The contents of advanced mathematics include: function and limit, differential calculus of univariate function, integral calculus of univariate function, analytic geometry of space, differential calculus of multivariate function, integral calculus of multivariate function (multiple integral and curve and surface integral), series (polynomial series, power series and Fourier series), differential equation and preliminary field theory (gradient, divergence and curl).

Generally speaking, advanced mathematics is a combination of simple calculus, probability theory and mathematical statistics, as well as in-depth algebra and geometry.

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Specific: function and limit, derivative and differential, application of derivative, indefinite integral, spatial analytic geometry, differential calculus of multivariate function, integral calculus of multivariate function, ordinary differential equation, infinite series.