待定系數法（Dài dìng xì shù fǎ）

Pronunciation: dài dìng xì shù fǎ

Basic Meaning: undetermined coefficient method

Detailed Explanation: The undetermined coefficient method is a mathematical technique used to solve non-homogeneous linear differential equations. It involves assuming a particular form for the solution and determining the coefficients by substituting the assumed solution into the equation.

Usage Scenarios: The undetermined coefficient method is commonly used in solving differential equations with non-constant coefficients, especially when the equation is non-homogeneous.

Story Origin: The undetermined coefficient method was first introduced by mathematician Joseph Fourier in the early 19th century. He developed this method as a way to solve differential equations with non-constant coefficients.

Structure of the Idiom: 待定 (undetermined) + 系數 (coefficient) + 法 (method)

Example Sentences:

1. 待定系數法是求解非齊次線性微分方程的一種常用方法。

(Dài dìng xì shù fǎ shì qiú jiě fēi qí cǐ xiàn xì wēi fēn fāng chéng de yī zhǒng cháng yòng fāng fǎ.)

The undetermined coefficient method is a commonly used technique for solving non-homogeneous linear differential equations.

2. 我們可以利用待定系數法來求解這個復雜的微分方程。

(Wǒmen kěyǐ lìyòng dài dìng xì shù fǎ lái qiú jiě zhè ge fù zá de wēi fēn fāng chéng.)

We can use the undetermined coefficient method to solve this complex differential equation.

Memory Techniques:

1. Associate the phrase "待定系數法" with the image of a mathematician holding a set of coefficients that are waiting to be determined.

2. Break down the phrase "待定系數法" into smaller parts and create a story or mnemonic using each part to help remember the meaning and pronunciation.

Extended Learning:

1. Further explore the applications of the undetermined coefficient method in other areas of mathematics, such as partial differential equations.

2. Study other methods used to solve non-homogeneous linear differential equations, such as variation of parameters method.

Example Sentences from Different Age Groups:

1. Children: 我用待定系數法解了一個數學問題。

(Wǒ yòng dài dìng xì shù fǎ jiě le yī gè shù xué wèn tí.)

I solved a math problem using the undetermined coefficient method.

2. Teenagers: 我們在數學課上學習了待定系數法的應用。

(Wǒmen zài shù xué kè shàng xué xí le dài dìng xì shù fǎ de yìng yòng.)

We learned about the application of the undetermined coefficient method in our math class.

3. Adults: 待定系數法是解決非齊次線性微分方程的重要方法之一。

(Dài dìng xì shù fǎ shì jiě jué fēi qí cǐ xiàn xì wēi fēn fāng chéng de zhòng yào fāng fǎ zhī yī.)

The undetermined coefficient method is one of the important methods for solving non-homogeneous linear differential equations.