One. Number, limit and continuity

1. Main contents: concept of function, concept of compound function, properties and images of basic elementary function, concept and four operations of limit, properties of function limit, two important limits, existence criteria of limit (squeezing criterion and monotone bounded criterion), comparison of infinitesimal, concept of function connection, discontinuity and basic types, properties of continuous function on closed interval (maximum, minimum, monotone bounded criterion)

2. Key points: the concept of function, the concept of compound function, the concept of basic function, the nature of basic elementary function, the concepts of image and limit, the concept, nature and application of four operations, and finding the limit and continuity of function.

3. Difficulties: the definitions of ∑-N and ∑-δ of the limit, and the equivalent infinitesimal of the limit.

Two. differential of function

1 main contents: the concepts of derivative and differential, derivative and differential, the geometric meaning of derivative, the relationship between function derivative and continuity, and four operations and methods of derivative (complex variable function derivative, implicit function derivative, parameter derivative and higher order derivative). The concepts of Rolle, Lagrange, Cauchy mean value theorem and function mean value theorem are used to judge the monotonicity and monotone interval of a function, and to find the extreme value, inflection point, concavity and convexity, arc differential and curvature.

Emphasis: the concepts of derivative and differential, the geometric meaning and application of derivative, the four operations and solutions of derivative, Rolle and Lagrange mean value theorem and application, the monotonicity of derivative judging function, the polarity, maximum value and inflection point of derivative finding function and judging its concavity and convexity.

3 Difficulties: Find the derivative and study the behavior of the function with the derivative.

Three. Integral calculus of unary function

The main contents and emphases of 1: the concepts and properties of indefinite integral and definite integral, the basic formula of indefinite integral (22), the partial exchange and integration of definite integral and indefinite integral, and the application of definite integral (finding area, volume, plane curve and arc length, variable force work, liquid pressure and gravity) Newton? Leibniz formula.

2 Difficulties: the application of generalized integral definite integral.

Four: Vector Algebra and Spatial Analytic Geometry

1 main content: spatial rectangular coordinate system; Concept and representation of vector, operation of vector (linear, point multiplication, cross multiplication and mixed multiplication), unit vector, direction cosine, coordinate representation of vector, operation of vector and coordinate, angle of vector. Plane equation (point formula, general formula, intercept formula, two-point formula) and basic laws, straight line equation (symmetry formula, parameter formula, general formula) and its solution, surface equation and the concepts of several surfaces, determination of the positional relationship between straight line and plane, and the distance from point to plane.

Emphasis: space rectangular coordinate system, the concept of vector, the operation of vector and its representation in coordinates, plane equation, straight line equation and its solution, several surfaces (ellipsoid, hyperboloid, paraboloid), straight line and the determination of plane position relationship.

Difficulties: cross multiplication of vectors, solving related problems with the positional relationship between plane and straight line, and projection of curves and surfaces.

Five. Differential calculus of multivariate functions.

The main content and emphasis of 1, the concept of multivariate function, the concepts of partial derivative and total differential, and the solution of first-order partial derivative (compound function, implicit function, etc. ), the concept and solution of extreme value and conditional extreme value of multivariate function, the application of directional derivative, gradient and partial derivative (finding the tangent, normal plane, tangent plane and surface of space curve).

2 Difficulties: Derivation of complex function, implicit function and higher-order partial derivative, and finding conditional extreme value.

Six. Multivariate function integral calculus

1 main contents and emphases: the concepts, properties and calculation of double integral and triple integral.

2 Difficulties: the calculation of triple integral.