Griffiths QM Problem 4.3: Constructing Spherical Harmonics for l=m=0 and l=2, m=1

In this video I will show you how to solve problem 4.3 as it appears in the 3rd edition of griffiths introduction to quantum mechanics. The problem states:
Use equations 4.27, 4.28 and 4.32 to construct Y00 and Y21. Chekc that they are normalized and orthogonal

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My name is Nick Heumann, I am a recently graduated physicist. I love to teach physics, so I decided to give YouTube a try. English is not my first language, but I hope that you can understand me well enough regardless.
▬ Contents of this video ▬▬▬▬▬▬▬▬▬▬
00:00 Introducing the Problem & Reminder
01:13 Calculating Y00
03:28 Checking that Y00 is Normalized
05:44 Calculating Y21
11:02 Check that Y21 is Normalized
16:13 Checking orthogonality