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Now showing items 1-10 of 12

#### MathsCasts: Integration by Parts Scheme: Supplement

(Swinburne Commons, 2016)

We use the integration by parts scheme to address integrals with powers of x multiplied by ln(x)

#### MathsCasts: A Scheme to Make Integration by Parts Easier: Part 2

(Swinburne Commons, 2016)

The scheme already discussed for writing down the reults from integration by parts is applied to cyclic integration by parts where the integrand contains a product of an exponential and a sin or cosine.

#### MathsCasts: Directional Derivative Using the Grad Operator

(Swinburne Commons, 2016)

We write the directional derivative on a surface z=z(x,y) in terms of the grad operator acting on z as a dot product with a unit vector in the direction required.

#### MathsCasts: The Rule for Differentiation of an Inverse Function

(Swinburne Commons, 2016)

We investigate the rule for differentiating an inverse function then make some observations about reciprocals of 1st and 2nd derivatives.

#### MathsCasts: Trigonometric Integrals in the Complex Plane: Part 1

(Swinburne Commons, 2016)

We prepare integral from 0 to 2 Pi of 1/(2+cos(theta)) for integration in the complex plane.

#### MathsCasts: Proof of Sum and Difference Formulae for Sin and Cos Using Euler's Formulae

(Swinburne Commons, 2016)

We prove the formulae for sin(A+B) and cos(A+B) using Euler's results for sine and cos. The other sum and difference formulae work in a similar way.

#### MathsCasts: Trigonometric Integrals in the Complex Plane: Part 2

(Swinburne Commons, 2016)

We complete the integration introduced in part 1, using Cauchy's residue theorem.

#### MathsCasts: Trigonometric Integrals in the Complex Plane: Part 5

(Swinburne Commons, 2016)

We attempt to evaluate an integral that is not well-defined and investigate how this problem manifests itself in the complex contour version of the integral.

#### 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.