九至十二年级Applied Mathematics课程已上线
Mathematical modelling with functions
The modelling cycle (simplify, formulate, solve, interpret, validate) with linear, quadratic and exponential models of real situations, and honest discussion of assumptions and limitations.
math.applied.modelling-with-functions
前置知识
Exponential and logarithmic functionsQuadratic equations and functionsRatios, rates and proportional reasoning
25 项必需的前置知识（一直追溯到底）
你将学会
- Formulate linear, quadratic and exponential models from situations and data.
- Interpret the parameters of a model and use it to make predictions with stated assumptions.
- Validate a model against data and explain where and why it fails.
定义
- A mathematical model is a simplified mathematical description of a real situation, together with its assumptions.
- Validation compares a model's predictions with observations.
定理
- A quantity growing continuously at rate r doubles every (ln 2)/r units of time.
- Every model leaves out features of reality; it is judged by whether it serves its purpose.
- Extrapolating far beyond the range of the data is risky.
常见误解
- Treating a model's output as fact rather than as a consequence of its assumptions.
- Choosing the model that best fits past data regardless of whether it is plausible.
可选发现
- Mathematical biology Models of populations and epidemics are built from differential equations.
延伸阅读
- Edward A. Bender, An Introduction to Mathematical Modeling (1978)
- COMAP and SIAM, Guidelines for Assessment and Instruction in Mathematical Modeling Education (GAIMME) (2016)