Rebuild tutorials

notebook/introduction/01-ode_introduction.ipynb

@@ -3,7 +3,7 @@
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-        "# An Intro to DifferentialEquations.jl\n### Chris Rackauckas\n\n## Basic Introduction Via Ordinary Differential Equations\n\nThis notebook will get you started with DifferentialEquations.jl by introducing you to the functionality for solving ordinary differential equations (ODEs). The corresponding documentation page is the [ODE tutorial](https://docs.juliadiffeq.org/dev/tutorials/ode_example/). While some of the syntax may be different for other types of equations, the same general principles hold in each case. Our goal is to give a gentle and thorough introduction that highlights these principles in a way that will help you generalize what you have learned.\n\n### Background\n\nIf you are new to the study of differential equations, it can be helpful to do a quick background read on [the definition of ordinary differential equations](https://en.wikipedia.org/wiki/Ordinary_differential_equation). We define an ordinary differential equation as an equation which describes the way that a variable $u$ changes, that is\n\n$$u' = f(u,p,t)$$\n\nwhere $p$ are the parameters of the model, $t$ is the time variable, and $f$ is the nonlinear model of how $u$ changes. The initial value problem also includes the information about the starting value:\n\n$$u(t_0) = u_0$$\n\nTogether, if you know the starting value and you know how the value will change with time, then you know what the value will be at any time point in the future. This is the intuitive definition of a differential equation.\n\n### First Model: Exponential Growth\n\nOur first model will be the canonical exponential growth model. This model says that the rate of change is proportional to the current value, and is this:\n\n$$u' = au$$\n\nwhere we have a starting value $u(0)=u_0$. Let's say we put 1 dollar into Bitcoin which is increasing at a rate of $98\\%$ per year. Then calling now $t=0$ and measuring time in years, our model is:\n\n$$u' = 0.98u$$\n\nand $u(0) = 1.0$. We encode this into Julia by noticing that, in this setup, we match the general form when"
+        "## Basic Introduction Via Ordinary Differential Equations\n\nThis notebook will get you started with DifferentialEquations.jl by introducing you to the functionality for solving ordinary differential equations (ODEs). The corresponding documentation page is the [ODE tutorial](https://docs.juliadiffeq.org/dev/tutorials/ode_example/). While some of the syntax may be different for other types of equations, the same general principles hold in each case. Our goal is to give a gentle and thorough introduction that highlights these principles in a way that will help you generalize what you have learned.\n\n### Background\n\nIf you are new to the study of differential equations, it can be helpful to do a quick background read on [the definition of ordinary differential equations](https://en.wikipedia.org/wiki/Ordinary_differential_equation). We define an ordinary differential equation as an equation which describes the way that a variable $u$ changes, that is\n\n$$u' = f(u,p,t)$$\n\nwhere $p$ are the parameters of the model, $t$ is the time variable, and $f$ is the nonlinear model of how $u$ changes. The initial value problem also includes the information about the starting value:\n\n$$u(t_0) = u_0$$\n\nTogether, if you know the starting value and you know how the value will change with time, then you know what the value will be at any time point in the future. This is the intuitive definition of a differential equation.\n\n### First Model: Exponential Growth\n\nOur first model will be the canonical exponential growth model. This model says that the rate of change is proportional to the current value, and is this:\n\n$$u' = au$$\n\nwhere we have a starting value $u(0)=u_0$. Let's say we put 1 dollar into Bitcoin which is increasing at a rate of $98\\%$ per year. Then calling now $t=0$ and measuring time in years, our model is:\n\n$$u' = 0.98u$$\n\nand $u(0) = 1.0$. We encode this into Julia by noticing that, in this setup, we match the general form when"
       ],
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@@ -640,11 +640,11 @@
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