## MathsCasts I

### by Swinburne University of Technology • Language: eng
• Episodes: 298
• Last: 9 Jul 2013
These MathsCasts are produced by the mathematics support centres at Swinburne University, the University of Limerick and Loughborough University. They are part of an ongoing collaborative research project to develop high quality resources and investigate the effectiveness of MathsCasts to support mathematics learning. They are mostly targeted at prerequisite to first year level, in a range of subjects such as: Engineering, Sciences, Business, Computing and Technology. We have also commenced production of second year mathematics topics.

#### Episodes (298)

• ##### Powers of complex numbers (MathsCasts)
Published: 9 Jul 2013 Duration: 05:27
Gives the general formula then applies this to an example. Cartesian form is convert to polar form, then the required power of the number is calculated, and finally the result is converted back into Cartesian form.

• ##### Simplifying algebraic fractions with cancellation Part 1 (MathsCasts)
Published: 26 Jun 2013 Duration: 07:42
We look at how to simplify algebraic fractions when there is a number and/ or power of a letter that is common to all terms on the numerator and denominator, thus allowing us to simplify the original fraction by cancelling out this common f... Read more →

• ##### The scalar triple product (MathsCasts)
Published: 19 Jun 2013 Duration: 11:57
Investigates the scalar triple product in the context of the volume of a parallellepiped.

• ##### Equation of the tangent to a curve (MathsCasts)
Published: 12 Jun 2013 Duration: 06:43
We find the equation of the tangent to a curve at a specific point, by first finding the general expression for the derivative of the curve, then evaluating it at the point, and then using this information to find the equation of the tangen... Read more →

• ##### Introduction to implicit differentiation (MathsCasts)
Published: 23 May 2013 Duration: 09:54
Gives a basic example of implicit differentiation to find dy/dx, and compares this to the result from explicit differentiation for the same example. Second example is a circle, with graphical interpretation of dy/dx in two points.

• ##### Transposition with required variable in the denominator (MathsCasts)
Published: 21 May 2013 Duration: 05:16
In this recording we look at how to rearrange a formula where the letter that we want to make the subject is in the denominator. That is, we look how to make f the subject when presented with an expression of the form a/b = c/d + e/f.

• ##### The Laplacian of f(r) and proof that 1 over r is harmonic (MathsCasts)
Published: 20 May 2013 Duration: 11:31
We derive a general formula for the Laplacian acting on a function f(r) then demonstrate that the Laplacian is zero in the case that f(r) = 1/r, thereby showing that 1/r is harmonic.

• ##### The curl of the gradient and the divergence of the curl are zero (MathsCasts)
Published: 16 May 2013 Duration: 11:09
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).

• ##### The curl of the curl (MathsCasts)
Published: 15 May 2013 Duration: 12:28
We derive a formula to simplify the process of taking the curl of the curl of a vector field. The algebra is rather complicated!

• ##### Half-range Fourier Series: Part 3 (MathsCasts)
Published: 15 May 2013 Duration: 13:07
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 sine series for a linear f(t).

• ##### Finding the grad of a simple scalar function f(x,y,z) (MathsCasts)
Published: 14 May 2013 Duration: 03:30
We choose a simple scalar function f(x,y,z) and calculate its gradient.

• ##### Finding the divergence and curl of a simple vector field (MathsCasts)
Published: 13 May 2013 Duration: 06:12
We calculate the divergence and curl of a simple vector field

• ##### Chain rule or not? (MathsCasts)
Published: 9 May 2013 Duration: 04:36
Six short examples useful as preparation for implicit differentiation. Some require the chain rule, others are straightforward differentiations.

• ##### A matrix to the power of a matrix (MathsCasts)
Published: 8 May 2013 Duration: 08:17
We ask if a matrix can be raised to the power of a matrix and do a simple 2 by 2 example.

• ##### Matrix representation of complex numbers (MathsCasts)
Published: 6 May 2013 Duration: 10:18
We show how complex number arithmetic can be performed using matrices for the complex numbers.

• ##### Adding and Subtracting Surds (MathsCasts)
Published: 3 May 2013 Duration: 07:48
We look at cases when we can add and subtract surds- namely when terms can be re-written with the same number under the square root sign. Two examples are given- in the second example the surds need to be simplified before adding/ subtracti... Read more →

• ##### Complex Impedance - Part 3 (MathsCasts)
Published: 1 May 2013 Duration: 10:20
We look at a numerical example for an RLC circuit and calculate the complex impedance and phase difference.

• ##### Complex Impedance - Part 2 (MathsCasts)
Published: 30 Apr 2013 Duration: 12:12
We continue investigation of the RLC circuit, introducing complex versions of voltage and current. The complex impedance results naturally from these quantities and gives a clear picture of why the current and voltage differ by a phase, and... Read more →

• ##### Adding and subtracting fractions (MathsCasts)
Published: 29 Apr 2013 Duration: 08:46
We look at several examples of adding and subtracting fractions, by first obtaining a common denominator.

• ##### Complex Impedance - Part 1 (MathsCasts)
Published: 24 Apr 2013 Duration: 10:01
We investigate the RLC circuit and obtain a relation between voltage and current without use of complex quantities. We see that the relation is rather cumbersome and not transparent.