High School
Calculus AB - Calculus 1
Calculus BC - Calculus 1 + part of Calculus 2
College:
Calculus 1: Single variable calculus
Calculus 2: Multi-variable Calculus
Calculus 3: Vector Calculus
Calculus 4: Differential Equation
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You must have a strong basis in Algebra, Algebra II, Geometry and Trigonometry. Usually high schools offer a pre-Calculus course which is somewhat of a conglomeration of the aforementioned courses. Then you would move into differential calculus, integral calculus, vector (multi-variable) calculus, and finally differential equations, which is considered to be at the top of the hierarchy of the calculus courses. So take Algebra, Algebra II, Geometry and Trigonometry to get your strong foundation before begining the calculus sequence.
Many, many people have added to calculus, but Newton is generally recognized as having started the western study into it.
Well it depends on which calculus class you are longing for. If you want AB Calculus then you are not required to take pre-calculus; however you must finish all of state's required math courses. Which is probably Algebra, geometry, algebra 2/trig.If you want BC calculus, you need Pre calc and all of the required math classes. BC calculus is a lot more difficult and it will require a lot more time after school. If you are not willing to spend as much time as required , dont dare to take it
Math is fundamental in medicine mainly because of the fact that most things in biology can be calculated with math, such as growth rates and statistics. Calculus is just a core class to provide a foundation to other math courses.
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.