about Trigonometry , Algebra and Logarithms.

Try to understand this subtle topic.The first sentence of my Physics book is this,Mathematics is the language of Physics.Well, when I first heard about the word involute and evolute (In curves) which turns out to be used in making Gear profiles, or the time when I heard about solving complex Electrical resistor problems using simple methods from Matrices, or the time when I saw how to apply Integrations in Thermodynamics(I won’t get into it), or to understand how markets and economics work based on some function and you can predict the future which doesn’t sound true, all of this sounded pretty confusing in the start.But I bet you’ll gain a much broader sense of understanding if you keep doing what you are doing because you are trying to find out why, which as many eminent personalities have stated that, it is the right way to life.One must understand that, Mathematics is the hidden key to understand what is happening behind the scenes of a problem.If you learnt that,[math]\displaystyle\int \dfrac{1}{\sqrt{x^2+a^2}}\, dx = log|x+\sqrt{x^2+a^2}| + C[/math]Please try to understand what does it mean in every single way. (Be it graphical, analytical, or in your point of vision of the world)And now try to use it in every single way possible. It’ll unleash the thinking power in you.Let me pass you a quote given by a great Physicist, Engineer, Inventor.The day science begins to study non-physical phenomena, it will make more progress in one decade than in all the previous centuries of its existence.- Nikola Tesla.Try reading evergreen Math books like Calculus by Thomas Finney or Advanced Eng. Mathematics by Erwin Kreyszig. I won’t ask you more, just do these two books and you’ll understand the beauty of Calculus.It is like the backbone of the structure of the whole Universe so subtly placed that you don’t notice it.It is like the Superhero which wears a mask and saves people.Some fields in Physics where Calculus is used are Heat, Fluid flow, Potentials, Fields, String equations, wave equations, Laplacians, Vibrations in Circular membranes and so on…Simple examples -Your phone is running because of some Calculus,Your fan is running because of AC which is a form of Calculus,air conditioners work on the heat flow principles which involve Calculus,Your bike’s engine is working on the principles of conversion of energy from chemical to heat to mechanical which needed a way lot more Calculus than you imagined,You travel in planes which are created on the principles of Aerodynamics whose key concept would again be Calculus,Your ironing boxes, bulbs might have had some Calculus induced in them before they are in front of you.Okay, this proves it. Every machine made thing/item required a machine. But Calculus is used to design those machines. So basically, it is goddamn EVERYWHERE!(It’s like “Tum jis school mein padhte ho, main us school ka headmaster hun”English - Calculus says: The school in which you are studying, I’m the principal of it.)What about the fields of Chemistry, Economics, Biology, Geology, or any other ‘logy’ in which Calculus is used?You have been taught the basics of all these Mathematics, which are the rules of the game called Life. How do you apply them is pretty simple. Take something you understand and put in these cool equations and do magic.The scientific man does not aim at an immediate result. He does not expect that his advanced ideas will be readily taken up. His work is like that of the planter —for the future. His duty is to lay the foundation for those who are to come, and point the way. - Nikola Tesla.Do you know any of these influential people like Newton, Erwin Schrödinger, Faraday, Gauss, Feynman, Nikola Tesla, Werner Heisenberg, Curie, Poisson, APJ Abdul Kalam, CV Raman, Bose, Vikram Sarabhai?Do you think they came out without mathematics on their fingertips?These people aren’t with us anymore (sad but we have to accept it).But what about the future? Is this it? No more inventions? No more creations? No more new theories? No more development?How are we going to play this better than those who already did?This is why you are being taught about the basics of Calculus. Who knows if you could be the next Einstein? You may not feel like it, but that’s the true purpose of teaching you these.Next time someone asks you about the importance/applications of Calculus in day to day life, get the shit out of him.Have a great day!Note 1: I’m a little bent towards physics examples only, please excuse me for that.Note 2: The books mentioned above are to be understood and solved to gain complete expertise on the subject. Mere memorizing the stuff won’t help you in any way.Note 3: Please study to improve yourselves and not for examinations. Let them go bad but you need to get what you need to.

basically 5 chapter comesch-5 continuity and differentiabilitych-5 application of differentiationch-6 integralsch-7 application of integralsch-8 differential equation