This insight implements Newton's method as an InsightMaker model.
It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)
Fun to try a couple of different cases, so I have built four choices into this example. You can choose the function ("Function Choice" of 0, 1, 2, or 3) using the slider.
This is an introductory example from Olinick's book An Introduction to Mathematical Models in the Social and Life Sciences.
"A recent study focused on the relationship between the birth weights of English women and the birth weights of their daughters. The weights were split into three categories: low (below 6 pounds), average (between 6 and 8 pounds), and high (above 8 pounds). Among women whose own birth weights were low, 50 percent of the daughters had low birth weights, 45 percent had average weights, and 5 percent had high weights. Women with average birth weights had daughters with average weights half of the time, while the half was split evenly between low and high categories. Women with high birth weights had female babies with high weights 40 percent of the time, with low and average weights each occuring 30 percent of the time." p. 274-275.
For the Markov chain, you should make sure that you're taking time steps of length 1 in the settings, and Euler. RK-4 effectively looks beyond a single previous step, so it has a sort of memory!
Thanks Mike! Interesting examples, as always.... Andy Long
This insight implements Newton's method as an InsightMaker model.
It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)
Fun to try a couple of different cases, so I have built four choices into this example. You can choose the function ("Function Choice" of 0, 1, 2, or 3) using the slider.
This is an introductory example from Olinick's book An Introduction to Mathematical Models in the Social and Life Sciences.
"A recent study focused on the relationship between the birth weights of English women and the birth weights of their daughters. The weights were split into three categories: low (below 6 pounds), average (between 6 and 8 pounds), and high (above 8 pounds). Among women whose own birth weights were low, 50 percent of the daughters had low birth weights, 45 percent had average weights, and 5 percent had high weights. Women with average birth weights had daughters with average weights half of the time, while the half was split evenly between low and high categories. Women with high birth weights had female babies with high weights 40 percent of the time, with low and average weights each occuring 30 percent of the time." p. 274-275.
For the Markov chain, you should make sure that you're taking time steps of length 1 in the settings, and Euler. RK-4 effectively looks beyond a single previous step, so it has a sort of memory!
Thanks Mike! Interesting examples, as always.... Andy Long
This is an introductory example from Olinick's book An Introduction to Mathematical Models in the Social and Life Sciences.
"A recent study focused on the relationship between the birth weights of English women and the birth weights of their daughters. The weights were split into three categories: low (below 6 pounds), average (between 6 and 8 pounds), and high (above 8 pounds). Among women whose own birth weights were low, 50 percent of the daughters had low birth weights, 45 percent had average weights, and 5 percent had high weights. Women with average birth weights had daughters with average weights half of the time, while the half was split evenly between low and high categories. Women with high birth weights had female babies with high weights 40 percent of the time, with low and average weights each occuring 30 percent of the time." p. 274-275.
For the Markov chain, you should make sure that you're taking time steps of length 1 in the settings, and Euler. RK-4 effectively looks beyond a single previous step, so it has a sort of memory!
Thanks Mike! Interesting examples, as always.... Andy Long
This is a simple example of (part of a) simple SIR (Susceptible, Infected, Recovered) model, suggested by De Vries, et al. in A Course in Mathematical Biology.
They wanted to illustrate the comparative behavior of differential equations and discrete difference equations. We know that differential equations are generally solved numerically by discretizing them, so that the comparison is a little bit rigged....
This is an introductory example from Olinick's book An Introduction to Mathematical Models in the Social and Life Sciences.
"A recent study focused on the relationship between the birth weights of English women and the birth weights of their daughters. The weights were split into three categories: low (below 6 pounds), average (between 6 and 8 pounds), and high (above 8 pounds). Among women whose own birth weights were low, 50 percent of the daughters had low birth weights, 45 percent had average weights, and 5 percent had high weights. Women with average birth weights had daughters with average weights half of the time, while the half was split evenly between low and high categories. Women with high birth weights had female babies with high weights 40 percent of the time, with low and average weights each occuring 30 percent of the time." p. 274-275.
For the Markov chain, you should make sure that you're taking time steps of length 1 in the settings, and Euler. RK-4 effectively looks beyond a single previous step, so it has a sort of memory!
Thanks Mike! Interesting examples, as always.... Andy Long
This insight implements Newton's method as an InsightMaker model.
It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)
Fun to try a couple of different cases, so I have built four choices into this example. You can choose the function ("Function Choice" of 0, 1, 2, or 3) using the slider.
This is an introductory example from Olinick's book An Introduction to Mathematical Models in the Social and Life Sciences.
"A recent study focused on the relationship between the birth weights of English women and the birth weights of their daughters. The weights were split into three categories: low (below 6 pounds), average (between 6 and 8 pounds), and high (above 8 pounds). Among women whose own birth weights were low, 50 percent of the daughters had low birth weights, 45 percent had average weights, and 5 percent had high weights. Women with average birth weights had daughters with average weights half of the time, while the half was split evenly between low and high categories. Women with high birth weights had female babies with high weights 40 percent of the time, with low and average weights each occuring 30 percent of the time." p. 274-275.
For the Markov chain, you should make sure that you're taking time steps of length 1 in the settings, and Euler. RK-4 effectively looks beyond a single previous step, so it has a sort of memory!
Thanks Mike! Interesting examples, as always.... Andy Long
This is an introductory example from Olinick's book An Introduction to Mathematical Models in the Social and Life Sciences.
"A recent study focused on the relationship between the birth weights of English women and the birth weights of their daughters. The weights were split into three categories: low (below 6 pounds), average (between 6 and 8 pounds), and high (above 8 pounds). Among women whose own birth weights were low, 50 percent of the daughters had low birth weights, 45 percent had average weights, and 5 percent had high weights. Women with average birth weights had daughters with average weights half of the time, while the half was split evenly between low and high categories. Women with high birth weights had female babies with high weights 40 percent of the time, with low and average weights each occuring 30 percent of the time." p. 274-275.
For the Markov chain, you should make sure that you're taking time steps of length 1 in the settings, and Euler. RK-4 effectively looks beyond a single previous step, so it has a sort of memory!
Thanks Mike! Interesting examples, as always.... Andy Long
This is an introductory example from Olinick's book An Introduction to Mathematical Models in the Social and Life Sciences.
"A recent study focused on the relationship between the birth weights of English women and the birth weights of their daughters. The weights were split into three categories: low (below 6 pounds), average (between 6 and 8 pounds), and high (above 8 pounds). Among women whose own birth weights were low, 50 percent of the daughters had low birth weights, 45 percent had average weights, and 5 percent had high weights. Women with average birth weights had daughters with average weights half of the time, while the half was split evenly between low and high categories. Women with high birth weights had female babies with high weights 40 percent of the time, with low and average weights each occuring 30 percent of the time." p. 274-275.
For the Markov chain, you should make sure that you're taking time steps of length 1 in the settings, and Euler. RK-4 effectively looks beyond a single previous step, so it has a sort of memory!
Thanks Mike! Interesting examples, as always.... Andy Long
This insight implements Newton's method as an InsightMaker model.
It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)
Fun to try a couple of different cases, so I have built four choices into this example. You can choose the function ("Function Choice" of 0, 1, 2, or 3) using the slider.
This insight implements Newton's method as an InsightMaker model.
It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)
Fun to try a couple of different cases, so I have built four choices into this example. You can choose the function ("Function Choice" of 0, 1, 2, or 3) using the slider.
This insight implements Newton's method as an InsightMaker model.
It is important to use Euler's method, with step-size of 1. That's what allows us to get away with this!:)
Fun to try a couple of different cases, so I have built four choices into this example. You can choose the function ("Function Choice" of 0, 1, 2, or 3) using the slider.
This is an introductory example from Olinick's book An Introduction to Mathematical Models in the Social and Life Sciences.
"A recent study focused on the relationship between the birth weights of English women and the birth weights of their daughters. The weights were split into three categories: low (below 6 pounds), average (between 6 and 8 pounds), and high (above 8 pounds). Among women whose own birth weights were low, 50 percent of the daughters had low birth weights, 45 percent had average weights, and 5 percent had high weights. Women with average birth weights had daughters with average weights half of the time, while the half was split evenly between low and high categories. Women with high birth weights had female babies with high weights 40 percent of the time, with low and average weights each occuring 30 percent of the time." p. 274-275.
For the Markov chain, you should make sure that you're taking time steps of length 1 in the settings, and Euler. RK-4 effectively looks beyond a single previous step, so it has a sort of memory!
Thanks Mike! Interesting examples, as always.... Andy Long
This is an introductory example from Olinick's book An Introduction to Mathematical Models in the Social and Life Sciences.
"A recent study focused on the relationship between the birth weights of English women and the birth weights of their daughters. The weights were split into three categories: low (below 6 pounds), average (between 6 and 8 pounds), and high (above 8 pounds). Among women whose own birth weights were low, 50 percent of the daughters had low birth weights, 45 percent had average weights, and 5 percent had high weights. Women with average birth weights had daughters with average weights half of the time, while the half was split evenly between low and high categories. Women with high birth weights had female babies with high weights 40 percent of the time, with low and average weights each occuring 30 percent of the time." p. 274-275.
For the Markov chain, you should make sure that you're taking time steps of length 1 in the settings, and Euler. RK-4 effectively looks beyond a single previous step, so it has a sort of memory!
Thanks Mike! Interesting examples, as always.... Andy Long
This is an introductory example from Olinick's book An Introduction to Mathematical Models in the Social and Life Sciences.
"A recent study focused on the relationship between the birth weights of English women and the birth weights of their daughters. The weights were split into three categories: low (below 6 pounds), average (between 6 and 8 pounds), and high (above 8 pounds). Among women whose own birth weights were low, 50 percent of the daughters had low birth weights, 45 percent had average weights, and 5 percent had high weights. Women with average birth weights had daughters with average weights half of the time, while the half was split evenly between low and high categories. Women with high birth weights had female babies with high weights 40 percent of the time, with low and average weights each occuring 30 percent of the time." p. 274-275.
For the Markov chain, you should make sure that you're taking time steps of length 1 in the settings, and Euler. RK-4 effectively looks beyond a single previous step, so it has a sort of memory!
Thanks Mike! Interesting examples, as always.... Andy Long