Calculus 2 Lecture 10.4: Using Polar Coordinates and Polar Equations

Calculus 2 Lecture 10.4: Using Polar Coordinates and Polar Equations

[keldonchase]

Day 1:
Introduction to Polar Coordinates: 0:00
First Example (Graphing Polar Coordinates, positive r length): 7:32
Second Example (Graphing Polar Coordinates, positive r length): 10:36
First Example (Graphing Polar Coordinates, negative r length): 13:10
Second Example (Graphing Polar Coordinates, negative r length): 15:16
Brief Review of Graphing Polar Coordinates: 16:33
Introduction to Translating Between Polar Coordinates and Rectangular Coordinates: 17:10
First Example (Translating From Polar to Rectangular Coordinates): 20:28
Second Example (Translating From Polar to Rectangular Coordinates): 24:03
First Example (Translating From Rectangular to Polar Coordinates): 27:35
Second Example (Translating From Rectangular to Polar Coordinates): 33:41
First Example (Converting a Polar Equation into a Rectangular Equation): 39:41
Day 2:
Introduction to Symmetry: 46:52
First Example (Checking for Symmetry): 48:42
First Example (Graphing a Polar Graph Symmetric about Polar Axis): 52:54
Second Example (Graphing a Polar Graph Symmetric about Polar Axis and Theta = pi/2) : 1:03:22
Third Example (Graphing a Rectangular Graph Symmetric about the X-Axis and the Y-Axis): 1:26:22
Day 3:
Introduction to Finding Tangent Lines of Polar Graphs: 1:37:35
First Example (Finding the Slope of a Tangent Line): 1:46:47
Finding Horizontal and Vertical Tangent Lines to Polar Graphs: 1:59:16

[opelgtman]

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[danieljones]

at 1:11:00 I believe the correct trig identity is cos(a-b)= cos(a)cos(b)+sin(a)sin(b), not minus. But the answer is the same. I love these videos and Professor Leonard has given me such a better understanding of math than my previous classes. Thank you sir!

[ZnNlove]

Didn't know superman was a part time calculus professor ^^

[annika]

Professor Leonard, because of you I passed Calc 2 and ended with an A-. I know I am one of the many comments that say that but I am truly grateful for you. At the beginning of the semester, I did badly on my first exam and felt that I would never get through calc 2. Then, I started watching your videos and I began to actually understand everything. I had a B- at first and thought I would have to settle for a B, but I was able to get a 95 on the final and never in the world thought I would get an A-!! It could not have been without you! You are very good at teaching and I aspire to teach like you one day. Keep up the humor in the videos too! Thank you for the free amazing content!!!!

[KyleserBlogspotCa]

These are great videos! Though I would like to make a suggestion. Seeing as your videos are pretty long it would be a great idea to put topics and time stamps in the description so that if someone wanted to watch a specific category they could find it easily. Other than that, these are amazing. Thanks. 

[harmsyamial]

the best tutor in the history of the world has ever known, He helped me enormously to get through calculus with a deep and full understanding of the material whilst other teachers and professors are lacking in easing the concept. I found a lot of helpful things in Professor Leonard that I have not seen in any instructor elsewhere, , , , thank Leonard, , I love man

[ishtiaqhussain]

At 1:08:45 I suppose it’s meant to be a + sign rather than negative (check the identity for cos(a-b)). But it doesn’t make a difference in the result. Lmk if I am mistaken. Prof Leonard! I admire your dedication to teaching. If I ever lecture/teach, I will try to do in your way.
Edit: It has been noted in comments by others I realise.

[sirling]

Thank you, Superman. You helped a lot, not all the professors are like you, so we have to find a guy like you to save our math grade.

[ProfessorLeonard]

kinkehpanda Good Catch!! I meant + but I must have missed that.  Thank you.  For everyone else, make a note.

[OVERORLY]

Dude How much money do you want to teach linear algebra

[fartleka]

Hi Leonard. I have been watching your videos for the past few days and you are amazing. I failed my calc exam because I hate studying the material that I don't even fully understand (so I didn't study), but watching your videos has changed my perspective completely. It now makes sense. I'm determined to actually study now that I have these resources. Thank you for making this material available for us struggling students for free (although I'd love it if you were my actual calculus teacher!!!). I actually PAY ATTENTION and ENJOY watching your videos because you explain things in a way that retains its complexity and terminology... but in a simple, step-by-step way. I have already watched 3 of your videos totaling to ~8 hours. I can't even stay fully engaged for a 1.5 hour lecture at my university! That is where the teaching difference is

[MasonMcKinney-jxjp]

These videos are a miracle from heaven, allowing me to self-study for AP Cal BC in just 3 months as a homeschooler. Anyway, I feel bad by pointing out a silly mistake because of how perfect Prof Leonard always is. But I'll do it for everyone watching in 2024 and beyond. At 1:10:00-1:11:15 he used a subtraction cos identity incorrectly. Leonard accidentally put a minus in between the identity's solution as opposed to a plus. Because cos(a-b) results in cosacosb+sinasinb. Hope this helps!

[Ali-dntl]

Amazing videos! Although super long, they're clear, detailed, and super easy to understand.
I now watch your video before my professor teaches the section and im killin calc 2.
Thank You So Much!

[echo-channel]

cos(A - B) should be [ cosA cosB + sinA sinB ] but the calc still works out in the demo as 1, i.e. 1-0 => 1+0. Awesome videos!

[venkatamarutiramtarigoppul]

1:03:05 this shows how considerate he is towards his students . Thank you proffesor leonard fo explaining so good

[loic]

This chapter is so much easier than the previous chapter... dumb series. I have my exam tomorrow and im really confident :) Thank you so much :D

[adamharoon]

My Calc 2 course is covering this topic now. Thank you so much for these wonderful videos Professor Leonard! I never thought I would come to enjoy mathematics.

[thebassofmontecristo]

The "buttioid". The best thing I got from this video! :) Just kidding! Fantastic work!

[vivienne_lavida]

Best calc professor ever!! Thank you so much for your handwork and videos!