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 …
Course: Advanced Precalculus: Geometry, Trigonometry and Exponentials
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 …
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 …
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 …
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 distance and circles
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 …
Geometry of the plane: points, segments, lines
In this video, Francis introduces the general equation of a line in the plane. In particular conditions for two lines being parallel or perpendicular are discussed. You can access a …
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 …
It’s your turn on geometry of the plane: points, segments, lines
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 …
It’s your turn on More inverse trig functions, and a few others
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 …
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 the function arctan
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 …
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 …
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 …
These articles are from the online course:
Advanced Precalculus: Geometry, Trigonometry and Exponentials
