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11th grade math 11th grade math differential calculus differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change it is one of the two traditional divisions of calculus the other being integral calculus the primary objects of study in differential calculus are the derivative of a function related notions such as the differential and their applications the derivative of a function at a chosen input value describes the rate of change of the function near that input value the process of finding a derivative is called differentiation geometrically the derivative at a point equals the slope of the tangent line to the graph of the function at that point for a real-valued function of a single real variable the derivative of a function at a point generally determines the best linear approximation to the function at that point differential calculus and integral calculus are connected by the fundamental theorem of calculus which states that differentiation is the reverse process to integration know more about how to factor cubic polynomials tutorcircle.com page no 1/4

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differential equations a differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders differential equations play a prominent role in engineering physics economics and other disciplines differential equations arise in many areas of science and technology specifically whenever a deterministic relation involving some continuously varying quantities modeled by functions and their rates of change in space and/or time expressed as derivatives is known or postulated this is illustrated in classical mechanics where the motion of a body is described by its position and velocity as the time value varies newton s laws allow one given the position velocity acceleration and various forces acting on the body to express these variables dynamically as a differential equation for the unknown position of the body as a function of time in some cases this differential equation called an equation of motion may be solved explicitly an example of modelling a real world problem using differential equations is the determination of the velocity of a ball falling through the air considering only gravity and air resistance the ball s acceleration towards the ground is the acceleration due to gravity minus the deceleration due to air resistance gravity is considered constant and air resistance may be modeled as proportional to the ball s velocity this means that the ball s acceleration which is a derivative of its velocity depends on the velocity finding the velocity as a function of time involves solving a differential equation.differential equations are mathematically studied from several different perspectives mostly concerned with their solutions the set of functions that satisfy the equation learn more how to draw a heptagon tutorcircle.com page no 2/4

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random variable random variable or stochastic variable is a variable whose value is subject to variations due to chance i.e randomness in a mathematical sense as opposed to other mathematical variables a random variable conceptually does not have a single fixed value even if unknown rather it can take on a set of possible different values each with an associated probability a random variable s possible values might represent the possible outcomes of a yet-to-be-performed experiment or an event that has not happened yet or the potential values of a past experiment or event whose already-existing value is uncertain e.g as a result of incomplete information or imprecise measurements they may also conceptually represent either the results of an objectively random process e.g rolling a die or the subjective randomness that results from incomplete knowledge of a quantity the meaning of the probabilities assigned to the potential values of a random variable is not part of probability theory itself but instead related to philosophical arguments over the interpretation of probability the mathematics works the same regardless of the particular interpretation in use random variables can be classified as either discrete i.e it may assume any of a specified list of exact values or as continuous i.e it may assume any numerical value in an interval or collection of intervals the mathematical function describing the possible values of a random variable and their associated probabilities is known as a probability distribution the realizations of a random variable i.e the results of randomly choosing values according to the variable s probability distribution are called random variates tutorcircle.com page no 3/4 page no 2/3

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