D(C)=0(C is a constant), d(xμ)=μxμ- 1dx, d(ax)=ax㏑adx, d(ex)=exdx, d (ax ㏒) =/(x * ㏑.
First of all, calculus
Calculus, the basic branch of mathematics. The content mainly includes function, limit, differential calculus, integral calculus and its application. Function is the basic object of calculus research, limit is the basic concept of calculus, and differential and integral are the limits of concrete process and form.
/kloc-in the second half of the 7th century, British mathematician isaac newton and German mathematician G.W. Leibniz summarized and developed the work of the previous hundred years and established calculus, but their starting point was intuitive infinitesimal, so they still lacked a strict theoretical basis.
/kloc-in the 9th century, A.-L. Cauchy and K. Weierstrass established calculus on the basis of limit theory; In addition, the establishment of the real number theory in the second half of the19th century gave the limit theory a strict theoretical basis, thus perfecting the foundation and thinking method of calculus.
Second, the historical background
The turning point of mathematics is Cartesian variable. With variables, movement enters mathematics; With variables, dialectics enters mathematics; With variables, differential calculus and integral calculus became necessary and came into being immediately, and they were largely completed by Newton and Leibniz, not invented by them. -Engels
From the European Renaissance at the beginning of15th century, the large-scale development of industry, agriculture, navigation and commodity trade has formed a new economic era. The religious reform and suspicion of the imprisonment of the church thought, the introduction of advanced science and technology from the East through Arabia, and the influx of Greek documents into Europe after the collapse of the Byzantine Empire all gave intellectuals at that time a brand-new look.
/kloc-in the 0/6th century, Europe was in the embryonic stage of capitalism and its productive forces developed greatly. The development of production practice puts forward new topics for natural science, which urgently requires the development of basic disciplines such as mechanics and astronomy, which are deeply dependent on mathematics, so as to promote the development of mathematics.