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Our simulation will start with the observed population in 1950, \py{p0}, and add \py{annual_growth} each year. To store the results, we'll use a \py{TimeSeries} object:
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Our simulation will start with the observed population in 1950, \py{p_0}, and add \py{annual_growth} each year. To store the results, we'll use a \py{TimeSeries} object:
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\index{TimeSeries}
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@@ -2978,7 +2978,7 @@ \section{Differential equations in SymPy}
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%
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\[ f{\left (t \right )} = C_{1} \exp(\alpha t) \]
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This is the {\bf general solution}, which still contains an unspecified constant, $C_1$. To get the {\bf particular solution} where $f(0) = p_0$, we substitute \py{p0} for \py{C1}. First, we have to create two more symbols:
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This is the {\bf general solution}, which still contains an unspecified constant, $C_1$. To get the {\bf particular solution} where $f(0) = p_0$, we substitute \py{p_0} for \py{C1}. First, we have to create two more symbols:
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\index{general solution}
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\index{particular solution}
@@ -4131,8 +4131,7 @@ \section{Sweeping beta}
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\end{itemize}
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% TODO: Consider using Greek letters in the code and figures. But in that case, also
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% figure out how to get them through LaTeX intact.
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% TODO: Make the gamma symbol appear in the line below and in the figures.
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If the value of \py{gamma} is \py{0.25}, the value of \py{label} is the string \py{'gamma = 0.25'}.
\py{Params} objects are similar to \py{System} and \py{State} objects; in fact, all three have the same capabilities. I have given them different names to document the different roles they play.
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Chapter~\ref{chap18} also introduces \py{run_ode_solver} which computes numerical solutions to differential equations.
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\py{run_ode_solver} uses a slope function, which is similar to an update function:
@@ -6006,10 +6003,9 @@ \section{Drag force}
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\section{Implementation}
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\label{penny_drag}
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As the number of system parameters increases, and as we need to do more work to compute them, we will find it useful to define a \py{Params} object to contain the quantities we need to make a \py{System} object.
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As the number of system parameters increases, and as we need to do more work to compute them, we will find it useful to define a \py{Params} object to contain the quantities we need to make a \py{System} object. \py{Params} objects are similar to \py{System} and \py{State} objects; in fact, all three have the same capabilities. I have given them different names to document the different roles they play.
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% TODO: If we take Params out of Chapter 18, we have to introduce it here
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%\py{Params} objects are similar to \py{System} and \py{State} objects; in fact, all three have the same capabilities. I have given them different names to document the different roles they play.
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% TODO: This is not actually the first use of Params
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