Chat with our AI personalities
Simple answer: Calculus involves derivation and integration, precal doesn't. Pre calculus gives you some of the algebraic, geometric and trigonometric understanding that is required to comprehend the concepts in calculus. Without the knowledge from precal, calculus would not be easily understood, as it is taught in schools today.
Some high schools have a class called "math analysis" which is before calculus, so yes. To mathematicians, however, "analysis" is a synonym for "modern" calculus, and as such, there are classes usu. taught at universities with a similar name, but far beyond basic calculus.
Usually 12th, but as early as 10th depending on how good your HS math department is and how smart you are.
Once you've completed differential and integral calculus, multivariable calculus is often next step, and beyond that there is advanced calculus which generalizes calc to multidimensional spaces and uses vector-valued functions. Often concurrent with high level calculus in college courses is linear algebra and differential equations. There's nothing really 'after' calculus, because any topic in mathematics has a myriad of problems, theories, and potential applications to be explored. Calculus is, however, normally the highest level of math taught in US high schools and is a basic required course for any science/engineering major in college.
I think by "regular calculus" it is meant simple derivatives and integrations. Regular calculus would be first year calculus probably not including multi-variable calculus or calculus of variations or vector calculus. Wikipedia gives a good explanation of calculus. If you want to sound smart, call it "The Calculus". It is the study of the rate of change (how things change, in relation to other things, often time) In most Universities, regular calculus are the standard analysis of Calculus, concentrating more on the application of it rather than the concept. in comparison is either called "advanced calculus" or in my U, "Honours Calculus" which takes analysis to a whole new level. Both first year course, but the advanced one concentrates on the understanding of concepts, theorems rather than applications alone. It comes in the form of "mathematical proof". Regular Calculus does proofs too, but not as often. --------------------------------------------- Regular calculus is most probably calculus taught in high school or university level, which is simple, mostly single-variable calculus. But then, there are also different calculi called non-Newtonian calculi. These are the non-standard, non-regular calculi, in which different operators are defined. For example, "regular calculus" might mean an additive calculus (where the integral is defined by adding up extremely small pieces), while an integral in multiplicative calculus might involve multiplying infinitely many pieces close to 1.