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Now showing items 31-40 of 90

#### MathsCasts: Converting a Double Integral from Cartesian to Circular Polar Coordinates

(Swinburne Commons, 2012)

After a brief review of circular polar coordinates, a double integral is written using Cartesian coordinates. We draw the region of integration and describe it in terms of polar coordinates in order to rewrite the integral ...

#### MathsCasts: Determining Linear (in)dependence

(Swinburne Commons, 2012)

We investigate the linear dependence or independence of a set of 3 vectors in 3 dimensions, and show how the determinant of a 3 by 3 matrix can assist in this process.

#### MathsCasts: Simplifying Surds

(Swinburne Commons, 2013)

We look at how to simplify surds. This is done by finding the largest perfect square that is a factor of the number under the square root and hence bringing this part of the expression outside the square root.

#### MathsCasts: Finding the Laplace Transform of an Integral

(Swinburne Commons, 2013)

Knowing the Laplace transform of a function f(t) allows us also to calculate the transform of the integral of f(t). We show the simplest method of doing this here.

#### MathsCasts: Compass Directions Part 1

(Swinburne Commons, 2013)

We introduce the points of the compass and solve a simple example using distances and basic directions (N,S,E,W) to find resulting distance and angle.

#### MathsCasts: Reversing the Order of Integration of a Double Integral: Part 1

(Swinburne Commons, 2013)

Part 1 of 3. We show how to swap the order of integration in a double integral depending on x and y. We use the same examples as for the region of integration for double integrals. We start with constant integration limits ...

#### MathsCasts: Eigenvectors of a 2x2 Matrix

(Swinburne Commons, 2013)

We use the same 2 by 2 matrix whose eigenvalues were found in another MathsCast (Eigenvalues of a 2 by 2 matrix) and find the associated eigenvectors.

#### MathsCasts: Solving Quadratic Inequalities: Example 2

(Swinburne Commons, 2012)

We investigate inequalities involving quadratic expression and show how to use a combination of algebraic rearrangement and graph sketching to find solutions. The solutions are written as inequalities and as intervals.

#### MathsCasts: Sketching the Region of Integration of Double Integrals

(Swinburne Commons, 2012)

We examine some double integrals with Cartesian variables x and y. We investigate the integration limits and relate them to the 2D region of integration in the x-y plane. This is preparatory to reversing the order of integration.

#### MathsCasts: The Laplace Transform of the Error Function erf(t)

(Swinburne Commons, 2013)

We show how to calculate the Laplace transform of the error function erf(t)