kalkulust

Kalkulust is not a standard term in mathematics and is most likely a misspelling or transliteration of kalkulus, the word used for calculus in several languages. The intended topic is calculus, the branch of mathematics that studies change and motion through limits, derivatives, integrals, and infinite series. Calculus has two main branches: differential calculus, which focuses on rates of change and slopes of curves, and integral calculus, which concerns accumulation, areas, and antiderivatives. The fundamental theorem of calculus links these two areas by showing that differentiation and integration are inverse processes.

Key notions include limits, derivatives, integrals, and series. Notation such as f'(x) or dy/dx for derivatives, and ∫ f(x) dx for integrals, is standard. Limits describe the value a function approaches as its input nears a point. Derivatives provide instantaneous rates of change, while integrals compute accumulated quantities and, in the definite case, area under a curve.

Historically, calculus was developed in the 17th century by Isaac Newton and Gottfried Wilhelm Leibniz and later refined by many mathematicians, including Cauchy and Riemann. Calculus has wide applications in physics, engineering, economics, biology, and computer science, supporting problems of optimization, motion, growth, and numerical analysis.

In education, calculus is typically introduced in high school or early university and then expanded to multivariable and vector calculus at higher levels. See also calculus; differential calculus; integral calculus; multivariable calculus; numerical methods.