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Transform second order ODE into 2D and 3D dynamical systems
Transform a second order ODE into 2D nonautonomous and 3D autonomous dynamical systems of ODEs.
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Last modified 15/11/2018 17:30
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Solving equations
Solve for $x$ and $y$: \[ \begin{eqnarray} a_1x+b_1y&=&c_1\\ a_2x+b_2y&=&c_2 \end{eqnarray} \]
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Last modified 15/11/2018 17:27
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Last modified 15/11/2018 17:21
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Last modified 15/11/2018 17:07
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Solve three congruences with the Chinese Remainder Theorem
Solving three simultaneous congruences using the Chinese Remainder Theorem:
\[\begin{eqnarray*} x\;&\equiv&\;b_1\;&\mod&\;n_1\\ x\;&\equiv&\;b_2\;&\mod&\;n_2\\x\;&\equiv&\;b_3\;&\mod&\;n_3 \end{eqnarray*} \] where $\operatorname{gcd}(n_1,n_2,n_3)=1$
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Last modified 15/11/2018 16:59
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Use Bézout's algorithm to solve $as + bt = \gcd(a,b)$,
Given two numbers, find the gcd, then use Bézout's algorithm to find $s$ and $t$ such that $as+bt=\operatorname{gcd}(a,b)$.
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Last modified 09/11/2018 09:32
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Solve simultaneous equations by finding inverse matrix,
Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix.
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Last modified 08/11/2018 19:17
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Last modified 08/11/2018 16:49
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