Calculus Help and Definitions

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Calculus is a rigorous and very popular subject. The study of it focuses primarily on limits, derivatives, integrals, and infinite series. It is taught primarily in the college and university levels; however, it has become an optional field of study in the high schools. When taught in high school, it is offered as an advanced placement course. Out of all of the math courses, taking this one is another milestone in your college career, especially if you are planning on pursuing a scientific or engineering type degree. This course contains an extensive sequence about as long as algebra.

Most people who made it through algebra will make it through this if they have to take it. This subject is doable as long as you dedicate the time and practice to it. In any case, if you are not going into a scientific, technical, or engineering type career, I wouldn’t waste my time with this subject.

There are many theorems and functions in this subject. While you will not have to deal with too many definitions, you still will have many theorems and rules so be sure to look through these links and other resources when available.

Calculus Help and Definitions

antiderivative – an integral of a function f is a function F whose derivative is equal to f.

chain rule – is a formula for the derivative of the composite of two functions.

change of variables – occurs in a partial differential equation when it can be reduced to a simpler form with a known solution.

definite integral – is an integral of a function between an upper and lower limit.

derivatives – is the instantaneous change of one quantity relative to another.

differential cal – deals with instantaneous rates of changes.

implicit differentiation – an application of chain rule allowing one to calculate the derivative of a function given implicitly.

indefinite integral – is an integral of a function with no or infinite bounds.

infinite series – is a sum with an infinite number of ordered summands.

integral cal – generalizes summation to find areas, masses, volumes, sums and totals for continuously varying functions.

integrals – is usually used interchangeably with antiderivatives; see definite and indefinite integrals for specific definitions.

limits of a function – is the behavior of a function near a particular input.

matrix cal – contains multivariables that define the matrix derivative.

mean value theorem – given a section of a smooth curve, there is at least one point on that section at which the derivative of the curve is equal to the “average” derivative of the section.

product rule – is the derivatives of products of functions.

quotient rule – is differentiating problems where one function is divided by another.

Riemann sum – a method for approximating the total area underneath a curve on the graph.