(Applicable to architectural engineering major: Correspondence College)
According to the teaching plan, this course is divided into two stages: the first stage: face-to-face teaching for 50 hours, self-study for 1 10 hours; The second stage: 40 hours of face-to-face teaching and 92 hours of self-study.
First, the nature and tasks of the course.
Advanced mathematics is a compulsory basic theoretical course for architectural engineering majors in adult colleges and universities. Through the study of this course, students can master the basic concepts, methods and basic operational skills of advanced mathematics. It will lay the necessary mathematical foundation for future study of follow-up courses and further acquisition of modern scientific and technological knowledge. At the same time, students are trained to have certain analytical ability, calculating ability and self-study ability.
Second, the learning content and basic requirements:
The first stage: "Advanced Mathematics" (1) self-study guide.
Chapter 1: Function Chapter 2: Limit and Continuity
(face-to-face 15 class hours, self-study for 30 class hours)
1. Understand the concept and field of function, master the expression method of function, and establish the function relationship in simple application problems; Understand the parity, monotonicity, periodicity and boundedness of functions; Understand the concepts of compound function and elementary function. Familiar with the properties and graphics of basic elementary functions.
2. Understand the concepts of sequence limit and function limit, the concepts of left limit and right limit of function, and the necessary and sufficient conditions and uniqueness of function limit; Four algorithms to master the limit; Know two criteria for the existence of limit and master two important limits; Understand the concepts of infinitesimal and infinity and their relationship, know the order and properties of infinitesimal, and use equivalent infinitesimal to find the limit.
3. By understanding the concept of function continuity, we can distinguish the types of function discontinuity points; Knowing the continuity of sum, difference, product and quotient of continuous functions, and knowing the properties of continuous functions on closed intervals, we will prove the existence of the roots of the equation by using the intermediate value theorem.
Chapter III Derivative and Differential
(face-to-face 10 class hours, self-study 20 class hours)
1. Understand the concept of derivative, the geometric meaning of derivative, find out the tangent equation and normal equation of plane curve, understand the concept of left and right derivatives, know the necessary and sufficient conditions for the existence of derivative at one point, be familiar with the derivative laws of four operations of function, the derivative laws of compound function and inverse function, master the derivative formula of basic elementary function, master the solution of first and second derivatives of elementary function, and find the n-order derivative of simple function. Can find the derivative of implicit function, can use logarithmic derivative method, can find the derivative of parametric function,
2. Understand the definition of differential, the geometric meaning of differential and the relationship between derivative and differential. The relationship between differentiability and differentiability.
Familiar with differential formula and differential operation rules, know the invariance of differential form, and use differential to make simple approximate calculation.
3. Master the differential algorithm and use differential to find the approximate value of the function.
The fourth chapter is the application of the mean value theorem and derivative.
(face-to-face 10 class hours, self-study 20 class hours)
1. Know Rolle Theorem, Lagrange Theorem and Cauchy Theorem. Familiar with L'H?pital's law, you will find the limit of indefinite form.
2. Understand the concept of extreme value of function, master the method of judging monotonicity of function and finding extreme value of function with derivative, and find the maximum and minimum value of simple application problems with derivative.
3. Can judge the concavity and convexity of the function curve, find the inflection point of the function curve, find the horizontal and vertical asymptotes, and make graphs of simple functions.
4. Knowing the concepts of curvature and radius of curvature, we can calculate curvature and radius of curvature.
Chapter V Chapter VI Definite Integral and Indefinite Integral
(9 hours for face-to-face teaching and 25 hours for self-study)
1. Understand the concepts of original function and indefinite integral, and know the properties of indefinite integral. Familiar with the basic integral formula, master the integral method of indefinite integral, the integral method of substitution and integration by parts.
2. Understand the concept of definite integral, know the properties of definite integral, know the upper limit integral of variable and its derivative theorem, and master the basic formula of calculus (Newton-Leibniz formula).
3. The integral method of partial substitution has mastered definite integral, understood the concepts of two kinds of generalized integral, and can find simple generalized integral.
Chapter VII Application of Definite Integral
(6 hours in person, self-study 15 hours)
1. Understand the differential element method of definite integral.
2. We can use infinitesimal method to calculate the area of some simple plane figures and the volume of the rotator, and we can find out the arc length of the plane curve.
3. Simple variable force work and liquid pressure problems can be solved by differential element method of definite integral.
The second stage: Advanced Mathematics (II) Self-study guide book
Chapter 8: Vector Algebra and Spatial Analytic Geometry
(face-to-face 10 class hours, self-study 20 class hours)
1, understand the concept of vector, master the linear operation of vector, the scalar product and cross product of vector, understand the concept of spatial rectangular coordinate system, find the distance between two points in space, be familiar with the coordinate expressions of vector, vector modulus, direction cosine and unit vector, master the vector operation with coordinate expressions, and know the included angle formula and parallel vertical conditions of two vectors.
2. Be familiar with point equation and general equation of plane, point equation, parameter equation and general equation of straight line, and solve plane and straight line equations according to conditions.
3. Understand the concept of surface and its equation, the equation of cylindrical surface whose generatrix is parallel to the coordinate axis, the equation of rotating surface (including conical surface) with the coordinate axis as the rotation axis, the spatial curve and its general equation, and several commonly used quadric surfaces and their geometric figures.
Chapter 9 Differential calculus of multivariate functions
(face-to-face 10 class hours, self-study for 30 class hours)
1, understand the concept of multivariate function and know the geometric meaning of binary function. Understand the concepts of limit and continuity of binary function, know the continuity of binary elementary function in its definition domain, and know the properties of continuous function in bounded closed region.
Understand the concepts of partial derivative and total differential, know the necessary and sufficient conditions for the existence of total differential, find the partial derivative and total differential of elementary function, know the derivative law of multivariate composite function, find the second-order partial derivative of elementary function, know the condition that the mixed partial derivative of binary function has nothing to do with derivative order, and find the derivative of implicit function.
3. To understand the concept of extreme value of binary function, we can find the extreme value of binary function, tangent equation and normal plane equation of space curve, tangent equation and normal plane equation of surface. Understanding the concept of conditional extremum will solve some simple application problems of maxima and minima.
Chapter 10, Chapter 11: Integrals of Multivariate Functions.
(face-to-face 10 class hours, self-study 20 class hours)
1, understand the concept and properties of double integral, master the calculation method of double integral in rectangular coordinate system and polar coordinate system, and use double integral to calculate the volume, mass and centroid of plane thin plate.
2. Understand the concept of arc length and coordinate curve integral, know the properties of these two kinds of curve integral, master the calculation methods of two kinds of surface integral, know the conditions that Green's formula and curve integral have nothing to do with path, and then calculate curve integral by using Green's formula and irrelevant conditions.
Chapter 13 Ordinary differential equations
(face-to-face 10 class hours, self-study 22 class hours)
1. Understand the concepts of differential equations and differential equations, such as order, solution, general solution, special solution and initial conditions.
2. Master the solutions of differential equations of separable variables and first-order linear differential equations.
3. Two kinds of reduced higher order differential equations can be solved.
4. Understand the structure of general solutions of second-order linear homogeneous and nonhomogeneous differential equations, and master the solution of second-order linear homogeneous differential equations with constant coefficients. Freedom will be required as follows