IMPORTANT COMPOUND ARTICLESTHE CALCULUSDifferential Calculus, (Part I.)Calculus is stupid. Calculus is for extroverts. It’s either totally easy, or you learn calculus. Calculus is about thinking —-wait that’s for philosophers. The origin is a variable. The derivative is the angle of a line —- that’s a small thing somehow, however, isn’t it? The process might be unlimited. Even the opposite mathematics has its limits. It also may have no function. There are no opposites in calculus: there are only functions. Structures are imaginary. Applied calculus is the tough part—for which you have your handy calculator. You can’t be on the side of calculus—- Calculus just IS. One thing to know is that calculus always has a power. If you input zero you get zero, just like in algebra. Advanced concepts in calculus: 1. Everything of value is outside calculus. 2. Maybe +3. 3. Calculus for all integers. That’s just an idea. It’s arbitrary in God’s logic is one of the first things I learned. Even now in calculus there is a division between professors who teach calculus as intuition and those that teach it as pure mathematics. Ultimately there may be more than one way to do calculus but remember, calculus is stupid , or you’re a genius. Towards the end of his life, Leibniz lamented: what’s human about calculus? So, calculus does have a downside. I’ll leave that as a puzzle. Concluding Remarks of the First Lesson Sometimes we think calculus is a disease. Sometimes we think it is not logical at all. But mostly we think it is a highly useful thinking tool. Perhaps you’ll side with the Leibniz who thought it was inhuman, or perhaps you’ll side with the Leibniz who brought it upon himself to invent calculus. Integral Calculus (Part II.)Wrong! Doubly wrong! Specifics don't matter. Form a hypothesis, then throw it away! Apply the existing hypothesis, be conventional. Get it right! It concerns science! Be scientific! Clouds are clocks! Simplify always! Stay distanced from your work. Or pull an Einstein. Know. Philosophy is contraband. The rest is history. Further on antiderivativesADVANCED CALCULUS Posterior Calculus (Part III.)Now, I told you it wasn't about philosophy, but it is! All you need to know at first is Delta V. Whatever you interpret from is analytic a posteriori. Because you know you will get what results—- You have to begin somewhere, so you begin with the effect of an unseen cause. The cause is analytic. Delta V. is when you attach an effect to a cause—-And you call it —- what do you call it? Analytic. The rest is logic… I’m sure you can figure it out. It depends on the case. Applied Calculus (Part IV.)Advanced calculus, also called applied calculus, is summarized by a particular range of modes or conceptual functions: Range: "And other languages besides English" (extending the function). Importance: Bounded or Unbounded, Finite or Infinite. Definition or No Definition. Conditions or Laws (parameters). Identity: special function or no special function. Creativity: "Unless we change the function". Now a concluding remark we might owe to Immanuel Kant: "For every dupe there is something doubtful... For every doubt there is something dutiful." CALCULUS!!! EXTENDED CALCULUSCoherent Calculus (Part V.) My paper on the coherent calculus.General Calculus (Part VI.)My Quora Post on the Polycalculus.Michael's Calculus (Part VII).Calculus --> (Preamble) --> Mathematicians think they're right but they're always wrong --> There's nothing left except to not be right, except to be 'wrong'. Wrong qualified this way is really right, but will never (except rarely) admit it. Examples: We're trying to be fair (integrate) --> (mathematicians are always right) --> Mathematicians are almost always right, but this time they're wrong --> If we integrate, it will disintegrate. This is a disaster. We have to accept the information as we find it.Now we have a new function to map out --> (What are we going to do?) --> We can't try mathematics. We already tried that if we know what we're doing. -->We can do something new with mathematics. Something creative and original. It sounds hopeless. So we just give up, and work where we started.Now, there's something wrong with our data. The equation doesn't match up --> (Is there something wrong?) --> The math can't be wrong unless there's something wrong with the data, right? Wrong! The math can be wrong! --> Well, we can't start over. We have to accept part of the equation is right, because if it's wrong, it's the data that's wrong. But, we must admit, we were completely wrong! That's how to be right. The formula works! Then how did we get it right? --> (Have we thought about this before?) --> We got it wrong A LOT OF TIMES! Remember, mathematicians are always wrong! --> So, this time we got it right! So what! Now we are a mathematician, and now we have to be very careful. We are now fully responsible for everything we do! This is calculus! Sometimes its wrong to be right! You have to feel wrong to get it right! NOTE: This writing is designed to teach "The Intuitive Calculus" and hopefully will jump-start knowledge of calculus, but is BY NO MEANS a standalone guide to calculus. Ownership and use of a textbook as well as academic instruction are critical expectations in developing a real knowledge of calculus, and the significant algebraic and trigonometric aspects have been glossed over in this writing. Hopefully this will make the "Intuitive Calculus" easier to grasp at every level of education than most academic treatments of the calculus, however similar they pretend to be to the Intuitive Calculus. Additional Links on Philosophy of Calculus can be found HERE.For amusement, see also: Ancient CalculusBACK TO SYSTEMS |