The quotient rule for differentiation is proved from first principles.

The quotient rule from 1st principles (MathsCasts)

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We solve simultaneously the equations of a plane and a cone and show that the intersections are circles, parabolas, ellipses, hyperbolas, straight lines or just the origin.

Why are circles, ellipses, parabolas and hyperbolas called 'conic sections'? Part 2 (MathsCasts)

Deals with the details of calculating Fourier series coefficients for a function.

Calculating a Fourier series (MathsCasts)

Demonstrates that symmetry of functions helps us to shorten the calculation of the integrals needed for the Fourier coefficients.

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Introduces the idea of half-range Fourier series and addresses the question of why we use them.

The quotient rule from 1st principles (MathsCasts)

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