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Answers for “为什么在数学建模中假设和近似是必要的?”

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Assumptions and approximations are necessary steps in mathematical modeling used to simplify complex real-world problems so they can be represented mathematically, without losing the core essence of the problem.

Conditions: Applied during the transition from a real-world problem to a mathematical model

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Analytical methods involve finding exact solutions using algebraic or calculus techniques, whereas numerical methods involve approximating solutions using algorithms and computation.

Conditions: Applicable to mathematical problems derived from real-world scenarios.

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A real-world problem requiring mathematical modeling is optimizing the cutting of seed potatoes. If cut too small, the seed is not viable; if cut too large, good seed is wasted.

Conditions: The problem involves optimization under constraints.; Manual methods are inefficient or impossible.

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Mathematical modeling is the process of translating a real-world problem into a mathematical model by making specific assumptions and approximations while still capturing the essence of the original problem.

Conditions: Must start with a real-world problem; Must result in a mathematical model; Requires making assumptions and approximations