lecturenotes10_17

# lecturenotes10_17 - Solving Differential Equations in...

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Click to edit Master subtitle style Solving Differential Equations in Matlab November 17th, 2008

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Overview 1. Numerical Solutions to ODEs a. Function functions b. ODE solvers 2. Symbolic Solutions
Differential Equations The most fundamental aspects of any biological entity is the way it changes with time, interacts with its environment, functions, and dies Any model of a biological system must describe the way it changes over time. It must include time derivatives Therefore it is described by differential equations !

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Ordinary Differential Equations (ODEs) Differential equations are equations that describe the dynamic behaviour of a variable or system over time. Much of engineering is based on differential equations ODEs are differential equations involving the function and its derivatives (one variable) ODEs can sometimes (often) be solved analytically
The Solution to a DE What is the solution to a differential equation? ¢ The solution is the function f(y,t) that makes the relationship true. ¢ So, we are looking for the implied relationship between time (or another independent variable) and the dependent variable.

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Numerical Solutions If an analytical equation cannot be found (or is inconvenient to find) we use numerical
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lecturenotes10_17 - Solving Differential Equations in...

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