Applicable form? Basic definition? Action standard? Pay special attention to
2 Econometrics
Problem solving steps? Mathematical thought
1 When comparing two fractions, if the numerator and denominator of one fraction are only a little bigger than the numerator and denominator of the other fraction, it is often difficult to compare the size relationship by "direct division" and "identity method", but the difference method can solve this problem well. Basic Definition Among the two fractions that meet the "applicable form", we define the fraction with large numerator and denominator as "big fraction", the fraction with small numerator and denominator as "small fraction", and the new fraction obtained by dividing the numerator and denominator of these two fractions separately as "difference fraction". For example, 324/53. 1 is compared with 3 13/5 1.7, where 324/53. 1 is "big score" and 313/51. If the difference is greater than the fraction, the fraction is greater than the fraction; 2. If the difference value is less than the small value, the large value is less than the small value; 3. Difference is equal to small points, and big points are equal to small points. For example, "11/kloc-0 instead of 324/53. 1 compare with 3 13/5 1.7" because1/kloc-0. 3 13/5 1.7 (which can be obtained simply by "direct division" or "assimilation"), so 324/53.1> 3 13/5 1.7。 Special attention should be paid to: 1. The "difference method" itself is an "accurate algorithm" rather than an "estimation method", and the obtained size relationship is an accurate relationship rather than a rough relationship; Second, "difference method" and "similarity method" are often used together, and "difference method after similarity method" and "difference method after similarity method" are two situations that are often encountered in data analysis and rapid calculation. Thirdly, direct division is often needed when comparing the difference score obtained by the difference method with the small score. Fourth, if the two scores are very close, we even need to use the "difference method" twice, which is relatively complicated, but if it is skillfully used, it can greatly simplify the calculation. 2 Econometrics editing difference method, a proper term in econometrics, is an effective method to overcome the correlation of related series. It transforms the original econometric model into a difference model and then carries out OLS estimation, which is divided into first-order difference method and generalized difference method (also known as iteration method). Steps to solve the problem: 1. Establish differential equation; 2. Construct a difference scheme; 3. Solve the difference equation; 4. Precision analysis and test mathematical ideas. By using Taylor series expansion and other methods, the derivative in the control equation is discretized by replacing the difference quotient of the function values on the grid nodes, so as to establish the equations with the values on the grid nodes as unknowns. Convert differential problems into algebraic problems. The comparison between large numbers and decimals is 9/5 and 7/4 (9-7)/(5-4) = 2/1 2/greater than1,so 9/5 is greater than 7/4.