In college mathematical analysis, we first learn the basic concepts of real numbers and complex numbers, including the completeness, density and continuity of real numbers, as well as the algebraic and geometric properties of complex numbers. Then learn the concept of limit, including sequence limit and function limit, as well as their properties and calculation methods.
Next, we learn the concept of continuity, including the continuity and discontinuity of functions, as well as the properties and applications of continuous functions. Then, we learn the concept of derivative, including its definition, properties and calculation methods, as well as its application.
In addition, we also learn the concept of differential, including its definition, properties and calculation methods, as well as its application. Then learn the concept of integral, including the definition, properties and calculation methods of indefinite integral and definite integral, and the application of integral.
Finally, we also studied the concept of series, including the convergence judgment method of positive term series and staggered term series, and the convergence judgment method of power series and Fourier series.
In a word, college mathematical analysis covers such important concepts as real number, complex number, function and its limit, continuity, differential and integral, which lays a solid foundation for us to further study advanced mathematics and other disciplines.