十堰职业技术学院《高等数学》课程组（College of higher mathematics, shiyan vocational college of technology）

十堰职业技术学院《高等数学》课程组（College of higher mathematics, shiyan vocational college of technology） 十堰职业技术学院《高等数学》课程组(College of higher mathematics, shiyan vocational college of technology) 2. Key points and difficulties Key points: function, limit and continuous concept, function limit operation; Difficulty: the concept of mathematical model, the concept of limit of function, the method of the limit of piecewise function. (2) derivative and differential (10 hours) 1. Teaching content and basic requirements Grasp the concept of derivative and differential; To understand the derivative and the geometric meaning of differentiation; Function differentiable, differentiable and continuous relationship; Using derivatives to describe the rate of change in some actual problems; Master the basic formula of derivatives and derivatives; To understand the concept of higher derivative, the n-th derivative of the order; To understand the first derivative of the implicit function and the parametric function. 2. Key points and difficulties Key points: the concept of derivative and differential; The operation of derivatives and derivatives; Difficulty: describe the rate of change in some actual problems with derivative (3) the application of the value theorem and the derivative (12 hours) 1. Teaching content and basic requirements To understand the differential mean value theorem, we can use l 'hopital's rule to find the limit; The method of discriminating the monotonicity of the function and the method of the extremum of function, grasping the test of the concave of the curve and the turning point of the curve; Can describe the simple function of the graph, grasp the simple maximum and the minimum value of the application question. 2. Key points and difficulties Key points: the discrimination of function monotonicity, the method of extreme value, the most value application. Difficulty: the most valued application of a function. (4) indefinite integral and definite integral (24 hours) 1. Teaching content and basic requirements To understand the concept and nature of indefinite integral and definite integral; Proficient in the basic formula of indefinite integrals, skilled in the first class substitution integration method and integration method by integration of indefinite integrals and definite integrals; Understanding of rational function with trigonometric functions, rational expression of integral will check list, understanding is a function of variable upper limit definite integral of variable upper limit, mastering Newton leibniz formula, understand the concept of improper integral, will also have a simple improper integral; Master the basic concept of definite integrals, master the microelement method of definite integrals, and use the microelement method to find some geometric quantities and physical quantities; The general solution structure of linear differential equations with constant coefficients is understood. To understand the concepts of differential equations, order, solution, general solution, initial conditions and special solutions. The solution of differential equations of separable variables and first order linear differential equations are obtained. The second order constant coefficient homogeneous linear differential equation solution. 2. Key points and difficulties Key points: the concept of indefinite integral and definite integral; The calculation of indefinite integral and definite integral, first class substitution method; Newton - leibniz formula; The area of the plane figure, using the definite integral of the microelement method to calculate the geometrical quantity and physical quantity; The differential equations of separable variables and the solutions of first order linear differential equations. Difficulty: indefinite integral concept; Indefinite integral calculus. Variable limit integral; Improper integral of unbounded function; The geometrical quantity and physical quantity to be calculated are expressed by definite integral. The solution of first order linear differential equation and second order constant coefficient homogeneous linear differential equation. (5) multivariate function differential (10 hours) 1. Teaching content and basic requirements Understand the necessary and sufficient conditions for full differential existence; The concept of conditional extremum; To understand the concept of multivariate functions; The limit of binary functions and the concept of continuity; The concept of partial derivative and total differential; The concept of extremum of binary functions; I will take a second derivative of the second derivative of a function of two variables; The partial derivative of the complex function and the implicit function; The tangent equation for the curve. 2. Key points and difficulties Emphasis: the second derivative of the second order partial derivative; To find the partial derivatives of complex functions (abstract functions not required) and implicit functions; The tangent equation of the curve; Difficult points: partial derivatives of complex functions and implicit functions. (6) double integral (4 hours) 1. Teaching content and basic requirements To understand the nature of double integrals; To understand the concept of double integral; The calculation method of double integrals (rectangular coordinates, polar coordinates); The double integral is used to calculate some geometric quantities (volume, surface area) and some simple physical quantities (quality, center, etc.). 2. Key points and difficulties Key point: master the calculation method of double integral (rectangular coordinates, polar coordinates). Difficult points: the double integral can be used to calculate some geometric quantities (volume, surface area) and some simple physical quantities (quality, center, etc.). (7) infinite series (8 hours) 1. Teaching content and basic requirements To understand the convergence, divergence and convergent series of infinite series; The necessary conditions for the convergence of series and the basic properties of infinite series; The convergence of the geometric series and the P series; The concept of absolute convergence and conditional convergence of infinite series; Relationship between absolute convergence and convergence; Some basic properties of power series in its convergence interval; To understand the concept of radius of convergence of power series; Grasp the convergence radius of simple power series and the method of convergence interval (the convergence of the endpoint is not required); The basic properties of the Maclaurin series expansion and power series are used to extend some simple functions into power series. 2. Key points and difficulties Key points: grasp the convergence of geometric series and P series; Grasp the convergence radius and the convergence interval of simple power series. Difficult points: the basic properties of the Maclaurin series expansion and power series are used to extend some simple functions into power series. (viii) application of MATLAB in calculus (4 hours) 1. Teaching content and basic requirements MATLAB software introduces and its application, the student union USES MATLAB software to solve the limit of function, function's derivative, function's integral and the extreme value of the one yuan function. 2. Key points and difficulties Key points: MATLAB software is used to find the limit of function, function's derivative, integral of function and the extreme value of the unitary function. Difficult: MATLAB application. (9) determinant and matrix (14 hours) Teaching content and basic requirements The definition of the NTH determinant; The nature of the determinant and the calculation of the determinant; Learn about cramer's rule. Familiar with linear operation of matrix, multiplication operation, transpose operation; To understand the concept of inverse matrix and its necessary and sufficient conditions; A method for the inverse matrix of second - and third-order matrices - adjoint matrix method. To understand and grasp the concept of elementary transformation of solution matrix; To understand the concept of elementary matrix and the relationship between elementary transformation and elementary matrix. Skillful grasp of inverse matrix - initial transformation method; Familiar with the rank and property of matrix, and familiar with the rank of matrix - elementary transformation method. 2. Key points and difficulties Emphasis: the definition of the n-th determinant; The operation of the matrix, the inverse matrix, the elementary transformation of the matrix, the rank of the matrix. Difficulty: the basic calculation method of the determinant; The rank of the inverse matrix and the matrix. (10) linear equations (16 hours) 1. Teaching content and basic requirements To understand the concept of n dimensional vector, to master the linear operation of vectors; To understand the linear correlation, linear independent definition and relevant important conclusions of vector group; To understand the rank of the maximum independent group and vector group in vector group, to understand the relationship between the rank of matrix and the rank of vector group, and master the rank of vector group with elementary transformation; To understand the concept of basic system, master the method of solving the general solution of linear equations. To understand the discrimination theorem of solution of linear equations; To understand the concept of general solution, master the method of solving the general solution - elementary transformation method. 2. Key points and difficulties Key points: the concept of vector, the rank of vector group, the theory and solution of linear equation solution, and the method of fundamental solution Difficulty: correlation of vector group; The basic solution method. (11) random events and their probabilities (8 hours) 1. Teaching content and basic requirements Random events and the sample space, frequency and probability, the relationship between events, event operations and the nature of the independence of the events, the basic properties of probability, classical subscheme, geometrical scheme, conditional probability, the formula of addition, multiplication formula of full probability formula and Bayes formula (Bayes theorem), independent random test. Asked the students on the basis of understanding the relationship between events, use of permutation and combination of knowledge, mastering the classical subscheme, repeated independent test probability calculation, and the nature of the application of probability, full probability formula and bayes formula and probability calculation formula of binomial probability. 2. Key points and difficulties Key: the independence of the operation properties and events, the probability of the basic properties of the sample space and the sample points, conditional probability, full probability formula and bayes formula and binomial probability formula, the formula of addition, multiplication formula. Difficulties: classical generality, full probability formula and Bayes formula, independent randomization test. (12) distribution and numerical characteristics of random variables (8 hours) 1. Teaching content and basic requirements The concept of random variables and their distribution functions, discrete random variables and their distributions, continuous random variables and their distributions, the independence of random variables. Basic properties of mathematical expectation, variance, standard deviation and calculation method, the mathematical expectation of stochastic variable function, distribution of several common (binomial distribution, poisson distribution, uniform distribution and normal distribution) of the expectation and variance. The concept of discrete random variable and its probability distribution is understood, and the distribution of Poisson and its application are mastered. Understand and master the concept of continuous random variables and probability density, grasp the relation between probability density and distribution function, and master the uniform distribution, exponential distribution, normal distribution and application. Students are required to master the above key points and understand the difficulty of this chapter, namely the distribution of random variable functions. Know the digital features of random variables (expectation, variance, standard deviation, covariance and correlation coefficient) of the concept and calculation, and using numerical characteristics of specific properties to calculate the distribution of digital features, to master the distribution of common digital features. 2. Key points and difficulties Key: the random variables and their probability distribution, the concept of random variable distribution function and its property, the probability distribution of discrete random variable, continuous random variable of probability density, common the probability distribution of random variables: the binomial distribution, poisson distribution, uniform distribution and normal distribution, the distribution of random variable function. Basic properties of mathematical expectation, variance, standard deviation and calculation method, the mathematical expectation of stochastic variable function, distribution of several common (binomial distribution, poisson distribution, uniform distribution and normal distribution) of the expectation and variance. Difficulties: uniform distribution, normal distribution, distribution of random variable functions. The mathematical expectation and variance of the random variable function. (13) preliminary statistics (8 hours) 1. Teaching content and basic requirements General, individual, simple random sample, statistic quantity, empirical distribution function, sample mean, sample variance. The concept of point estimation and interval estimation, the interval estimation of a single normal population mean. Let's say that the basic idea of the test, the mean of a single normal population and the hypothesis of variance. Unitary nonlinear regression, multivariate linear regression. Understand and grasp the overall, a simple random sample, the concept of statistics, the sample mean and variance, master and able to skillfully use normal population sampling distribution (standard normal distribution, distribution, t, and F). It is important to understand the point estimation of parameters, the mean of single normal population and the confidence interval of variance. To understand the basic thought of hypothetical test, grasp the basic steps of hypothesis testing, and grasp the hypothesis testing of the mean and variance of a single normal state. This paper focuses on the basic idea and basic method of unary linear regression analysis and the nonlinear regression problem that can be reduced to a linear regression. 2. Key points and difficulties Key points: understand and master the sampling distribution of normal population (standard normal distribution, distribution, t distribution, F distribution). The mean of the single normal population and the confidence interval of the variance. Understand the basic thought of hypothetical test, grasp the basic steps of hypothesis testing, and grasp the hypothesis test of the mean and variance of a single normal state. The basic idea and basic method of unitary linear regression analysis can be used to evaluate the unknown parameters in the regression equation. Difficulties: the application of the sampling distribution of normal distribution (standard normal distribution, distribution, t distribution, F distribution). The mean of the normal population and the confidence interval of the variance. The basic idea of hypothetical test, the basic step of hypothesis testing Understanding. The nonlinear regression problem can be reduced to a linear regression. (14) the application of MATLAB in linear algebra and probability statistics (4 hours) 1. Teaching content and basic requirements MATLAB software introduces and its application, the student union USES MATLAB software to carry on the matrix algebra operation, solving linear equations, solving linear programming problem; The probability density function, parameter estimation and hypothesis testing are calculated using MATLAB software. 2. Key points and difficulties Main points: MATLAB software is used to calculate the matrix algebra, solve linear equations, solve linear programming problem; The probability density function, parameter estimation and hypothesis testing are calculated using MATLAB software. This document is personally spent years, collected and sorted, carefully selected! Difficult: MATLAB application. Vi. Description 1. Features or teaching characteristics of the course Mathematics comes from practice and serves practice, so this course teaching characteristic is: close close professional course on problem solving teaching and daily life, and not just pure mathematics teaching, give priority to with application, the principle of necessary, for sufficient degree, reducing complex theory proof and mathematical calculation. 2, relationships with other courses. Economic mathematics is the foundation of various specialized courses of financial management, and many economic management problems can be abstracted into mathematical problems and finally solved by mathematical ideas and methods. Therefore, the economics and mathematics management classes of the major courses. 3. Use teaching materials and reference books Selection of teaching materials: Economic mathematics, China higher education society Editor: rich science education press "Calculus" Chinese higher education education mathematics professional committee Chief editor: bai su-eng-lv offers wuhan university press "Linear algebra and probability statistics" China higher education education mathematics professional committee Editor: the university of wuhan university press, China Teaching reference books: Foundation of economic mathematics, China higher education society Chief editor: hou incident science education press The editor of calculus: zhao shuo, Chinese people's university press (revised) Editor of linear algebra: zhao shu-wei, renmin university of China press (3rd edition) "Probability theory and mathematical statistics" editor: zhao shu-li, Chinese people's university press (revised) The chief editor of linear algebra: bai suying liaoning university press 4. Assessment and grading methods Take the assessment method which is combined with the final examination. Routinely include assessment of homework, ask questions, to speak in class and mathematics open-ended questions, such as writing a small paper is used for solving the problem of an application) appraisal, peacetime grades (30%), the final exam (70%). The examination should be strictly required, and the class of the same teaching plan should be carried out in the same teaching plan 5. Teaching methods and Suggestions In the course of teaching, starting from the training goal of higher vocational education, properly handle the systematicness of the subject "and" "for the purpose of application, as required, for sufficient degree", the relationship between The comprehensive realization of higher mathematics curriculum as an important basic course teaching basic requirements. At the same time, we should pay attention to the link of the relevant course, to grasp the concepts, strengthen the application, and develop the skills to focus on the teaching. To combining with the characteristics of the teaching content to cultivate the habit of students independent learning, to pay attention to the arrangement of recitation and selection of homework, so that the students can timely and correctly completed homework independently. At the same time, we must pay attention to train students' innovation ability, transform practical problems into mathematical models and improve students' ability to solve mathematical models through elective courses in mathematics. Another, or to explore suitable for higher vocational education characteristics and requirements of teaching methods, pay attention to the application of modern teaching means, play the enthusiasm of both teaching and learning, and improve the teaching quality and teaching efficiency, within the prescribed period range, the implementation of guarantee outline. The basic requirements of teaching are divided into three levels: the concept and theory of understanding, understanding and mastery; The operation method and the skill according to "basic mastery or energy, will", "master", "mastery" to grasp. When implementing an outline, we should carefully study the ability level requirements of different levels, earnestly achieve the grading teaching, and grasp the teaching quality. Teaching hours distribution ordinal Teaching content school The lecture recitation seminar one The function, the limit, the continuous 12 10 2 2 Derivatives and derivatives 10 8 2 3 Application of derivatives 12 10 2 4 Indefinite integrals and definite integrals 24 20 4 5 Differential calculus of multiple functions 10 8 2 6 Double integral 4 4 0 7 Infinite series 8 6 2 8 MATLAB is applied in calculus 4 4 0 9 Determinant and matrix 14 12 2 10 System of linear equations 16 14 2 11 Random events and their probabilities 8 6 2 12 Distribution of random variables and their numerical characteristics 8 6 2 13 Preliminary statistics 8 6 2 14 MATLAB is used in linear algebra and probability statistics 4 4 0 subtotal 142 118 24 Vii. Achievements in teaching reform (teaching research topic and research paper) 1. Teaching research topic (1) the college students' ideological and moral character "courses" teaching reform of the research on theory and practice of corpus "lesson" participation "type < > of economic mathematics in higher vocational colleges teaching the application research of 2005.12 (in) (2) research on the application of research-based teaching in the teaching of economic mathematics Research project of humanities and social sciences in the higher vocational college of education department of heilongjiang province (3) the construction and exploration of high mathematics quality courses Heilongjiang new century higher education teaching reform project project 2007.12 (host) (4) the construction of a harmonious relationship between teachers and students in higher vocational colleges Heilongjiang new century higher education teaching reform project project 2007.12 (participation) (5) research on the application of "appreciation of education" in economic mathematics teaching in higher vocational colleges Institute of higher education of heilongjiang province (in research) (host) (6) "practical research on improving the teaching quality of economics mathematics" by using the "research class" model The key project of the 11th five-year plan of education science in heilongjiang province Research on the theory and practice of improving teaching quality in universities by using new courses (in research) (7) tourism demand forecast of applied neural network Research project of humanities and social sciences in the higher vocational college of education department of heilongjiang province (in research) (participation) 2. Teaching research paper (1) the study on improving academic achievement methods (independence) Financial management and teaching (journal of financial management and teaching) 2003 (1) (2) teaching research on simplified form of plane beam equation (author) Financial management and teaching (journal of financial management) 2004 (2) (3) philosophical thinking on the function of calculus education (two authors) Financial management and teaching (journal of financial management) 2005 (1) (4) "strengthening basic knowledge teaching and focusing on students' ability to educate themselves" (independent) "Finance theory and teaching" (journal of "harkin") 2007 (2) (5) it is necessary to pay attention to the arithmetic roots in derivatives and integrals (independent) China education research group, 2007.9 (6) exploration and thinking on the construction of high vocational college advanced mathematics courses (author) Journal of the education college in heilongjiang province, 2007.10 (7) "preliminary study on teaching model of economic mathematics" (author) "Finance theory and teaching" (journal of Harvard University) 2007. (4) (8) "the construction of mathematical intensive courses in higher vocational college" (two authors) "Finance theory and teaching" (journal of Harvard University) 2007. (4) (9) guidance on learning methods for students in teaching (independent) China science and technology information 2007 (23) (10) comparison of four methods of calculation (independent) "The practice and understanding of mathematics" 2008.2 (11) "building a harmonious atmosphere, highlighting appreciation of education" (an author) "Finance theory and teaching" (journal of harkin) 2008.2 (12) the application of the shallow research teaching model in the teaching of economic mathematics. Heilongjiang river, 2008.6 Viii. Student evaluation 1. Students of the accounting department are qiao yu-han and qi zhe; Finance department 04 undergraduate zhu yunpeng, cao hao Higher mathematics teaching, we find everything new and fresh, university teachers is different from primary and secondary school teachers, teacher's teaching humor, more can make the students' learning interest, to students and teachers are also very responsibility, is not as previously heard of that university teachers make "suckers" finished class, coupled with the teacher's lecture quality is above reproach, the teacher took us into a strive to explore, top area. After class, I also tutored the poor students, and the exercise books were also full of red, which clearly pointed out our mistakes and corrected them. 2. Class 07.2 students guo zhenping, gong jie and Chen bo The lecture is meticulous and patient, the blackboard is neat, the classroom rhythm is reasonable, the difficulty of the homework and the examination paper is explained well, the classroom strengthens the communication with the student, makes the class atmosphere harmonious. A list of academic achievements Su-ying bai (1) discussion on improving the method of achievement of poor students (independent) Financial management and teaching (journal of financial management) 2003 (1) (2) teaching research on simplified form of plane beam equation (author) Financial management & teaching (journal of financial management and teaching) 2004 (2) (3) philosophical thinking on the function of calculus education (two authors) Financial management and teaching (journal of financial management) 2005 (1) (4) strengthening basic knowledge teaching and focusing on students' ability to educate themselves. (independent) "Finance theory and teaching" (journal of "harkin") 2007 (2) (5) "in the derivatives and integrals, you should pay attention to the roots" (independence) China education research group, 2007.9 (6) exploration and thinking on the construction of high vocational college advanced mathematics courses (author) Journal of heilongjiang education college, 2007.10 (7) "preliminary study on teaching model of economic mathematics" (author) "Finance theory and teaching" (journal of Harvard University) 2007. (4) (8) "the construction of mathematical intensive courses in higher vocational college" (two authors) "Finance theory and teaching" (journal of Harvard University) 2007. (4) (9) guidance on learning methods for students in teaching (independent) China science and technology information 2007 (23) (10) comparison of four methods of calculation (independent) "The practice and understanding of mathematics" 2008.2 (11) "building a harmonious atmosphere, highlighting appreciation of education" (an author) "Finance theory and teaching" (journal of harkin) 2008.2 (12) the application of the shallow research teaching model in the teaching of economic mathematics. Heilongjiang river, 2008.6 This document is personally spent years, collected and sorted, carefully selected!