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Level curves of quadratic functions

In this video, Francis introduces a classification of the level curves of a quadratic function depending on their discriminant. You can access a copy of the slides used in the …

Parabolas and hyperbolas

In this video, Francis introduces the canonical equation of parabolas and hyperbolas, vertically and horizontally oriented, respectively. You can access a copy of the slides used in the video in …

Archimedes: the area under a parabola

In this video, Francis introduces the exhaustion method to find the area of a shape by inscribing inside it a sequence of rectangles. You can access a copy of the …

Ellipses

In this video, Francis introduces the canonical equation of an ellipse, horizontally or vertically oriented. You can access a copy of the slides used in the video in the PDF …

It’s your turn on ellipses

Do your best in trying to solve the following problems. In any case some of them are solved in the video and all of them are solved in the pdf …

Distance and circles

In this video, Francis introduces the equation of a circle in the plane. You can access a copy of the slides used in the video in the PDF file at …

More inverse trig functions, and a few others

In this video, Francis introduces the inverse of the sine and the cosine functions restricting their domain to the intervals ([-pi/2,pi/2]) and ([0,pi]) respectively, and their codomain to their range …

It’s your turn on harmonic motion

Do your best in trying to solve the following problems. In any case some of them are solved in the video and all of them are solved in the pdf …

The function arctan

In this video, Francis introduces the inverse of the tangent function restricting its domain to the interval (]-pi/2,pi/2[) on whichthe tangent function is one-to-one and on which it attains all …

Harmonic motion

In this video, Francis presents some properties of functions having a periodic behaviour, as those modelling motions caused by vibrations or oscillations. You can access a copy of the slides …