[Mathematical model modeling note 1]

1, prototype and model (duality body)
  Prototype: refers to people in the real world care, research or actual objects production and management of (the object actually exists)
  model: refers to a particular part of the purpose of the prototype information retrieval , constructed refined prototype substitute
  a prototype according to different purposes, have different model
 
2, model classification
  material model (avatar model): explicit model (physical), physical model (according to similar principles of construction) or the like
  over the model (abstract model): mental model, symbolic model, the mathematical model (mathematical symbols describe the real objects), etc.
 
3, the mathematical model
  for some purpose, to the reality of a specific object, in accordance with its inherent laws, to make some simplifying assumptions, mathematical tools, to obtain a mathematical structure

example of modeling a stable chair can put it on uneven ground
  model assumes analysis:
              1. considered object: a chair, floor
              2. ideal conditions:
                        1) a chair: as long as four legs, can contact with the ground legs as a point of connection to the four corners of a square
                        2) floor: ground level continuous change, any party Do not appear intermittently (ie continuous curved surface)
                        3) and ground Chair: for a chair, the ground is relatively flat, while the chair can fall anywhere in the at least three legs
              3. Mathematical description:
                        1) the position of chair : symmetrical center point, rotation angle is represented by a change in position
                        2) distance from the ground Legs: disposed two distance functions (f, g ≥ 0 is a continuous function and wherein at least one of 0)

modeling example two business people how to safely cross the river
  model assumptions Analysis:
              1. considered object: Merchant , entourage, boat
              2. ideal conditions: the subject has been given is the ideal state
              3. mathematical description:
                        1) this is a decision model
                        2) state (this shore personnel status), decisions (persons on board), the relationship between the variables of decision-making and

modeling example three poisoning rescuer how
  model assumptions analysis:
              1. considered object: the total amount of children's blood, gastrointestinal drug absorption rate, the rate of drug efflux blood
              2. ideal conditions:
                        1) the total amount of blood is half the adult children
                        2) absorption rate proportional to the dose rate and conversion
              3. mathematical description: column solving differential equations, and is proportional to the ratio determined according to the half-life, drawing analysis

basic methods of mathematical modeling 4: mechanism analysis (objective things, the internal mechanism has Learn)
                   (unclear internal mechanism) test analysis

5. mathematical modeling general steps: model preparation (collecting information, clear modeling purposes)
         　　　　　　    The model assumes (capture the essence of the problem, make assumptions)
                 　　　　   model consists (with the internal laws of mathematical description language Object)
                 　　　　   model solution (related to mathematical methods to solve)
                　　　　    model analysis (mathematical analysis)
                 　　　　   model test (test the applicability of the model)
                 　　　　   model applications