e-Learning Mathematics

We will introduce most of these formulas over the course of the next several sections. We will start in this section with some of the basic properties and formulas. We will give the properties and formulas in this section in both “prime” notation and “fraction” notation. Formulas

L'Hospital's rule is the definitive way to simplify evaluation of limits. It does not directly evaluate limits, but only  simplifies evaluation if used appropriately . In effect, this rule is the ultimate version of ‘cancellation tricks’, applicable in situations where a more down-to-earth genuine algebraic cancellation may be hidden or invisible. 3 Steps of L'Hôpital's rule

There are two  different types  of  calculus .  Differential calculus  divides things into small ( different ) pieces and tells us how they change from one moment to the next, while integral  calculus  joins (integrates) the small pieces together and tells us how much of something is made, overall, by a series of changes.

Integration vs Differentiation  Integration and Differentiation are two fundamental concepts in calculus, which studies the change. Calculus has a wide variety of applications in many fields such as science, economy or finance, engineering and etc. Differentiation Differentiation is the algebraic procedure of calculating the derivatives. Derivative of a function is the slope or the gradient of the curve (graph) at any given point. Gradient of a curve at any given point is the gradient of the tangent drawn to that curve at the given point. For non linear curves, the gradient of the curve can vary at different points along the axis. Therefore, it is difficult to calculate the gradient or the slope at any point. Differentiation process is useful in calculating the gradient of the curve at any point. Another definition for derivative is, “the change of a property with respect to a unit change of another property.” Let f(x) be a function of an independent variable x. If a small

In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data. Integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function  f  of a real variable  x  and an interval  [a, b]  of the real line, the definite integral {\displaystyle \int _{a}^{b}f(x)\,dx} is defined informally as the signed area of the region in the  xy -plane that is bounded by the graph of  f , the  x -axis and the vertical lines  x  =  a  and  x  =  b . The area above the  x -axis adds to the total and that below the  x -axis subtracts from the total. The operation of integration, up to an additive constant, is the inverse of the operation of differentiation. For this reason, the term  integral  may also refer to the related notion of the antiderivative, a function  F  whose derivative is the given function  f . In this case,

In  mathematics , a  matrix  (plural:  matrices ) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. ... There is no product the other way round, a first hint that  matrix  multiplication is not commutative. Any  matrix can be multiplied element-wise by a scalar from its associated field. There is a video lecture for understanding matrix well.