1. Differential calculus of unary functions.
1, understand the concept of function and know the representation of function; Will find the domain and function value of a function.
2. Grasp the parity, monotonicity, periodicity and boundedness of the function.
3. Understand the definitions of compound function and inverse function, and you will find the inverse function of monotone function.
4. Grasp the properties and images of basic elementary functions and understand the concept of elementary functions.
5. Understand the concept and nature of limit and master the algorithm of limit.
6. Understand the concepts of infinitesimal and infinitesimal and their relationship, and master the nature and comparison of infinitesimal.
7. Understand pinching Criterion and Monotone Bounded Criterion, and master two important limits:
8. Understand the definition of function continuity and discontinuity, understand the classification of function discontinuity points, use continuity to find the limit and judge the type of function discontinuity points.
9. Understand the boundedness theorem, maximum theorem and intermediate value theorem of continuous functions on closed intervals, and use the above theorems to derive some simple propositions.
10, understand the definition and geometric meaning of derivative, and find the derivative of function according to the definition.
1 1. Understand the relationship between differentiability and continuity of functions.
12, master the derivative formula of basic elementary function, the four operation rules of derivative, the derivative rule of compound function, the derivative rule of implicit function, the derivative rule of logarithm, the derivative rule of parameter equation, and understand the derivative rule of inverse function.
13, understand the concept of higher derivative, and master the solution of the first and higher derivatives of elementary functions.
14. Understand the definition of differential, the relationship between differentiability and differentiability, four differential algorithms and the invariance of first-order differential forms; You can find the differential of a function.
15. Understand Rolle Theorem, Lagrange Theorem, Cauchy Theorem and Taylor Theorem. Rolle theorem will be used to prove the existence of the roots of the equation, and Lagrange mean value theorem will be used to prove some simple inequalities.
16, master the law of lobida to find the limit of indefinite formula.
17. Understand the concept of extreme value of function and the necessary and sufficient conditions for the existence of extreme value.
18, will find the monotone interval and extreme value of the function, will find the maximum and minimum value of the function, will solve some simple application problems, and will prove some simple inequalities.
19, understand the definition of concave-convex function and curve inflection point, and find the concave-convex interval of function and curve inflection point.
20, will find the asymptote of the curve, will describe some simple function graphics.
Second, the integration of unary functions.
1. Understand the concepts and properties of primitive function and indefinite integral.
2. Master the basic formula of indefinite integral.
3, master the variable integral method and integration by parts of indefinite integral.
4. Understand the definition of variable upper-bound integral function and master the method of derivative of variable upper-bound integral function.
5. Understand the concept and geometric meaning of definite integral, and master the basic properties of definite integral.
6. Master Newton-Leibniz formula and substitution integral method of definite integral parts.
7. If the infinitesimal method of definite integral is mastered, the area of the plane figure and the volume of the rotating body of the plane figure rotating around the coordinate axis can be obtained.
8. Understand the concepts of generalized integral of bounded function on infinite interval and loss integral of unbounded function on finite interval, and master their calculation methods.
3. Vector Algebra and Spatial Analytic Geometry.
1. Understand the concepts of space rectangular coordinate system and vector, master the coordinate representation of vector, and find the modulus and direction cosine of vector.
2. Master the linear operation of vector, the calculation method of vector quantity product and cross product, and understand its geometric meaning.
3. Master the conditions that two vectors are parallel and vertical.
4. Point equation, general equation and intercept equation of plane can be solved. The positional relationship between two plane can be determined.
5. Knowing the general equation of a straight line, we can find the symmetry (point-to-point) equation and parameter equation of the straight line. Will determine the positional relationship between two straight lines.
6. Determine the positional relationship between the straight line and the plane.
Fourth, multivariate function calculus.
1. Understand the concept of binary function, and you can find the domain of some simple binary functions.
2. Understand the limit, continuous definition and basic properties of binary functions.
3. Master the solution of the first and higher order partial derivatives of explicit functions.
4, will find the extreme value of binary function, will use Lagrange multiplier method to find the conditional extreme value.
5. Master the solution of total differential of binary function.
6, master the calculation method of double integral.
Fifth, differential equations.
1, understand the definition of differential equation and the concepts of order, solution, general solution and special solution.
2. Proficient in solving differential equations, homogeneous differential equations and first-order linear differential equations of separable variables.
3. Understand the properties of the solution of the second-order homogeneous linear differential equation with constant coefficients and the structure of the general solution.
4. Master the solution of second-order homogeneous linear differential equation with constant coefficients.
Six, infinite series
1. Understand the concept of convergence and divergence of infinite series.
2. Understand the necessary conditions of series convergence and the main properties of series.
3. Know the convergence and divergence of geometric series.
4. Be familiar with the ratio discrimination and comparison discrimination of positive series.
5. Understand the definition of convergence radius, convergence interval and convergence domain of power series.
6. Master the method of finding the convergence radius, convergence interval and convergence domain of power series.
Seven, linear algebra.
1, understand the concept of determinant and master its properties.
2. Master the calculation of determinant.
3, will use the Cramer rule.
4, master the linear operation and algorithm of matrix, matrix multiplication and algorithm.
5. Understand the concept and judgment rules of invertibility of square matrix, and master the method of finding the inverse of invertible matrix.
6. Understand the concept of matrix rank and master the method of finding matrix rank.
7. Can solve simple matrix equations.
8, master the elementary transformation of matrix.
9. Master the judgment conditions and structure of homogeneous linear equations with non-zero solutions, and master the judgment and structure of non-homogeneous linear equations.
10, master the solution of linear equations.
Eight, probability theory is preliminary.
1, understand the concept of random events, and master the relationship and operation between events.
2. Understand the statistical definition of probability, master the basic properties of probability and the addition formula of probability.
3, master the calculation formula of classical probability, you will find the probability of some events.
4. To understand the concept of event independence, we can use the independence of events to calculate the probability.
5. Understand the concept of random variables and find the distribution of some simple random variables.
6. Understand the concepts of mathematical expectation and variance of random variables, master the basic properties of mathematical expectation and variance, and find the mathematical expectation and variance of some simple random variables.
* Note: The requirements for theories and concepts in this syllabus are, from high to low: understanding, cognition and understanding; The requirements for methods and calculations from high to low are: mastery, mastery and knowledge.