Completing the square
A free 2 hours long course
This is a two hour long free course on the method of completing the square.
Prerequisites
High-school maths, mainly arithmetic.
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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Course Objectives & Outcomes
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.
Completing the square in two variables, one at a time, for identifying conic sections: circles, ellipses, parabolas, and hyperbolas.
Completing the square in three variables, one at a time, for identifying quadric surfaces: spheres, ellipsoids, hyperboloids, double cones, etc.
Completing the square in one variable for solving quadratic equations with help of the discriminant and the quadratic formula; derivation of the formula.
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.
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.
Reviews (51)
Kavi A.
Udemy student
Wonderful!
Hassan K.
Udemy student
Always an amazing course worthwhile, as I expected!
Walter A.
Udemy student
This is a fantastic course. Require to be patient at the beginning, but everything will flow correctly.
Dr. E.
Lecturer
The instructor is extremely pleasant. The pace is perfect, not too fast and not too slow. Everything is crystal clear. Moreover the explanations are highly accurate and the instructor builds a solid foundation before moving on. The applications are interesting too. Great course and great instructor!
Andrés E.
Udemy student
Great course, and Professor Hania is a fantastic instructor. Highly recommended.
Robert G.
Udemy student
I'm always satisfied when i follow any one of your courses.
Thank.
Thank.
Carlos S.
Udemy student
I simply love Professor Hania’s courses. I am learning mathematics like never before. In about two months (taking two free courses and two paid courses), I have already significantly developed my mathematical skills and intuition.
One important point worth mentioning is that, in the paid courses, the Q&A section is outstanding—Professor Hania answers every question in great detail.
I just want to thank her for all the support so far.
One important point worth mentioning is that, in the paid courses, the Q&A section is outstanding—Professor Hania answers every question in great detail.
I just want to thank her for all the support so far.
Margaret C.
Udemy student
She is so endearing! I really enjoyed it, and it was a good refresher and extension to what I already knew.
C T.
Udemy student
explanations are clear done in easy to understand steps
Peter S.
Udemy student
I'm doing this for revision; I would liek to know it in more detail hence taking advantage of this free course.
Tim K.
Udemy student
Dr Hania rocks! My high school math was over 50 years ago and I am taking her classes to learn what I missed or have forgotten. Since high school I have completed 2 bachelor degrees and 1 master degree; I rate Hania as one of the top 2 or 3 college level instructors I studied with (and I've had dozens of instructors!). I enrolled in her new Discrete Math course and look forward to learning more with her outstanding instruction! Thanks, Hania!
Pavel K.
Udemy student
I have seen some of the best like Eddy Woos lectures and this lecture gives me the opportunity to deepen the knowledge and realy think deeper how completing thes square is connected to distributive property that is connected to calculating the Area of a rectangle. Connected learning is the way to go and not blindly following the proceedures. Think about the rools, break them and see that the result change from what we expect.
Great explanation Hania!
Great explanation Hania!
Ayush R.
Udemy student
Amazing
Chris R.
Udemy student
Calm, clear and just the right amount of detail!!!
Rafiu A.
Udemy student
Absolutely spot on. Dr Hania is wonderful.
Andrzej K.
Udemy student
This instructor is one of the best. The presentation of the material is second to none.
Kious
Udemy student
Clear and well paced
Austin H.
Udemy student
Awesome information!
Alejandro S.
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.
Gerald R.
Udemy student
Excellent teaching...
James R.
Udemy student
It was a GREAT course!
Roberto F.
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.
Benjamin O.
Udemy student
The instructor has clear mastery of the course
Debbie C.
Udemy student
great explanation and friendly, encouraging teacher
Bill M.
Udemy student
Nice little course to learn the instructors teaching style while gaining a foundation for the larger courses. Nicely done!
Amir
Udemy student
She's amazing at teaching Math. Not comparable to other instrustors
James G.
Udemy student
Good explanations and examples.
Andy W.
Udemy student
excellent
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!
All in all, a wonderful free course and great for flexing your algebraic muscles!
Richard H.
Udemy student
Explanations are clear and follow a logical order and path that makes understanding new concepts easier without making known concepts take too long and making the course drag.
Wanda W.
Udemy student
Great courses about a very important topic which often doesn't get enough attention in high school, but is really needed at the university (college) level. Hania does a great job explaining completing the square and its applications. She also gives good examples of problem solving that cover the most common cases. This is my 8th course by Hania and Martin that I've completed and I can recommend all of them.
Aime F.
Udemy student
I like the way she explains
Vishnu B.
Udemy student
Excellent, great mentor, the perspective is different.
Eli J.
Udemy student
Brilliant math teacher explains everything so very clearly. Fantastic.
Jonathan F.
Udemy student
Thank you so much for taking the time to create these courses!
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.
Shelton S.
Udemy student
Best teacher on Udemy!
Matt F.
Udemy student
Excellent free short course. These are great.
Dave O.
Udemy student
Extremely comprehensive course on 'Completing the Square' that will go far beyond what most users will ever need!
Daniel S.
Udemy student
excellent
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.
Tim H.
Udemy student
Very detailed explanations and easy to understand. Thank You!
Maciej K.
Udemy student
Excellent explanations! Very clear.
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 !
Bruno P.
Udemy student
Useful & C!ear ! Thank you.
Juan M.
Udemy student
Best math teacher in the game.
Marty M.
Udemy student
very helpful to learn with
Tong L.
Udemy student
Excellent teaching!
Almir B.
Udemy student
Hania is the teacher everbody dreamed to have during school life.
Andrzej P.
Udemy student
A very nice series of lectures on the topic, with many different applications and examples covered. I really liked the worked problems, clear and well explained.
Joseph B.
Udemy student
I have struggled sometimes with this concept and have only recently began to use it when factoring was not practical. This course will help me solidify my skills such that I can share them with others with whom I work.