Gaogang 177 1
Outline of Jiangsu Higher Education Self-study Examination
Description of 27054 Engineering Mathematics Examination
Editor of Nanjing University of Science and Technology (20 17)
Jiangsu province higher education self-study exam Committee office
First, the nature and objectives of the course
I. Nature and characteristics of the training course
Engineering Mathematics is an important theoretical basic course for engineering majors, including Probability Theory and Mathematical Statistics and Complex Variable Function and Integral Transformation.
Probability theory and mathematical statistics are mathematical disciplines that study the statistical laws of random phenomena, and are important basic theoretical courses for engineering majors (undergraduates). The quantitative study of statistical regularity of probability random phenomena by probability theory is the theoretical basis of this course. Mathematical statistics studies and processes random data from the perspective of application, establishes effective statistical methods and makes statistical inference. Through the study of this course, students should master the basic concepts, theories and methods of probability theory and mathematical statistics, and have the ability to solve practical problems by using probability statistics methods.
Complex function and integral transformation are important basic theoretical courses, including complex function and integral transformation. Complex variable function is an analysis course to study complex-valued functions of complex independent variables. In a sense, it is the promotion of calculus and becomes a course independently, because it has its own research object and unique processing method. Analytic function is the central content of complex variable function research, residue calculation and its application, conformal transformation are unique problems of complex variable function. Integral transformation is to transform one type of function into another that is simpler and easier to handle. This course introduces Fourier transform and Laplace transform. Integral transformation can be used to solve some integral equations, differential equations, differential integral equations and calculate some real integrals. Through the study of this course, we will lay the necessary foundation for studying engineering mechanics, electrotechnics, electromagnetics, vibration mechanics and radio technology in the future.
Second, the curriculum objectives
The goal of engineering mathematics course;
Through the study of this course, students can understand the basic concepts of probability theory and mathematical statistics, describe random phenomena with the concepts of random events, random variables and their distributions, clarify the relationship between various distributions and numerical characteristics, understand the basic ideas of the law of large numbers and the central limit theorem, and master the principles and applications of data statistical analysis methods such as parameter estimation and hypothesis testing. Learn to effectively collect, sort out and analyze data with random characteristics, infer or predict practical problems, and provide basis and suggestions for taking certain decisions and actions, and have the ability to analyze and process data with random characteristics.
Make students master the basic theory and method of complex variable function, acquire the basic operation skills of complex variable function, deepen their understanding of related problems in calculus, cultivate their ability to analyze and solve problems by using complex variable function method, learn Fourier transform and Laplace transform, and use these two transformations to solve problems in subsequent courses, laying a good foundation for subsequent courses.
Third, the connection and difference with related courses.
This course is closely related to elementary mathematics and advanced mathematics courses, such as elementary probability and statistics in middle school mathematics, derivative and differential of univariate function, definite integral and generalized integral in advanced mathematics, differential calculus of multivariate function, double integral, curve integral, generalized integral with parameters, series and so on. Therefore, it is necessary to review the relevant contents of elementary mathematics and advanced mathematics courses in learning. This course is the basis of studying engineering mechanics, electrotechnics, electromagnetism, vibration mechanics and radio technology. Learn the basic knowledge of this course well and make necessary preparations for future study.
Fourthly, the emphasis and difficulty of the course.
The focus of this course is:
Basic concepts and knowledge commonly used in this course;
In probability theory and mathematical statistics, the probability and calculation of random events, conditional probability, multiplication formula, total probability formula and Bayesian formula;
Distribution law and properties of discrete random variables, distribution function of random variables, probability density and properties of continuous random variables, common distribution (binomial distribution, Poisson theorem; Poisson distribution, uniform distribution, exponential distribution; Normal distribution);
Joint distribution function, joint probability distribution, joint probability density, edge distribution function, edge density function, edge probability distribution and independence of two-dimensional random variables;
Mathematical expectation, variance, covariance and correlation coefficient of random variables; Mathematical expectation and variance of common random variables;
The concepts of population, sample and statistics, and three commonly used distributions in statistics;
Moment estimation, maximum likelihood estimation, unbiased effective estimator; Interval estimation of normal population parameters;
The basic idea of significance test, the steps of hypothesis test, the mean and variance test of normal population.
Complex number and its operation, geometric representation of complex number; Derivative of complex variable function, necessary and sufficient conditions of analytic function; The relationship between analytic function and harmonic function; Exponential function, logarithmic function, trigonometric function, power function; Concept, calculation and properties of complex variable function integral; Cauchy-Gusa basic theorem, compound closed-circuit theorem, Cauchy integral formula, higher derivative of analytic function; Complex series, power series, Laurent series; Residue calculation and its application in definite integral calculation: rotation angle and expansion rate of mapping; Fractional mapping, power function mapping, exponential function mapping; Laplace transform, properties and applications.
Difficulties in this course:
Bayesian formula; Probability density of random variable function; Distribution of random variable function; Edge distribution of two-dimensional random variables; The distribution of the sum of two random variables; The concept of moments of random variables; Three distributions commonly used in statistics; Sampling distribution theorem; Interval estimation of normal population parameters.
Calculation of complex variable function integral: Laurent series expansion; The application of residue in the calculation of definite integral: the comprehensive application of several conformal mappings: Dirac function and its Fourier transform; Application of laplace inverse transform and laplace transform.
Second, the evaluation objectives
In the assessment objectives of this syllabus, the requirements of the ability level to be achieved are stipulated in four levels: memory, understanding, simple application and comprehensive application. The ability of the four levels is rising, and the latter must be based on the former. The meaning of each competency level is:
Memory (1): Candidates are required to know and remember the main contents of relevant knowledge points specified in this course (such as definitions, theorems, laws, expressions, formulas, important conclusions, methods, etc.). ), and make correct statements, choices and judgments according to the different requirements of assessment.
Comprehension (2): Candidates are required to comprehend and understand the connotation and extension of relevant knowledge points stipulated in the syllabus, be familiar with their content points and the differences and connections between them, and make correct judgments and explanations according to the different requirements of the assessment.
Simple Application (Ⅲ): Candidates are required to use several knowledge points specified in this course to solve simple calculation, analysis and demonstration and simple application problems.
Comprehensive application (4): Candidates are required to use multiple knowledge points specified in this course to solve more complicated calculation, analysis, demonstration and application problems.
Click to download: 27054 Examination Outline of Engineering Mathematics (Gao Gang 177 1).
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