I referenced a book and a video, but both seem to have been deleted
from the internet by the authors (googling can still find them elsewhere). I've elected to just remove them from the book rather than fight copyright issues.
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"```\n",
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"and only the elements which equal `z` will be multiplied by `scale`.\n",
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"\n",
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"Teaching you NumPy is beyond the scope of this book. I will use idiomatic NumPy constructs and explain them the first time I present them. If you are new to NumPy there are many blog posts and videos on how to use NumPy efficiently and idiomatically. For example, this video by Jake Vanderplas is often recommended: https://vimeo.com/79820956.\n",
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"Teaching you NumPy is beyond the scope of this book. I will use idiomatic NumPy constructs and explain them the first time I present them. If you are new to NumPy there are many blog posts and videos on how to use NumPy efficiently and idiomatically.\n",
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"\n",
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"Here is our improved version:"
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"\n",
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"These work well for linear ordinary differential equations (ODEs), but do not work well for nonlinear equations. For example, consider trying to predict the position of a rapidly turning car. Cars maneuver by turning the front wheels. This makes them pivot around their rear axle as it moves forward. Therefore the path will be continuously varying and a linear prediction will necessarily produce an incorrect value. If the change in the system is small enough relative to $\\Delta t$ this can often produce adequate results, but that will rarely be the case with the nonlinear Kalman filters we will be studying in subsequent chapters. \n",
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"\n",
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"For these reasons we need to know how to numerically integrate ODEs. This can be a vast topic that requires several books. If you need to explore this topic in depth *Computational Physics in Python* by Dr. Eric Ayars is excellent, and available for free here:\n",
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"\n",
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"http://phys.csuchico.edu/ayars/312/Handouts/comp-phys-python.pdf\n",
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"\n",
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"However, I will cover a few simple techniques which will work for a majority of the problems you encounter.\n"
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"For these reasons we need to know how to numerically integrate ODEs. This can be a vast topic that requires several books. However, I will cover a few simple techniques which will work for a majority of the problems you encounter.\n"
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]
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},
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{
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