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Now showing items 41-50 of 133

#### MathsCasts: Multivariate Chain Rule: Part 2

(Swinburne Commons, 2012)

Example of using the multivariate chain rule where z=f(x,y) and x and y are both functions of t.

#### MathsCasts: Intersection of Two Lines in 3D

(Swinburne Commons, 2012)

An example of first finding the vector and scalar parametric equations of two straight lines in 3D, given we know two points on each line. Gaussian Elimination then confirms that the lines intersect at a common point, whose ...

#### MathsCasts: Complex Exponential to Cartesian Form

(Swinburne Commons, 2012)

Three examples are given to demonstrate how to convert complex numbers written in exponential polar form into Cartesian form.

#### MathsCasts: Complex Polar Form

(Swinburne Commons, 2012)

General explanation is given of how a complex number in Cartesian form can be converted to polar form z=rcis(@) and then 3 examples are given to illustrate this.

#### MathsCasts: Second Order DEs: Example 3

(Swinburne Commons, 2011)

Example of solving a second-order linear ordinary differential equation with constant coefficients in the case where the auxiliary equation has complex conjugate roots and the right hand side of the equation is an exponential ...

#### MathsCasts: Polar and Cartesian Curves

(Swinburne Commons, 2012)

This recording explains the relationship between Polar and Cartesian coordinates of a 2D curve. An example is then given of converting a polar equation into Cartesian form and an example is given of converting a Cartesian ...

#### MathsCasts: Converting a Parametric Curve to Cartesian Form

(Swinburne Commons, 2011)

This screencast gives two examples of converting the parametric equations of 2D curves into Cartesian equations, and includes a discussion on the importance of considering any restrictions of the domain of the resulting ...

#### MathsCasts: Equation of a Plane Given Three Points

(Swinburne Commons, 2011)

Application of vectors to the example of finding the equation of a plane through three points by first determining two vectors on the plane, then using the cross product to determine a normal vector to the plane, then using ...

#### MathsCasts: Chain Rule Part 2: Variables

(Swinburne Commons, 2011)

Applies the multivariate chain rule to an example where z(x,y), x(t), y(t), to find dz/dt

#### MathsCasts: Cramer's Rule for 3 Unknowns

(Swinburne Commons, 2011)

This screencast first gives the general form of Cramer's Rule for solving three equations in three unknowns and then covers a specific example to demonstrate the rule.