Function, Limit and Continuity (1) Function (1) Understand the concept of function: definition, representation and piecewise function. (2) Understand and master the simple properties of functions: monotonicity, parity, boundedness and periodicity. (3) Understanding the inverse function: the definition and image of the inverse function. (4) Master the four operations and compound operations of functions. (5) Understand and master the basic elementary functions: power function, exponential function, logarithmic function, trigonometric function and inverse trigonometric function. (6) Understand the concept of elementary function. (2) Limit (1) Understand the concept of sequence limit: sequence, the definition of sequence limit, and analyze the changing trend of function according to the concept of limit. Will find the left and right limits of a function at a point, and understand the necessary and sufficient conditions for the existence of a function at a point limit. (2) Understand the nature of limit of sequence: uniqueness, boundedness, four operation theorems, squeezing theorem, monotone bounded sequence, limit existence theorem, and master the four operation rules of limit. (3) Understand the concept of function limit: the definition of function limit at one point, the left-right limit and its relationship with limit, and the limit of function when X tends to infinity (x→∞, x→+∞, x→-∞). (4) Mastering the theorem of function limit: uniqueness theorem, squeezing theorem and four operation theorems. (5) Understanding infinitesimal and infinitesimal: the definition of infinitesimal and infinitesimal, the relationship between infinitesimal and infinitesimal, the properties of infinitesimal and infinitesimal, and the comparison of two infinitesimal orders. (6) Master the method of finding the limit with two important limits. (3) Continuity (1) Understand the concept of function continuity: the definition of function continuity at one point, left continuity and right continuity, the necessary and sufficient conditions for function continuity at one point, the discontinuous point of function and its classification. (2) Grasp the continuity of a function at one point: four operations of a continuous function, the continuity of a composite function and the continuity of an inverse function, find the discontinuous point of the function and determine its type. (3) Grasp the properties of continuous functions on closed intervals: boundedness theorem, maximum theorem, minimum theorem and intermediate value theorem (including zero point theorem), and use the intermediate value theorem to derive some simple propositions. (4) Understand that the elementary function is continuous within its defined interval, and use continuity to find the limit. Second, differential calculus (1) derivative and differential (1) of unary function Understand the concept of derivative and its geometric meaning, understand the relationship between derivability and continuity, and use the definition to find the derivative of the function at one point. (2) Find the tangent equation and the normal equation of a point on the curve. (3) Master the basic formula of derivative, four algorithms and the derivative method of compound function. (4) Mastering the implicit function derivative method, logarithmic derivative method and function derivative method determined by parameter equation will find the derivative of piecewise function. (5) By understanding the concept of higher derivative, we can find the n-order derivative of a simple function. (6) Understand the concept of function differentiation, grasp the law of differentiation, understand the relationship between differentiability and derivability, and find the first-order differentiation of functions. (2) Application of Mean Value Theorem and Derivative (1) Understand Rolle Mean Value Theorem, Lagrange Mean Value Theorem and their geometric significance. (2) Master Robida's Law to find "0/0", ∞ /∞, "0? Limit methods of infinitives of type ∞, ∞-∞, ∞+0 ∞, ∞00 and ∞0. (3) Mastering the method of judging the monotonicity of a function by derivative and finding the monotone increase and decrease interval of the function, and proving simple inequalities by increasing and decreasing functions. (4) Understand the concept of function extreme value, master the method of finding function extreme value and maximum (minimum) value, and solve simple application problems. (5) Will judge the convexity of the curve and find the inflection point of the curve. (6) Find the horizontal asymptote and vertical asymptote of the curve. Third, the unary function integral (1) indefinite integral (1) Understand the concepts of the original function and indefinite integral and their relationship, master the properties of indefinite integral, and understand the existence theorem of the original function. (2) Master the basic formula of indefinite integral. (3) Master the first method of substitution and the second method of substitution of indefinite integral (limited to triangular method of substitution and simple radical method of substitution). (4) Mastering the partial integral of indefinite integral. (2) definite integral (1) Understand the concept and geometric meaning of definite integral, and understand the integrable conditions. (2) Master the basic properties of definite integral. (3) Understand that variable upper bound definite integral is a variable upper bound function, and master the calculation method of variable upper bound definite integral derivative. (4) Master Newton-Leibniz formula. (5) Master the substitution integral method of definite integral and partial integral. (6) Understand the concept of infinite interval generalized integral and master its calculation method. (7) Mastering the calculation of plane graphic area by lower integral in rectangular coordinate system. Four. Vector Algebra and Spatial Analytic Geometry (1) Vector Algebra (1) understands the concept of vector, grasps the coordinate representation of vector, and finds the unit vector, direction cosine and the projection of vector on the coordinate axis. (2) Master the linear operation of vectors, and the calculation method of vector product and cross product. (3) Grasp the condition that two vectors are parallel and vertical. (2) Plane and straight line (1) will find the point equation and general equation of the plane. The perpendicularity and parallelism of the two planes will be determined. (2) Find the distance from a point to a plane. (3) By understanding the general equation of straight line, we can find the standard equation and parameter equation of straight line. Make sure that the two lines are parallel and vertical. (4) Determine the relationship between straight line and plane (vertical, parallel, straight line on plane). V. Calculus of multivariate function (1) Differential calculus of multivariate function (1) Understand the concept of multivariate function, the geometric meaning of bivariate function and the concepts of extreme value and continuity of bivariate function (no requirement for calculation). Will find the domain of binary function. (2) Understand the concepts of partial derivative and total differential, and know the necessary and sufficient conditions for the existence of total differential. (3) Master the calculation method of the first and second partial derivatives of binary functions. (4) Mastering the solution of the first-order partial derivative of composite function. (5) Can find the total differential of binary function. (6) Grasp the calculation method of the first partial derivative of the implicit function z=z(x, y) determined by the equation F(x, z)=0. (7) Will find the unconditional extreme value of binary function. (2) Double Integral (1) Understand the concept, properties and geometric significance of double integral. (2) Master the calculation method of double integral in rectangular coordinate system and polar coordinate system. Infinite series of intransitive verbs (1) Numerical series (1) Understand the concept of convergence and divergence of series. Master the necessary conditions of series convergence and understand the basic properties of series. (2) Master the ratio method of positive series. You can use the comparison and discrimination method of positive series. (3) Master the convergence and divergence of geometric series, harmonic series and P series. (4) In order to understand the concepts of absolute convergence and conditional convergence of series, Leibniz discriminant method will be used. (2) Power Series (1) Understand the concept, convergence radius and convergence interval of power series. (2) Understand the basic properties of power series in its convergence interval (sum, difference, item-by-item derivation, item-by-item integration). (3) Master the method of finding the convergence radius and convergence interval of power series (without discussing the endpoints). Seven. Ordinary differential equation (1) First-order differential equation (1) Understand the definition of differential equation, and understand the order, solution, general solution, initial condition and special solution of differential equation. (2) Master the solution of separable variable equation. (3) Master the solution of the first-order linear equation. (2) Second-order linear differential equation (1) Understand the structure of the solution of second-order linear differential equation. (2) Master the solution of second-order homogeneous linear differential equation with constant coefficients.