Completing the square

A free 2 hours long course

This is a two hour long free course on the method of completing the square.

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Prerequisites

High-school maths, mainly arithmetic.
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Curriculum

This course concentrates on just one topic, completing the square, which is usually introduced in high-school and then comes back in various courses on college or university level.

Completing the square

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A detailed list of the lectures can be found in a PDF outline by clicking this panel.

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Course Objectives & Outcomes

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Completing the square: how it is done and why the method works (variants for 1, 2, and 3 variables); a geometric illustration of the method and its name.
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Completing the square in two variables, one at a time, for identifying conic sections: circles, ellipses, parabolas, and hyperbolas.
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Completing the square in three variables, one at a time, for identifying quadric surfaces: spheres, ellipsoids, hyperboloids, double cones, etc.

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Completing the square in one variable for solving quadratic equations with help of the discriminant and the quadratic formula; derivation of the formula.
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Completing the square in one variable for plotting polynomials of second degree with help of graph transformations of the parabola y=x^2; finding new vertex.
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Completing the square in two or three variables for definiteness of 2×2 or 3×3 matrices / corresponding quadratic forms in 2 or 3 variables.

Engineer E.

Udemy student

It was a topic I had already covered in high school. I took this course as a refresher and I really appreciated the clarity of the explanations.

Alejandro C.

Udemy student

This is a very clear and easy-to-follow explanation. I wish my high school’s teachers had been half as pedagogical as she is.

James R.

Udemy student

It was a GREAT course!

Debbie C.

Udemy student

great explanation and friendly, encouraging teacher.

Justin M.

Udemy student

Due to the great explanations and plenty of examples, I was able to actually understand completing the square instead of just being familiar with the phrase from high school and college courses that I took over ten years ago. I’m glad to see you will do a Discrete Math course (wish it was sooner, but at least there is one planned). I hope to see a Probability & Statistics course sometime also.

Kenneth A.

Udemy student

I was pleasantly surprised to see the method applied to both two and three variables, with some context included – graphing conics, quadric surfaces and quadratic forms (no prior knowledge of these topics is needed, though). The problems and examples start simple but later ones don’t hold back on having to deal with fractions and awkward coefficients, too, which is nice.

All in all, a wonderful free course and great for flexing your algebraic muscles!

RLH

Udemy student

Very thorough explanation of completing the square. This topic was barely touched on in my pre calc or calculus classes in college.

Dave O.

Udemy student

Extremely comprehensive course on ‘Completing the Square’ that will go far beyond what most users will ever need!

Shelton S.

Udemy student

Best teacher on Udemy!

Eli J.

Udemy student

Brilliant math teacher explains everything so very clearly. Fantastic.

Amir

Udemy student

She’s amazing at teaching Math. Not comparable to other instrustors.

Almir B.

Udemy student

Hania is the teacher everbody dreamed to have during school life.

Nicholas N.

Udemy student

YOU’RE THE BEST ! I haven’t had an Instructor like you so detailed, knowledgeable with lots of follow though in her work !