The contents of double integral in advanced mathematics include its definition and geometric physical significance, its calculation with geometric significance, its basic properties, the basic method of calculating double integral with rectangular coordinates, the basic method of calculating double integral with rotational symmetry, the basic method of calculating double integral with polar coordinates, and the mutual transformation between polar coordinates and rectangular coordinates.

The projection method and cross-sectional area method for calculating triple integral are briefly introduced. The substitution formula of triple integral and the review of cylindrical coordinate system and spherical coordinate system are briefly introduced. The method and typical examples for calculating triple integral with spherical coordinate system are given. The solid volume is calculated with double integral, the surface area is calculated with double integral, the area of plane figure is calculated with double integral, and the gravity of objects to particles, the concept of centroid and the coordinate formula of centroid are calculated with double integral.

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In most cases, the solution of multiple integrals depends on transforming multiple integrals into a series of unitary integrals, and each unitary integral is directly solvable.

For triple integration, the integrand function can be regarded as density, which is the three-dimensional mass in space. Imagine that everyone cuts potatoes, which is equivalent to transforming the triple integral into the "definite integral" of three repeated integrals; Imagine slicing bread again, which is equivalent to converting triple integral into definite integral and double integral.

For double integrals, the integrand can be regarded as density, which is the mass of a plane region. Imagine the common fried cake, and you can see that the double integral is transformed into the repeated integral of two "definite integrals".

Baidu Encyclopedia-Multiple Integral