Advanced mathematics is a basic subject formed by calculus, algebra, geometry and their intersection. The main contents include: series, limit, calculus, spatial analytic geometry and linear algebra, series, ordinary differential equations. Basic subjects for postgraduate examinations in engineering, science and engineering and finance. Then the adult college entrance examination is upgraded to correspondence advanced mathematics (1): What test sites are there for the integral of unary function?

Knowledge points of advanced mathematics in 2023 adult college entrance examination (1): unary function integral calculus.

indefinite integral

1. knowledge range

(1) indefinite integral

Definition of primitive function and indefinite integral; Existence Theorem of Primitive Function and Properties of Indefinite Integral

(2) Basic integral formula

(3) Substitution integration method

The first substitution method (difference method) and the second substitution method.

(4) Component integration

(5) Integrals of some simple rational functions

2. Requirements

(1) Understand the concepts of original function and indefinite integral and their relationship, master the properties of indefinite integral, and understand the existence theorem of 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) Proficient in the partial integral of indefinite integral.

(5) The indefinite integral of a rational function with one variable can be found.

(2) definite integral

1. knowledge range

The concept of (1) definite integral

Definition of definite integral and its geometric meaning integrable condition

(2) Properties of definite integral

(3) Calculation of definite integral

Variable upper bound integral Newton-Leibniz formula substitution integral method partial integral

(4) Generalized integral of infinite interval

(5) Application of definite integral

The area of a plane figure, the volume of a rotating body, and the work done by a variable force when an object moves along a straight line.

2. Requirements

(1) Understand the concept of definite integral and its geometric meaning, and understand the conditions of function integrability.

(2) Master the basic properties of definite integral.

(3) Understand that the variable upper bound integral is a variable upper bound function, and master the method of finding the derivative of the variable upper bound definite integral.

(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) Grasp the area of the plane figure calculated by lower integral in rectangular coordinate system and the volume of the rotating body generated by the rotation of the plane figure around the coordinate axis.

Will use definite integral to find the work done by time-varying force moving along a straight line.

4. Vector Algebra and Spatial Analytic Geometry

(A) Vector Algebra

1. knowledge range

The concept of (1) vector

The coordinates of the projection vector of the modular unit vector on the coordinate axis represent the direction cosine of the normal vector.

(2) Linear operation of vectors

Multiplication of addition vector and subtraction vector of vector.

(3) Quantity product of vectors

Necessary and sufficient conditions for perpendicular included angle between two vectors.

(4) Necessary and sufficient conditions for two vectors of cross product to be parallel.

2. Requirements

(1) Understand the concept of vector, master the coordinate representation of vector, and find the projection of unit vector, direction cosine and 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 necessary and sufficient conditions for two vectors to be parallel and vertical.

(2) Plane and straight line

1. knowledge range

(1) common plane equation

General equation of point method equation

(2) the positional relationship between two planes (parallel, vertical and inclined)

(3) Distance from point to plane

(4) Spatial linear equation

Parameter equation of standard equation (also known as symmetric equation or point-to-point equation)

(5) the positional relationship between two straight lines (parallel and vertical)

(6) the positional relationship between a straight line and a plane (parallel, vertical and straight lines are all on the plane)

2. Requirements

(1) You can find the point equation and the general equation of the plane. The perpendicularity and parallelism of the two planes will be determined. You will find the angle between two planes.

(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).

(3) Simple quadric surface

1. knowledge range

The spherical generatrix is parallel to the coordinate axis.

2. Requirements

Understand the equations and graphs of spherical surface, cylinder whose generatrix is parallel to the coordinate axis, paraboloid of revolution, conical surface and ellipsoid.

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