## Search

Now showing items 81-90 of 90

#### MathsCasts: Evaluating Double Integrals by Reversing the Order of Integration

(Swinburne Commons, 2012)

We examine two double integrals in which the anti-differentiation is at first sight impossible. We then reverse the order of integration and sidestep the problem of seemingly impossible integration. The integrals are thus ...

#### MathsCasts: Further Properties of Odd and Even Functions

(Swinburne Commons, 2012)

We discuss combinations of even and odd functions involving sums, products etc and investigate their odd and even properties. We show the use of such properties in reducing the work needed to evaluate a certain kind of integral.

#### MathsCasts: Half-Range Fourier Series: Part 2

(Swinburne Commons, 2012)

We continue the theme of half range series and examine how the integrations can be simplified using the symmetry of the function. Here we examine a half-range cosine series for a linear f(t).

#### MathsCasts: Reversing the Order of Integration of a Double Integral: Part 3

(Swinburne Commons, 2013)

Part 3 of 3. Continuation from part one, looking at increasingly complicated examples of reversal of integration order.

#### MathsCasts: Finding the Divergence and Curl of a Simple Vector Field

(Swinburne Commons, 2013)

We calculate the divergence and curl of a simple vector field.

#### MathsCasts: The Curl of the Gradient and the Divergence of the Curl are Zero

(Swinburne Commons, 2013)

We show that div(curl(v)) and curl (grad f) are 0 for any vector field v(x,y,z) and scalar function f(x,y,z).

#### MathsCasts: The Laplace Transform of a Periodic Function

(Swinburne Commons, 2016)

We demonstrate how periodicity of a function affects the Laplace transform.

#### MathsCasts: Trigonometric Integrals in the Complex Plane: Part 3

(Swinburne Commons, 2016)

We evaluate another integral similar to that in parts 1 and 2 but containing a sine rather than a cosine. Here we prepare the integral for contour integration.

#### MathsCasts: Trigonometric Integrals in the Complex Plane: Part 4

(Swinburne Commons, 2016)

We complete the integration introduced in part 3, using Cauchy's residue theorem.

#### MathsCasts: Using Complex Exponentials to Integrate Exponential Times Cos or Sin Function

(Swinburne Commons, 2016)

We use the complex exponential to integrate e^(ax) times cos(bx) or sin(bx) as real and imaginary parts of the same integral. Integration by parts is thereby avoided.