Articles tagged with calculus

1. Differential Equations

   A differential equation (DE) connects a function with its derivative(s). In calculus, the function 𝑦⁡(𝑥) is known, and its derivative, 𝑦′⁡(𝑥), needs to be found. In differential equations, the derivative, 𝑦′⁡(𝑥), is known, and the function, 𝑦⁡(𝑥), needs to be identified. As with indefinite integration in calculus, the solution will throw up one or more arbitrary constants. The values of these constants must be determined by the initial conditions provided in the problem in order to obtain a unique solution.

2. From Calculus to Analysis: Limits

   At high school you were taught how to integrate and differentiate. You were exposed to all sorts of tricks and special techniques—such as the chain rule for differentiation, and integration by parts for integration. If you revelled in mastering and applying such techniques, you might find that what succeeds high school calculus, is a horse of an entirely different colour, called analysis, at university.