Calculus is essentially the collection of geometry, algebra, smarts, and arithmetic - all combined to help solve a greater problem that geometry, algebra, smarts, or arithmetic cannot solve on its own.
So basically, Newton used all of geometry to help developcalculus.
Calculus was already developed centuries ago in ancient China, India, and Egypt.
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Calculus was invented independently by Isaac Newton and Gottfried Leibnitz. Newton did it first and showed the actual usefulness of the discipline by deriving the Law of gravity from astronomical data. Leibnitz however developed a much superior notation and terminology, thus it is actually Leibnitz's calculus that we use today.
how much far do you need of studying?algebra?geometry?algebra2? trigonometry?pre-calculus?What can you do to prepare?
No, you can't. Although similar in concepts, Pre-Calculus is more advanced than Algebra 2. Algebra 2 is taken between Algebra 1 and Geometry or after Geometry and before Pre-Calculus. The reason that you can't take both at the same time is because of the curriculum. Pre-Calculus does not spend nearly as much time on linear topics (linear equations, linear programming, etc.) as Algebra 2 does. Pre-Calculus also almost always is 2 courses in one: Pre-Calculus and Trigonometry. Algebra 2 has very little, if any, trig. Topics that they have in common are quadratics equations/functions, polynomial equations/functions, rational functions, exponential & logarithmic functions (sometimes these are not covered in Algebra 2), possibly conic sections in Algebra 2, definitely in Pre-Calculus, factoring, and probability/sequences/series/statistics. In addition to trigonometry, pre-calculus also covers polar and parametric topics (these will NEVER NEVER NEVER be seen in Algebra 2) and an introduction to limits. So, you must take Algebra 2 before pre-calculus. If you want to take 2 math courses in 1 year, try algebra 1 and geometry (not very common), algebra 2 and geometry (somewhat common), and some schools allow honors students with a solid A in Algebra 2 (assuming you took Algebra 2 before Geometry, this differs between schools) allow you to take geometry and pre-calculus in the same year. The study of proofs is not a major topic in pre-calculus, and proofs make up a majority of geometry.
Infinitesimal calculus pretty much means non-rigorous calculus, i.e. calculus without the notion of limits to prove its validity. When Newton and Leibniz originally formulated calculus, they used derivatives and integrals in the same manner that they're still used today, but they provided no formalism as to how those techniques were mathematically valid, therefore causing quite a debate as to their worth. The infinitesimals themselves simply had to be accepted as valid, in and of themselves, for the theory to work.
Opinion: Calculus is much harder, mostly because of it's complexity. Calculus requires much more formula memorization and ingenuity.