数学Ⅰ①(PEAK)

In this course, we study the differentiation and integration of a function of one-variable (which is also called one-variable function or single-variable function). Intuitively, differential means the slope of the tangent line of a function at a given point, and integral measures the area bounded by the graph of the function and x-axis over a given interval. Both concepts need the concept “limit”, so the first part of this course will contain the definition of a function, limit of a sequence, continuous function and related topics. In the second part of this course, we study the differential of a function, the definition, calculation techniques, properties and applications. In the third part, we define the definite and indefinite integral of a function, study the fundamental theorem of calculus: the connection between differentiation and integration, and introduce the calculation techniques. Power series will also be introduced. In the end, we discuss how to solve some simple differential equations.