MOOC Scientific Computing and Mathematical Modeling(Central South University)1457998175 最新慕课完整章节测试答案
01 Mathematical Modeling and Error Analysis-Introduction
文章目录
- 01 Mathematical Modeling and Error Analysis-Introduction
- 02 Prediction Model of Urban Water Supply-Interpolation and Fitting Algorithm
- 03 Xiangjiang River Flow Estimation Model—Numerical Integration Method
- 04 Issues of Pension Insurance——Numerical Solution of Nonlinear Equations
- 05 Asteroid Orbit Equation Calculation Problems——Direct method for solving linear equations
- 06 The Regression Problem——Iterative Method for Solving Linear Equations
- 07 Infectious Disease Model——Introduction to the numerical solution of ordinary differential equations
- 08 Analytic Hierarchy Process
- 09 Comprehensive Evaluation of Yangtze River Water Quality
- 10 Statistical Forecast Methods and Forecast Models
Chapter1_Unit test
1、单选题：
1. The approximate value of 0.048657168 with 5 significant digits is________.
选项：
A: 0.04865
B: 0.048657
C: 0.0486
D: 0.0486571
答案: 【 0.048657】
2、单选题：
2. Let the absolute error of data be 0.025 and 0.006 respectively, then the absolute error of the product of is________.
选项：
A: 0.025
B: 0.025
C: 0.025 ＋0.006
D: 0.031
答案: 【 0.025 ＋0.006 】
3、单选题：
3. Suppose that the relative error of is ,then the relative error of is_________.
选项：
A: n*2%
B: 2%
C: n/2%
D: (2%)^n
答案: 【 n*2%】
4、单选题：
4. If the exact value is 100, the absolute and relative errors of the approximate value 99.9 are respectively __________.
选项：
A: 0.1, 0.01
B: 0.1, 0.001
C: 0.01, 0.001
D: 0.001,0.1
答案: 【 0.1, 0.001】
5、单选题：
5. Suppose that the absolute error limits of the observed data x1,x2,x3 are all 0.001，then the absolute error limits of x1+x2+x3 is______.
选项：
A: 0.001
B: 0.003
C: 0.002
D: 0.004
答案: 【 0.003】
6、单选题：
6. Rounding error is the error caused by ___________.
选项：
A: taking only a finite number of digits
B: the exact value of the model and the exact value obtained by numerical method
C: observation and measurement
D: mathematical model exact value and actual value
答案: 【 taking only a finite number of digits】
7、判断题：
The exact solution is the analytical solution.
选项：
A: 正确
B: 错误
答案: 【 错误】
8、判断题：
An algorithm is said to be numerically stable, if there is an error in the input data and the rounding error does not increase during the calculation, Otherwise, it is called unstable.
选项：
A: 正确
B: 错误
答案: 【 正确】
9、判断题：
Simplifying the steps helps reduce the number of operations.
选项：
A: 正确
B: 错误
答案: 【 正确】
10、判断题：
Truncation error is also called method error.
选项：
A: 正确
B: 错误
答案: 【 正确】
随堂测验1
1、判断题：
The process of mathematical modeling includes four processes: expression, solution, interpretation and verification.
选项：
A: 正确
B: 错误
答案: 【 正确】
随堂测验2
1、单选题：
Regarding the measurement of error, which one is inaccurate（）
选项：
A: Relative error
B: Absolute error
C: Percent error
D: Estimation error
答案: 【 Estimation error】
2、判断题：
When the absolute value of the error growth factor is large, after the data error is propagated in the calculation, it may cause a large error in the result. This type of problem where small changes in the original data can cause large changes in results is called a morbid problem or bad condition problem.
选项：
A: 正确
B: 错误
答案: 【 正确】
3、判断题：
In numerical calculations, we don’t need to avoid the following situations: approximate numbers of similar size are subtracted, the absolute value of the multiplier is large, and the divisor is close to 0.
选项：
A: 正确
B: 错误
答案: 【 错误】
02 Prediction Model of Urban Water Supply-Interpolation and Fitting Algorithm
Chapter2_Unit test
1、单选题：
The only condition for the existence of an n-degree interpolation polynomial is that .
选项：
A: it has n nodes
B: it has n+1 nodes
C: there are n interpolation conditions
D: n+1 nodes are distinct from each other
答案: 【 n+1 nodes are distinct from each other】
2、单选题：
The function value of Lagrange interpolation basis function l1(x) at node x0 is l1(x0)= ___.
选项：
A: 1
B: -1
C: 0
D: 2
答案: 【 0】
3、单选题：
The interpolation polynomial _________ with the number of nodes increasing.
选项：
A: increases
B: decreases
C: does not increase
D: may oscillate violently at some points
答案: 【 may oscillate violently at some points】
4、单选题：
For the selection of Newton forward interpolation formula and Newton backward interpolation formula, When the point to be calculated is near the starting point , the Newton______ interpolation formula should be used, When the point to be calculated is near the starting point , the Newton______ interpolation formula should be used.
选项：
A: forward, forward
B: forward, backward
C: backward, forward
D: backward, backward
答案: 【 forward, backward】
5、单选题：
Piecewise low-order interpolation overcomes the problem that high-order interpolation polynomials may oscillate, However, piecewise low-order interpolation function cannot guarantee _________ in the whole interpolation interval?
选项：
A: continuity
B: first derivative exists
C: first-order derivative continuous
D: Second derivative exists
答案: 【 first derivative exists】
6、单选题：
The fitting effect of fitting function is usually estimated without ________.
选项：
A: the sum of deviation
B: average deviation of the sum of the absolute value
C: the sum of squares of deviations
D: mean square error (mse)
答案: 【 the sum of deviation 】
7、单选题：
选项：
A: 2.1
B: 2.2
C: 2.3
D: 2.4
答案: 【 2.4】
8、单选题：
选项：
A: 
B: 
C: 
D: 
答案: 【 】
9、单选题：
选项：
A: -1
B: 0
C: 1
D: 2
答案: 【 2】
10、单选题：
选项：
A: -1
B: 0
C: 1
D: 2
答案: 【 1】
11、单选题：
选项：
A: -24 , -27
B: -12 , -15/2
C: 8, -5/4
D: -8, -11/4
答案: 【 -8, -11/4】
12、单选题：
选项：
A: 
B: 
C: 
D: 
答案: 【 】
随堂测验1
1、单选题：
If n+1 interpolation nodes are different from each other, the n-degree interpolation polynomial that satisfies the interpolation condition.
选项：
A: may not exist
B: exist but not unique
C: exist and unique
D: must not exist
答案: 【 exist and unique】
随堂测验2
1、单选题：
选项：
A: 1, 1
B: 1, 0
C: 0, 1
D: 0, 0
答案: 【 1, 0】
随堂测验3
1、判断题：
Lagrange interpolation polynomials of n + 1 nodes are just different from Newton interpolation polynomials in form and can be simplified to the same expression.
选项：
A: 正确
B: 错误
答案: 【 正确】
2、判断题：
In Newton's fundamental interpolation polynomial, all the difference quotient values had to be recalculated for each additional point.
选项：
A: 正确
B: 错误
答案: 【 错误】
随堂测验4
1、判断题：
The Runge phenomenon occurs because there are not enough interpolation nodes.
选项：
A: 正确
B: 错误
答案: 【 错误】
随堂测验5
1、单选题：
In the interpolation condition of cubic spline function, the maximum value of the （）-th derivative of a given data point can be interpolated at most.
选项：
A: 0
B: 1
C: 2
D: 3
答案: 【 2】
2、判断题：
Cubic spline interpolation only needs to interpolate the node position.
选项：
A: 正确
B: 错误
答案: 【 错误】
03 Xiangjiang River Flow Estimation Model—Numerical Integration Method
Chapter3_Unit test
1、单选题：
选项：
A: 2
B: 4
C: 8
D: 16
答案: 【 2】
2、单选题：
Composite Cotes quadrature formula has the convergence of （）-order.
选项：
A: 2
B: 4
C: 5
D: 6
答案: 【 6】
3、单选题：
When the step size is reduced to half of the original step size by using the composite Simpson quadrature formula, the remainder of the new approximation is approximately of the remainder of the original approximation.
选项：
A: 1/4
B: 1/16
C: 1/32
D: 1/64
答案: 【 1/16】
4、单选题：
选项：
A: 3.015
B: 3.03
C: 3.04
D: 3.06
答案: 【 3.04】
5、单选题：
1. The algebraic precision of Gauss quadrature formula with 3 different nodes is ( ).
选项：
A: 3
B: 4
C: 5
D: 7
答案: 【 5】
6、单选题：
选项：
A: 
B: 
C: 
D: 
答案: 【 】
7、判断题：
选项：
A: 正确
B: 错误
答案: 【 错误】
8、判断题：
The quadrature coefficient of Cotes is independent of the integrand, but related to the interval of integration.
选项：
A: 正确
B: 错误
答案: 【 错误】
9、判断题：
3. The composite quadrature formula is used to avoid the runge phenomenon when the higher order polynomial is used to approximate the original function.
选项：
A: 正确
B: 错误
答案: 【 正确】
10、判断题：
Romberg algorithm is used to speed up the convergence of numerical integrals.
选项：
A: 正确
B: 错误
答案: 【 正确】
11、判断题：
Gauss quadrature formula can be used to improve the algebraic accuracy.
选项：
A: 正确
B: 错误
答案: 【 正确】
12、判断题：
选项：
A: 正确
B: 错误
答案: 【 正确】
随堂测验1
1、单选题：
Which of the following is not necessary for numerical quadrature?
选项：
A: f(x) has a complicated structure, so it's hard to find the antiderivative.
B: The exact expression of f(x) is unknown, and only a table of functions provided by the experiment is given.
C: f(x) cannot be expressed as an elementary function.
D: The antiderivative of f(x) cannot be expressed as an elementary function.
答案: 【 f(x) cannot be expressed as an elementary function.】
2、判断题：
选项：
A: 正确
B: 错误
答案: 【 正确】
随堂测验2
1、单选题：
选项：
A: 1
B: 2
C: 3
D: 4
答案: 【 1】
2、单选题：
选项：
A: -1
B: 0
C: 1
D: 2
答案: 【 1】
3、判断题：
To calculate the cotes coefficient, we need to know the function value and interval of isometric points.
选项：
A: 正确
B: 错误
答案: 【 错误】
4、判断题：
Simpson's formula is also known as the parabola formula.
选项：
A: 正确
B: 错误
答案: 【 正确】
5、判断题：
The algebraic precision of the remainder of trapezoidal formula、Simpson's formula and Cotes formula is an arithmetic sequence.
选项：
A: 正确
B: 错误
答案: 【 错误】
6、判断题：
The so-called composite quadrature, is to divide the integral interval into several small areas, and use the low-order Newton-cotes formula to calculate the integral approximation between each small area, and then sum these approximations, so as to get the integral approximation.
选项：
A: 正确
B: 错误
答案: 【 正确】
随堂测验3
1、判断题：
As an extrapolation method, the Romberg algorithm increases the calculation amount, but also improves the error accuracy.
选项：