Basic principles of transformation
(1) Familiarity principle. If the problem is still not solved after the conversion, then the conversion is invalid. For example, "It is known that the values of the function y=(a-b)x+c when x=-5 and x=3 are 3 and-1 respectively. Find the analytical expression of this function. " If the problem is reduced to "solving a ternary linear equation system about A, B and C" by using the undetermined coefficient method.
Then, because this equation group has three unknowns and only two equations, it still cannot be solved, and the result of transformation is not a familiar problem, and the transformation is invalid. However, if it is simplified to "solving binary linear equations with a-b and C as unknowns", because the latter has ready-made solutions, it conforms to the principle of familiarity.
(2) the principle of simplification. That is to simplify complex problems. Or the above example, "when x=-5, x = 3…… ..." itself is a familiar normative problem, and A, B and C can be ignored directly, which makes the conversion easier. It can be seen that the conversion strategy has advantages and disadvantages.
(3) the principle of harmony. That is to say, it is harmonious to transform the expression form of mathematical problems into a unified form that conforms to our understanding. For example, "It is known that x 1 and x2 is the equation x? Two of -5x-4=0, find x 1? The value of x2+4x 1 ",the expression of evaluation is very asymmetric, and it must be converted into x 1+x2 and x 1x2 for power reduction.
Extended data
Main functions of conversion
(1) Guide the learning of new knowledge with transformed ideas. For example, to study the properties of trapezoidal midline, we classify trapezoidal midline as triangular midline to study.
(2) Use the idea of transformation to guide solving problems. For example, decompose the factors within the rational number: 2a? -1/2 using the idea of reduction to construct the application multiplication formula: 2a? - 1/2= 1/2(4a？ - 1)。
(3) Combing the knowledge structure with the idea of transformation. Organize, digest and refine the learned knowledge chapter by chapter, and organize scattered knowledge into an orderly knowledge network. For example, irrational number formula seeks and creates conditions through "denominator of rational number", equation reduces unknowns through elimination, fractional equation is transformed into integral equation through "denominator", or solved through "substitution" distribution, etc.
However, it should be noted that the two problems before and after the transformation are not necessarily equivalent problems, and the solution of the new problem is not necessarily the solution of the original problem, so a judgment needs to be made. For example, when a fractional equation is transformed into an integral equation, the roots may increase, so it is necessary to give up and increase the roots.
Baidu Encyclopedia-Thoughts on Conversion