74 results authored by Bill Foster  search across all users.

Biomedical Sciences Diagnostic Test  practice
A test of basic concepts to do with SI units and concentrations of solutions.
Exam (6 questions) Ready to use
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Last modified 18/09/2019 13:50
 Numeracy
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Transition to university

Testing and False Positives
Given a population size and data on a test for a condition on that population, use a tabular approach to find the increase in risk after a positive test in which there is a small chance of a false positive i.e. the probability that the test is positive even though the condition is not present. See Advice for a graphical version.
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Last modified 22/11/2017 06:01
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Interactive NewtonRaphson method
Write down the NewtonRaphson formula for finding a numerical solution to the equation $e^{mx}+bxa=0$. If $x_0=1$ find $x_1$.
Included in the Advice of this question are:
6 iterations of the method.
Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.
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Last modified 19/04/2017 11:03
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Dynamical system 7: Stable spiral.
Asking users to input coefficients of a system of diff equations so that the phase space is a stable spiral. All systems input by the user are graphed together with immediate feedback. Also included in the Steps are the graphs of the solutions for $x(t),\; y(t);\; x(0)=5,\;y(0)=5.$
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Last modified 14/04/2017 12:01
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Solution curves and Vector fields 1 : dy/dx=1sin(y)
Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=1\sin(y)$, and also by moving the point $(x_0,y_0)$ you can see the solution curves going through that point.
If you want to modify $f(x,y)$ simply change the definition of $f(x,y)$ and that of the variable str in the user defined function testfield in Extensions and scripts. You have to use javascript notation for functions and powers in the definition of $f(x,y)$.
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Last modified 14/04/2017 11:51
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Solution curves and Vector fields 1 : dy/dx=sin(x)sin(y)
Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=\sin(x)\sin(y)$, and also by moving the point $(x_0,y_0)$ you can see the solution curves going through that point.
If you want to modify $f(x,y)$ simply change the definition of $f(x,y)$ and that of the variable str in the user defined function testfield in Extensions and scripts. You have to use javascript notation for functions and powers in the definition of $f(x,y)$.
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Last modified 10/04/2017 22:09
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Solution curves and Vector fields 1 : dy/dx=sin(xy)
Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=\sin(xy)$, and also by moving the point $(x_0,y_0)$ you can see the solution curves going through that point.
If you want to modify $f(x,y)$ simply change the definition of $f(x,y)$ and that of the variable str in the user defined function testfield in Extensions and scripts. You have to use javascript notation for functions and powers in the definition of $f(x,y)$.
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Last modified 10/04/2017 17:51
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Bill's copy of NewtonRaphson 1.2
NewtonRaphson numerical method question to solve $g(x)=0$
Includes a graph of the function $g(x)$ in Advice using Jsxgraph.
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Last modified 06/04/2017 23:03
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Solution curves and Vector fields 3: $dy/dx=x^3y^3$
Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=x^3y^3$, and also by moving the point $(x_0,y_0)$ you can see the solution curves going through that point.
If you want to modify $f(x,y)$ simply change the definition of $f(x,y)$ and that of the variable str in the user defined function testfield in Extensions and scripts. You have to use javascript notation for functions and powers in the definition of $f(x,y)$.
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Last modified 31/03/2017 21:36
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Solution curves and Vector fields 2 : $dy/dx=x^2y^2$
Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=x^2y^2$, and also by moving the point $(x_0,y_0)$ you can see the solution curves going through that point.
If you want to modify $f(x,y)$ simply change the definition of $f(x,y)$ and that of the variable str in the user defined function testfield in Extensions and scripts. You have to use javascript notation for functions and powers in the definition of $f(x,y)$.
Question Ready to use
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Last modified 31/03/2017 21:24
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