People often use mathematics (using the function or equation) to describe the world in some kind of phenomenon: a mathematical model is ideal for real-world phenomena, but not a completely accurate representation of any mathematical model has its limitations, there is no model best only the most suitable, suitable model can provide valuable findings and results of this study will primarily as follows: to change modeling.
Mathematical model: when people object modeling, often in order to predict the future value of a time variable, such as object model may be the population, housing prices, the number of other infectious diseases, the mathematical model can often help people better understand the objects changing trends and intrinsic properties, analyze and respond to the future with a better helper.
Changes to model:
Future value = Present value + change;
change = future value - change;
we want to predict the future value would need to study the change. By the practical problems of data generated in a period of time, the data painted graphics, through the study of graphics, we can often identify to seize this trend patterns. If this behavior occurs in discrete time period, then the main method of differential equations to model; if the behavior occurs in continuous time, can be modeled using differential equations.
1.1 pairs for changes modeled by difference equations
in this section by the differential equation method primarily for reasons of changes in the form and analyze the effect of different conditions on the behavior and to predict future values.
Definitions:
Example 1: savings class of problems
assumed principal amount of $ 1000 deposit certificate is incremented at monthly rate of 1%, the following values represent the rate at monthly value:
A = {1000,1010,1020.10 , 1030.30, first-order difference is} ***:
Note: the first difference indicates a change in a series of cycles of time, is represented by interest earned in this example. In the modeling of changes in discrete time period is of great help, in this case, the change from month to the next month only interest income, if n is the number of months and is an n-th months after the total value of storage, then change the value of each month by the n-th points difference:
this one is an interest worth a total of n months later, the above equation can be expressed as an infinite number of algebraic equations, known as power systems, power It describes a system can change from one cycle to the next cycle, if an item in the sequence is known, can be calculated by the differential equation of the next.
If we vary this example, in the above example, if the extraction of 50 yuan per month from the account, then a cycle of change should be in the interest of the period minus deposit:
In most cases, this mathematics described as such changes will not be as accurate an example, often need to draw changes, observation mode, and then to describe the change in mathematical terms: a function of variation = Δan = F; or a change = Δan = an + 1-an = F; modeling changes in this way, or similar decision needs to decide the change is represented by a function f.