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What is calculus in layman terms?
Calculus is a branch of mathematics that involves the study of rates of change. Calculus helped to determine how particles, stars, and matter actually move and change in real time. Calculus is used in a multitude of fields that you wouldn’t ordinarily think would make use of its concepts.
Why is calculus called calculus?
In Latin, calculus means “pebble.” Because the Romans used pebbles to do addition and subtraction on a counting board, the word became associated with computation. Calculus has also been borrowed into English as a medical term that refers to masses of hard matter in the body, such as kidney stones.
What have you learned in basic calculus?
In basic calculus, we learn rules and formulas for differentiation, which is the method by which we calculate the derivative of a function, and integration, which is the process by which we calculate the antiderivative of a function.
What is the difference between stochastic calculus and ordinary calculus?
The fundamental difference between stochastic calculus and ordinary calculus is that stochastic calculus allows the derivative to have a random component determined by a Brownian motion. The derivative of a random variable has both a deterministic component and a random component, which is normally distributed.
What are the applications of stochastic calculus in finance?
In quantitative finance, the theory is known as Ito Calculus. The main use of stochastic calculus in finance is through modeling the random motion of an asset price in the Black-Scholes model. The physical process of Brownian motion (in particular, a geometric Brownian motion) is used as a model of asset prices, via the Weiner Process.
Are stochastic processes always differentiable?
Many stochastic processes are based on functions which are continuous, but nowhere differentiable. This rules out differential equations that require the use of derivative terms, since they are unable to be defined on non-smooth functions.
What is real-valued calculus and how do you do it?
Real-valued calculus, the type that you know as an advanced freshman undergrad, concerns itself with solving extremes: where on an interval is the function f ( x) at a minimum or maximum.