Refers to the integral value of the analytic function along the simple closed curve that moves forward arbitrarily around the isolated singularity in the ring domain divided by 2 π i, and the remainder is numerically equal to the coefficient of the negative power term in the Laurent expansion of the analytic function. According to different isolated singularities, different residue calculation methods are adopted. Residue is often used in some special types of real integrals, which greatly simplifies the calculation process of integrals.
Mathematics is a subject that studies concepts such as quantity, structure, change, space and information. Mathematics is a universal means for human beings to strictly describe the abstract structure and mode of things, and can be applied to any problem in the real world. All mathematical objects are artificially defined in essence. In this sense, mathematics belongs to formal science, not natural science. Different mathematicians and philosophers have a series of views on the exact scope and definition of mathematics.