For ENG1002 - Matlab Lab 4: Differentiation, Integration, Solving Differentiation equations.

For ENG1002 - Matlab Lab 4: Differentiation, Integration, Solving Differentiation equations.

For ENG1002 - Matlab Lab 4: Differentiation, Integration, Solving Differentiation equations.

Some questions demonstrating new features in Numbas v4.0: pattern-matching, inference of variable types in mathematical expression parts, and marking equations.

Find the solution of a constant coefficient second order ordinary differential equation of the form $ay''+by=0$. Complex roots.

Matrix addition, multiplication. Finding inverse. Determinants. Systems of equations.

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A quadratic is and a graph of it is given. A tangent is also sketched. The equation of the tangent line is asked for.

Solve 4 first order differential equations of two types:$\displaystyle \frac{dy}{dx}=\frac{ax}{y},\;\;\frac{dy}{dx}=\frac{by}{x},\;y(2)=1$ for all 4.

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Linear program described in words. Student must write out constraints as equations in standard form, then identify the optimal solution in a finished simplex tableau.

$f(x)= ae^{-bt}+c$ is given and plotted. A few points are plotted on the curve. $x$-coordinates are provided for two of them and $y$-coordinate provided for third. Student is required to determine other coordinates.

A quadratic is and a graph of it is given. A tangent is also sketch. The equation of the tangent line is asked for.

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+a^2y=0,\;y(0)=c$ and $y(1)=d$.  (Equal roots example).

A quadratic equation (equivalent to $(x+a)^2-b$) is given and sketched. Three equations are given that can be solved using the graph. There is a chance there will only be one solution.

A few quadratic equations are given, to be solved by completing the square. The number of solutions is randomised.

Solve the equation  5x - 8 = 32

student is to re-arrange the equations $pV=nRT$ and $mgh = \frac{1}{2}mv^2$

Solve 4 first order differential equations of two types:$\displaystyle \frac{dy}{dx}=\frac{ax}{y},\;\;\frac{dy}{dx}=\frac{by}{x},\;y(2)=1$ for all 4.

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Cramers Rule applied to 3 simultaneous equations

A quadratic is and a graph of it is given. A tangent is also sketch. The equation of the tangent line is asked for.

Question is to calculate the area bounded by a cubic and the $x$-axis. Requires finding the roots by solving a cubic equation. Calculator question

Matrix addition, multiplication. Finding inverse. Determinants. Systems of equations.

Matrix addition, multiplication. Finding inverse. Determinants. Systems of equations.

rebelmaths