74 results authored by Bill Foster - search across all users.

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  • Biomedical Sciences Diagnostic Test - practice

    by Bill Foster and 1 other

    A test of basic concepts to do with SI units and concentrations of solutions.

    Exam (6 questions) Ready to use

    CC BY Published

    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.

    Question Has some problems

    CC BY Published

    Last modified 22/11/2017 06:01

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  • Interactive Newton-Raphson method

    Write down the Newton-Raphson formula for finding a numerical solution to the equation $e^{mx}+bx-a=0$. 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.

    Question Ready to use

    CC BY Published

    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 $x(t),\; y(t);\; x(0)=-5,\;y(0)=5.$

    Question Ready to use

    CC BY Published

    Last modified 14/04/2017 12:01

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  • Solution curves and Vector fields 1 : dy/dx=1-sin(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 $f(x,y)$.

    Question Draft

    CC BY Published

    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 $f(x,y)$.

    Question Draft

    CC BY Published

    Last modified 10/04/2017 22:09

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  • Solution curves and Vector fields 1 : dy/dx=sin(x-y)

    Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=\sin(x-y)$, 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 $f(x,y)$.

    Question Ready to use

    CC BY Published

    Last modified 10/04/2017 17:51

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  • Bill's copy of Newton-Raphson 1.2

    Newton-Raphson numerical method question to solve $g(x)=0$

    Includes a graph of the function $g(x)$ in Advice using Jsxgraph.

    Question Ready to use

    CC BY Published

    Last modified 06/04/2017 23:03

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  • Solution curves and Vector fields 3: $dy/dx=x^3-y^3$

    Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=x^3-y^3$, 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 $f(x,y)$.

    Question Draft

    CC BY Published

    Last modified 31/03/2017 21:36

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  • Solution curves and Vector fields 2 : $dy/dx=x^2-y^2$

    Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=x^2-y^2$, 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

    CC BY Published

    Last modified 31/03/2017 21:24

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