I just failed my calc 2 this semester.I was about to give up on being an engineer, even I told my advisor that I would change my career path for the future and that I would enroll to other classes not related to engineering, however, I ended up thinking that because I failed once it doesn’t mean it’s over. I’ll watch this and do a lot of practice problems to do in the summer, I’ll be prepare to ace the class next semester, never give up guys
I needed this as well. Just had a bad grade in calc myself because of terrible algebra in fact so I'll work even harder. No going here and there, no silly wasting of time. Just gonna work my ass off from now on.
@@djay00009 it's inspiring another Indian like me failed cause I live in US and people here think Indians are super smart so it's a bit of an embarrassment that I failed.
I have gone through Calculus I and Calculus II of this channel. This one Calculus II has more gaps and flip-around than previous video that severely affects understanding. Here I put the chapter timeline by its topic in sequence, but unable to do anything for the gaps: Calculus II, 4.4.1 (2:49:46) - L'Hospital's Rule 4.4.2 (2:57:02) - L'hosptal's Rule on Other Intermediate Forms (1:13:03) - Trig identities (1:25:01) - Proof of the Angle Sum Formulas 6.1.1 (00:00) - Area between curves- 6.2.2 (11:11) - Volumes of solids of revolution 6.2.1 (21:33) - Volumes using cross sections 6.4.1 (39:50) - Work as an integral 6.5.1 (51:30) - Average value of a function 6.5.2 (59:05) - Proof of the Mean Value Theorem of integrals 7.1.1 (1:04:55) - Integration by parts 7.2.1 (1:29:37) - Integrals involving Odd powers of Sine and Cosine 7.2.2 (1:36:21) - Integrals involving Even powers of Sine and Cosine 7.2.3 (1:44:59) - Special trig Integrals 7.3.1 (1:47:36) - Integration using Trig substitution 7.4.1 (1:56:21) - Integrals of Rational functions 7.8.1 (2:03:21) - Improper integrals Type 1 7.8.2 (2:10:13) - Improper integrals Type 2 7.8.3 (2:14:20) - The comparison Theorem for Integrals 8.1.1 (31:34) - Arclength 10.1 (6:15:38) - Parametric Equations 10.2.1 (6:27:06) - Slopes of Parametric Curves 10.2.2 (6:32:47) - Area under a Parametric Curve 10.2.3 (6:38:07) - Arclength of Parametric Curves 10.3 (6:45:20) - Polar Coordinates 11.1.1 (2:19:43)- Sequence Definitions and Notation (2:39:41) sequences-More definitions (2:46:06) Monotonic and bounded Sequences 11.2.1 (2:31:05)- Series Definitions 11.3.1 (3:43:32)- The integral test 11.4.1 (3:56:48)- Comparison Test for Series 11.4.2 (4:03:29)- The limit comparison test 11.4.3 (4:09:24)- Proof of the Limit Comparison Test 11.6.1 (4:16:00)- Absolute Convergence 11.6.2 (4:25:03) - The Ratio test 11.6.3 (4:30:22) - Proof of the Ratio test 11.7 (4:39:34) - Series Convergence Test Strategy 11.8.1 (5:02:28) - Power Series 11.8.2 (5:05:42) - Convergence of Power Series 11.8.3 (5:21:07) - Power Series interval of Convergence Example 11.8.4 (5:30:46) - Proofs of Facts about Convergence of Power Series 11.9.1 (5:36:19) - Power Series as functions 11.9.2 (5:43:36) - Representing Functions with Power Series 11.10.4 (5:52:07) - Using Taylor Series to find Sums of Series 11.11.1 (6:02:18) - Taylor Series Introduction
⌨️ (0:00:00) Area Between Curves ⌨️ (0:11:11) Volumes of Solids of Revolution ⌨️ (0:21:33) Volumes Using Cross-Sections ⌨️ (0:31:34) Arclength ⌨️ (0:39:50) Work as an Integral ⌨️ (0:51:30) Average Value of a Function ⌨️ (0:59:05) Proof of the Mean Value Theorem for Integrals ⌨️ (1:04:55) Integration by Parts ⌨️ (1:13:03) Trig Identities ⌨️ (1:25:01) Proof of the Angle Sum Formulas ⌨️ (1:29:37) Integrals Involving Odd Powers of Sine and Cosine ⌨️ (1:36:21) Integrals Involving Even Powers of Sine and Cosine ⌨️ (1:44:59) Special Trig Integrals ⌨️ (1:47:36) Integration Using Trig Substitution ⌨️ (1:56:21) Integrals of Rational Functions ⌨️ (2:03:59) Improper Integrals - Type 1 ⌨️ (2:10:13) Improper Integrals - Type 2 ⌨️ (2:14:20) The Comparison Theorem for Integrals ⌨️ (2:19:43) Sequences - Definitions and Notation ⌨️ (2:31:05) Series Definitions ⌨️ (2:39:41) Sequences - More Definitions ⌨️ (2:46:06) Monotonic and Bounded Sequences Extra ⌨️ (2:49:46) L'Hospital's Rule ⌨️ (2:57:02) L'Hospital's Rule on Other Indeterminate Forms ⌨️ (3:06:48) Convergence of Sequences ⌨️ (3:30:38) Geometric Series ⌨️ (3:43:32) The Integral Test ⌨️ (3:56:48) Comparison Test for Series ⌨️ (4:03:29) The Limit Comparison Test ⌨️ (4:09:24) Proof of the Limit Comparison Test ⌨️ (4:16:00) Absolute Convergence ⌨️ (4:25:03) The Ratio Test ⌨️ (4:30:22) Proof of the Ratio Test ⌨️ (4:39:34) Series Convergence Test Strategy ⌨️ (4:50:26) Taylor Series Introduction ⌨️ (5:02:28) Power Series ⌨️ (5:05:42) Convergence of Power Series ⌨️ (5:21:07) Power Series Interval of Convergence Example ⌨️ (5:30:46) Proofs of Facts about Convergence of Power Series ⌨️ (5:36:19) Power Series as Functions ⌨️ (5:43:36) Representing Functions with Power Series ⌨️ (5:52:07) Using Taylor Series to find Sums of Series ⌨️ (6:02:18) Taylor Series Theory and Remainder ⌨️ (6:15:38) Parametric Equations ⌨️ (6:27:06) Slopes of Parametric Curves ⌨️ (6:32:47) Area under a Parametric Curve ⌨️ (6:38:07) Arclength of Parametric Curves ⌨️ (6:45:20) Polar Coordinates
I watched the calculus 1 video a week prior my spring semester and got a head start with limits and i ended the semester with a 105/100!! Yup i got extra credit. Definitely gonna watch this a week prior next fall semester.
I have calc 2 exam in like 2 days and I only started studying yesterday, probably not gonna manage, but I'll try my best. Your video is my savior in a way.
@@thisisangellorenzo I did 5 out of 6, but man bless symbolab and the organic chemistry tutor. I took a note for myself and for calc 3 I'll prepare from before the course starts. Also mind I was online and could help myself, I don't recommend studying less than a week before.
I reeaallly wish I had seen this sooner!!! I have my calc 2 final tomorrow and I feel like I'm FINALLY starting to understand some of these concepts from this video! I bet I could have gotten such a better grade on a few of my tests if I watched this at the beginning of the semester. THANK YOU SO MUCH!!!
I'm going to retake calc 2 in person next fall so this is going to save me so many tears. I finally understand where integration by parts came from and so much more
@@praveen7603 I'm doing a lot better this time actually like I have a solid B in the class now and can probably get an A if I do well on the next two exams
Me: Suffering during the first 2 weeks of Calculus 2 and thinking it will continue to the end of the semester My recommended: Supp dude, here is Calculus 2 - Full College Course Thank you, Your channel is awesome!
I’m in the same shoes as you were rn. I feel like I never to cal 1 because I forgot everything in the summer and can’t even find a anti derivative now! Have to review now
⭐ = Checkpoint (0:00:00) Area Between Curves (0:11:11) Volumes of Solids of Revolution (0:21:33) Volumes Using Cross-Sections (0:31:34) Arclength (0:39:50) Work as an Integral (0:51:30) Average Value of a Function (0:59:05) Proof of the Mean Value Theorem for Integrals (1:04:55) Integration by Parts (1:13:03) Trig Identities (1:25:01) Proof of the Angle Sum Formulas (1:29:37) Integrals Involving Odd Powers of Sine and Cosine (1:36:21) Integrals Involving Even Powers of Sine and Cosine (1:44:59) Special Trig Integrals (1:47:36) Integration Using Trig Substitution (1:56:21) Integrals of Rational Functions (2:03:59) Improper Integrals - Type 1 (2:10:13) Improper Integrals - Type 2 (2:14:20) The Comparison Theorem for Integrals (2:19:43) Sequences - Definitions and Notation (2:31:05) Series Definitions (2:39:41) Sequences - More Definitions (2:46:06) Monotonic and Bounded Sequences Extra (2:49:46) L'Hospital's Rule (2:57:02) L'Hospital's Rule on Other Indeterminate Forms (3:06:48) Convergence of Sequences (3:30:38) Geometric Series (3:43:32) The Integral Test (3:56:48) Comparison Test for Series (4:03:29) The Limit Comparison Test (4:09:24) Proof of the Limit Comparison Test (4:16:00) Absolute Convergence (4:25:03) The Ratio Test (4:30:22) Proof of the Ratio Test (4:39:34) Series Convergence Test Strategy (4:50:26) Taylor Series Introduction (5:02:28) Power Series (5:05:42) Convergence of Power Series (5:21:07) Power Series Interval of Convergence Example (5:30:46) Proofs of Facts about Convergence of Power Series (5:36:19) Power Series as Functions (5:43:36) Representing Functions with Power Series (5:52:07) Using Taylor Series to find Sums of Series (6:02:18) Taylor Series Theory and Remainder (6:15:38) Parametric Equations (6:27:06) Slopes of Parametric Curves (6:32:47) Area under a Parametric Curve (6:38:07) Arclength of Parametric Curves (6:45:20) Polar Coordinates
@@kuruvakoushik7613 I don't don't Calc 3 is a requirement for most engineering degrees but it does depend on the school. I'd ask your advisor if you're in school or your peers if you're going about this without college
@@gold4963 My son is in highschool in India he is passionate about STEM I just wanted to ask is Calculus 2 & 3 taught in American Collages or its a highschool level course?
@@smritiverma4600 it depends some people decide to only get to pre calc in or even just algebra 2 in high school while me an overachiever went for calc BC and is now driving toa college to get higher levels of calc done so really its just if you want to
I would love to see a course on Advanced Probabilities and Statistics one day, especially covering topics like Random Processes, Markov Chains etc. Like someone pointed out in another comment, a course on Linear Algebra too would be really nice. Besides that thanks for everything 💓
@@nobivy3524 I can give you mine. Learning Calc 1 and 2 on my own to skip college classes. I am applying and likely taking the placement test in the near future. Have been practicing, watching, and could not thank enough for these videos and Pauls's Online Notes. He provides example problems on his website and has explanations also.
My Calculus 2 met for 60 hours 40 minutes. It was hard. Calculus 3 was three-dimensional geometry, and I gave up. The benefit of RUclips is the professor doesn't have to take attendance, say what problems to do for homework, ask and answer questions, and give tests and review for them. It would be interesting to know what percent of an average college course is spent on things other than teaching.
@@devjoshi7062 I am from U.S. but the calc 3 class in my college is useless. Professor is going so fast she is doing integration by parts in her head and I can't even keep up.
Imagine how good I would be in literally everything by now if instead of overwhelming myself in college with professors who cant teach I just took a year off and studied by myself
Professor Linda Green, thank you for an incredible explanation and analysis of Calculus Two, a Full College Course. Everything in Calculus Two was explained and covered in full detail from start to finish. Th examples, problems and proofs are very helpful for all students taking Calculus Two worldwide. I took Calculus Two at the old Catonsville Community College in Catonsville, Maryland in the mid 1980's and I am still learning about topics /materials about Calculus that was not taught to me in a fourteen-week Semester.
⭐️ Course Contents ⭐️ ⌨️ (0:00:00) Area Between Curves ⌨️ (0:11:11) Volumes of Solids of Revolution ⌨️ (0:21:33) Volumes Using Cross-Sections ⌨️ (0:31:34) Arclength ⌨️ (0:39:50) Work as an Integral ⌨️ (0:51:30) Average Value of a Function ⌨️ (0:59:05) Proof of the Mean Value Theorem for Integrals ⌨️ (1:04:55) Integration by Parts ⌨️ (1:13:03) Trig Identities ⌨️ (1:25:01) Proof of the Angle Sum Formulas ⌨️ (1:29:37) Integrals Involving Odd Powers of Sine and Cosine ⌨️ (1:36:21) Integrals Involving Even Powers of Sine and Cosine ⌨️ (1:44:59) Special Trig Integrals ⌨️ (1:47:36) Integration Using Trig Substitution ⌨️ (1:56:21) Integrals of Rational Functions ⌨️ (2:03:59) Improper Integrals - Type 1 ⌨️ (2:10:13) Improper Integrals - Type 2 ⌨️ (2:14:20) The Comparison Theorem for Integrals ⌨️ (2:19:43) Sequences - Definitions and Notation ⌨️ (2:31:05) Series Definitions ⌨️ (2:39:41) Sequences - More Definitions ⌨️ (2:46:06) Monotonic and Bounded Sequences Extra ⌨️ (2:49:46) L'Hospital's Rule ⌨️ (2:57:02) L'Hospital's Rule on Other Indeterminate Forms ⌨️ (3:06:48) Convergence of Sequences ⌨️ (3:30:38) Geometric Series ⌨️ (3:43:32) The Integral Test ⌨️ (3:56:48) Comparison Test for Series ⌨️ (4:03:29) The Limit Comparison Test ⌨️ (4:09:24) Proof of the Limit Comparison Test ⌨️ (4:16:00) Absolute Convergence ⌨️ (4:25:03) The Ratio Test ⌨️ (4:30:22) Proof of the Ratio Test ⌨️ (4:39:34) Series Convergence Test Strategy ⌨️ (4:50:26) Taylor Series Introduction ⌨️ (5:02:28) Power Series ⌨️ (5:05:42) Convergence of Power Series ⌨️ (5:21:07) Power Series Interval of Convergence Example ⌨️ (5:30:46) Proofs of Facts about Convergence of Power Series ⌨️ (5:36:19) Power Series as Functions ⌨️ (5:43:36) Representing Functions with Power Series ⌨️ (5:52:07) Using Taylor Series to find Sums of Series ⌨️ (6:02:18) Taylor Series Theory and Remainder ⌨️ (6:15:38) Parametric Equations ⌨️ (6:27:06) Slopes of Parametric Curves ⌨️ (6:32:47) Area under a Parametric Curve ⌨️ (6:38:07) Arclength of Parametric Curves ⌨️ (6:45:20) Polar Coordinates
My study's timestamps . Day one (7:33) (21:24) . Day two (31:58) (39:51) (51:31) . Day three (59:07) (1:04:57) . Day four (1:13:06) (1:25:04) . Day five (1:36:27) . Day six (1:38:17) (1:41:00) . Day seven (1:45:00) . Day eight (1:47:50) . Day nine (1:48:23) (1:56:28) . Day ten (2:04:00) . Day eleven (2:05:57) (2:10:15) . Day twelve (2:14:24) . Day thirteen (2:19:46) . Day fourteen (2:21:45) (2:26:07) . Day fifteen (2:31:15) . Day sixteen (2:39:51) . Day seventeen (2:50:05) . Day eighteen (2:57:07) . Day nineteen (3:01:58)
i feel like my university intentionally makes these concepts harder. like we're being taught the same things but at the same time, the problems they give us are expert lvl problems. even my TA's struggle to solve them sometimes
In connection to the integral calculus, recently it was published a book about MIT integration bee, under the title " MIT Integration Bee, Solutions of Qualifying Tests from 2010 to 2023" You can simply find it!
People in comment section getting full marks in college semester by just watching a video its a good video to clear the basics but for my country not enough to qualify even college entrance exam 😭
@@masternobody1896 By standard, it goes up to Calculus 3 but it all depends on the college. Generally cal3 covers Ordinary differential equations and things like Laplace Transform. Some might have multivariable calculus (vector analysis) included in cal3 or a whole new course.
@@Moecodess I ended up passing the class but I failed the final for sure. Basically, the final was extremely heavy on understanding series and sequences using the different strategies given. You really got to understand those in-depth to pass. I was pretty much good on all the physics applications. Parametric equations and polar coordinates also got me on the final. Honestly, the best thing to do is start early on notes and homework and just do the class that way. I feel this video left a lot of gaps of understanding, especially in applying the series and sequences.
@@kaelart5876 to clear all your doubts, it was worth it, unless you feel like you're learning enough in class (in which case it's wasting your time). Otherwise, you can save a LOT of study time by watching this and taking notes, I did.
@@juandanielcastanierrivas9545 thanks man i've barely learned anything in class so im gonna invest my time on this one this week. good luck to the two of us
i am pretty sure if you guys collaborate with Khan Acdemy,you could make a video like:learn 1st to 12th grade math in 200 hours with practise material and stuff.
방학 이야기 지난 학기가 끝나고 3주 동안의 방학이 있었습니다. 저는 그 방학에 고향에 갔다 왔습니다. 고향에 있는 언니가 결혼을 해서 꼭 가야 했습니다. 고향에 가기 전에 저는 남대문 시장에 가서 언니의 결혼 선몰을 샀습니다. 언니가 좋아하는 화장품과 예쁜 가방을 골랐습니다. 언니는 그 결혼 선물을 받고 아주 좋아했습니다. 언니가 결혼을 방학에 하지 않았으면 저는 결혼식을 볼 수 없었을 겁니다. 고향에 있는 동안 정말 행복한 시간을 보냈습니다. 부모님과 이야기도 많이 하고 할아버지 댁에도 갔습니다. 한국에서는 먹을 수 없는 고향 음식도 많이 먹었습니다. 또 그동안 못 만난 친구들도 만나서 근처에 있는 바다에도 놀러 가고 등산도 같이 갔습니다. 그러는 동안 시간이 정말 빨리 갔습니다. 새 학기는 월요일부터 시작되었는데 저는 지난 주 수요일 밤에 한국에 돌아왔습니다. 고향에 더 있고 싶었지만 다음 학기를 준비하려고 일찍 돌아왔습니다. 나흘 동안 방 청소도 하고 한국어 공부도 했습니다. 고향에서 오랫동안 한국말을 하지 않아서 한국말을 많이 잊어버렸습니다. 그래서 초급 2반 수업이 시작되기 전에 지난 학기에 배운 것을 복습했습니다. 이번 학기 동안 한국어 공부도 열심히 하고 새로 만난 친구들과 잘 지내고 싶습니다. 이번 학기에도 재미있는 일이 많이 있으면 좋겠습니다.
Guys We need linear algebra Likes please!! Also thanks FCC for your works its amazing and helping a lot of students around the world, I always struggled with math specially calculus 2 I failed at it for 3 times! I got it in the end
Indeed. In the original video, Beau misspoke and said "in this 5 hour video..." but the video is 7 hours long, so we thought this would cause confusion. So we re-uploaded.
I hope to I hope to continue to present these lectures, as they are wonderful, and benefit from the study in them, and I fully rely on them. I hope to continue to present on other topics continuously.
I failed last semester, and I feel like the professor I have this semester doesn't teach too well. It was the only option I had this time around so I'm thinking of just watching this instead.
Maybe it's because I'm not from the States, but I learnt all this in Calculus I. I suppose Calculus II in my country is equivalent to Calculus III? I studied all this in the first year of my degree.
Did you study series in Calculus I? I'm from Brazil - the part of Integrals we study in Calculus I (at least at UnB), but all of series is related to Calculus II
@@gabrielciriatico6464 Yes, I studied both numerical and functional series. I think it was distributed as: Calculus I: one variable analysis and series. Calculus II: multivariable analysis. (I don't know if they are called exactly like that in English, I'm translating directly from Spanish)
I just failed my calc 2 this semester.I was about to give up on being an engineer, even I told my advisor that I would change my career path for the future and that I would enroll to other classes not related to engineering, however, I ended up thinking that because I failed once it doesn’t mean it’s over. I’ll watch this and do a lot of practice problems to do in the summer, I’ll be prepare to ace the class next semester, never give up guys
You made the right choice. You shouldn’t let one class decide what your life is going to be.
I had the same experience thank you for sharing yours
don't worry I failed my physics 1 because I cheated this time I won't cheat though.
I needed this as well. Just had a bad grade in calc myself because of terrible algebra in fact so I'll work even harder. No going here and there, no silly wasting of time. Just gonna work my ass off from now on.
@@djay00009 it's inspiring another Indian like me failed cause I live in US and people here think Indians are super smart so it's a bit of an embarrassment that I failed.
I have gone through Calculus I and Calculus II of this channel. This one Calculus II has more gaps and flip-around than previous video that severely affects understanding. Here I put the chapter timeline by its topic in sequence, but unable to do anything for the gaps: Calculus II,
4.4.1 (2:49:46) - L'Hospital's Rule
4.4.2 (2:57:02) - L'hosptal's Rule on Other Intermediate Forms
(1:13:03) - Trig identities
(1:25:01) - Proof of the Angle Sum Formulas
6.1.1 (00:00) - Area between curves-
6.2.2 (11:11) - Volumes of solids of revolution
6.2.1 (21:33) - Volumes using cross sections
6.4.1 (39:50) - Work as an integral
6.5.1 (51:30) - Average value of a function
6.5.2 (59:05) - Proof of the Mean Value Theorem of integrals
7.1.1 (1:04:55) - Integration by parts
7.2.1 (1:29:37) - Integrals involving Odd powers of Sine and Cosine
7.2.2 (1:36:21) - Integrals involving Even powers of Sine and Cosine
7.2.3 (1:44:59) - Special trig Integrals
7.3.1 (1:47:36) - Integration using Trig substitution
7.4.1 (1:56:21) - Integrals of Rational functions
7.8.1 (2:03:21) - Improper integrals Type 1
7.8.2 (2:10:13) - Improper integrals Type 2
7.8.3 (2:14:20) - The comparison Theorem for Integrals
8.1.1 (31:34) - Arclength
10.1 (6:15:38) - Parametric Equations
10.2.1 (6:27:06) - Slopes of Parametric Curves
10.2.2 (6:32:47) - Area under a Parametric Curve
10.2.3 (6:38:07) - Arclength of Parametric Curves
10.3 (6:45:20) - Polar Coordinates
11.1.1 (2:19:43)- Sequence Definitions and Notation
(2:39:41) sequences-More definitions
(2:46:06) Monotonic and bounded Sequences
11.2.1 (2:31:05)- Series Definitions
11.3.1 (3:43:32)- The integral test
11.4.1 (3:56:48)- Comparison Test for Series
11.4.2 (4:03:29)- The limit comparison test
11.4.3 (4:09:24)- Proof of the Limit Comparison Test
11.6.1 (4:16:00)- Absolute Convergence
11.6.2 (4:25:03) - The Ratio test
11.6.3 (4:30:22) - Proof of the Ratio test
11.7 (4:39:34) - Series Convergence Test Strategy
11.8.1 (5:02:28) - Power Series
11.8.2 (5:05:42) - Convergence of Power Series
11.8.3 (5:21:07) - Power Series interval of Convergence Example
11.8.4 (5:30:46) - Proofs of Facts about Convergence of Power Series
11.9.1 (5:36:19) - Power Series as functions
11.9.2 (5:43:36) - Representing Functions with Power Series
11.10.4 (5:52:07) - Using Taylor Series to find Sums of Series
11.11.1 (6:02:18) - Taylor Series Introduction
Thank you
wow amazing thank you
Thanks!
thank you so much!
Thank you so much
⌨️ (0:00:00) Area Between Curves
⌨️ (0:11:11) Volumes of Solids of Revolution
⌨️ (0:21:33) Volumes Using Cross-Sections
⌨️ (0:31:34) Arclength
⌨️ (0:39:50) Work as an Integral
⌨️ (0:51:30) Average Value of a Function
⌨️ (0:59:05) Proof of the Mean Value Theorem for Integrals
⌨️ (1:04:55) Integration by Parts
⌨️ (1:13:03) Trig Identities
⌨️ (1:25:01) Proof of the Angle Sum Formulas
⌨️ (1:29:37) Integrals Involving Odd Powers of Sine and Cosine
⌨️ (1:36:21) Integrals Involving Even Powers of Sine and Cosine
⌨️ (1:44:59) Special Trig Integrals
⌨️ (1:47:36) Integration Using Trig Substitution
⌨️ (1:56:21) Integrals of Rational Functions
⌨️ (2:03:59) Improper Integrals - Type 1
⌨️ (2:10:13) Improper Integrals - Type 2
⌨️ (2:14:20) The Comparison Theorem for Integrals
⌨️ (2:19:43) Sequences - Definitions and Notation
⌨️ (2:31:05) Series Definitions
⌨️ (2:39:41) Sequences - More Definitions
⌨️ (2:46:06) Monotonic and Bounded Sequences Extra
⌨️ (2:49:46) L'Hospital's Rule
⌨️ (2:57:02) L'Hospital's Rule on Other Indeterminate Forms
⌨️ (3:06:48) Convergence of Sequences
⌨️ (3:30:38) Geometric Series
⌨️ (3:43:32) The Integral Test
⌨️ (3:56:48) Comparison Test for Series
⌨️ (4:03:29) The Limit Comparison Test
⌨️ (4:09:24) Proof of the Limit Comparison Test
⌨️ (4:16:00) Absolute Convergence
⌨️ (4:25:03) The Ratio Test
⌨️ (4:30:22) Proof of the Ratio Test
⌨️ (4:39:34) Series Convergence Test Strategy
⌨️ (4:50:26) Taylor Series Introduction
⌨️ (5:02:28) Power Series
⌨️ (5:05:42) Convergence of Power Series
⌨️ (5:21:07) Power Series Interval of Convergence Example
⌨️ (5:30:46) Proofs of Facts about Convergence of Power Series
⌨️ (5:36:19) Power Series as Functions
⌨️ (5:43:36) Representing Functions with Power Series
⌨️ (5:52:07) Using Taylor Series to find Sums of Series
⌨️ (6:02:18) Taylor Series Theory and Remainder
⌨️ (6:15:38) Parametric Equations
⌨️ (6:27:06) Slopes of Parametric Curves
⌨️ (6:32:47) Area under a Parametric Curve
⌨️ (6:38:07) Arclength of Parametric Curves
⌨️ (6:45:20) Polar Coordinates
Thanks man
Boom 💥, nice job
@@qooooe your welcome
Thank you so much!
@@laddysingh4486 welcome :)
after 3 months ive finally finished this video. I just want to thank everyone involved for making such an awesome video free to watch
How many hours per day?
@@carlosmunoz2148 your mom
i dont get how thats funny but ok
@@carlosmunoz2148 413 Minutes / (3 months * 30 days) = 4.5 Minutes Per Day on average
trying to finish it in 2 weeks here 😅
I watched the calculus 1 video a week prior my spring semester and got a head start with limits and i ended the semester with a 105/100!! Yup i got extra credit. Definitely gonna watch this a week prior next fall semester.
How did you do?
facts how did you do buddy ? I’m currently in Calc 2 too
POV: your Calc final is tomorrow
im grade 3
I'm in preschool
@@zoasis7805 googoo gaga wahhhh
Your calc final is in 5 hours and you're on 1.5 speed
In 2 hours actually
gonna learn this over winter break so my spring semester is gonna be chill as heck
I have calc 2 exam in like 2 days and I only started studying yesterday, probably not gonna manage, but I'll try my best. Your video is my savior in a way.
Did you pass the exam?
@@thisisangellorenzo I did 5 out of 6, but man bless symbolab and the organic chemistry tutor. I took a note for myself and for calc 3 I'll prepare from before the course starts. Also mind I was online and could help myself, I don't recommend studying less than a week before.
lol im cramming rn for my exam in two days
I reeaallly wish I had seen this sooner!!! I have my calc 2 final tomorrow and I feel like I'm FINALLY starting to understand some of these concepts from this video! I bet I could have gotten such a better grade on a few of my tests if I watched this at the beginning of the semester. THANK YOU SO MUCH!!!
I'm going to retake calc 2 in person next fall so this is going to save me so many tears. I finally understand where integration by parts came from and so much more
What is ur score
@@praveen7603 I'm doing a lot better this time actually like I have a solid B in the class now and can probably get an A if I do well on the next two exams
@@pipinanaC8 Glad to hear that , all the best for future 👍
These have been a tremendous help for me going back and re-learning the math I took decades ago. Thank you so much!
Glad I finished the entire video before my cal 2 class next semester, I can finally enjoy my peanut butter sandwich now
i hope it was tasty
You finished the whole thing??!?! I'm peanut butter and jealous.
How’s the class going? Haha.
How did semester went got A in cal
Peanut butter ? Weak. Put bacon in jt
Me: Suffering during the first 2 weeks of Calculus 2 and thinking it will continue to the end of the semester
My recommended: Supp dude, here is Calculus 2 - Full College Course
Thank you, Your channel is awesome!
I’m in the same shoes as you were rn. I feel like I never to cal 1 because I forgot everything in the summer and can’t even find a anti derivative now! Have to review now
⭐ = Checkpoint
(0:00:00) Area Between Curves
(0:11:11) Volumes of Solids of Revolution
(0:21:33) Volumes Using Cross-Sections
(0:31:34) Arclength
(0:39:50) Work as an Integral
(0:51:30) Average Value of a Function
(0:59:05) Proof of the Mean Value Theorem for Integrals
(1:04:55) Integration by Parts
(1:13:03) Trig Identities
(1:25:01) Proof of the Angle Sum Formulas
(1:29:37) Integrals Involving Odd Powers of Sine and Cosine
(1:36:21) Integrals Involving Even Powers of Sine and Cosine
(1:44:59) Special Trig Integrals
(1:47:36) Integration Using Trig Substitution
(1:56:21) Integrals of Rational Functions
(2:03:59) Improper Integrals - Type 1
(2:10:13) Improper Integrals - Type 2
(2:14:20) The Comparison Theorem for Integrals
(2:19:43) Sequences - Definitions and Notation
(2:31:05) Series Definitions
(2:39:41) Sequences - More Definitions
(2:46:06) Monotonic and Bounded Sequences Extra
(2:49:46) L'Hospital's Rule
(2:57:02) L'Hospital's Rule on Other Indeterminate Forms
(3:06:48) Convergence of Sequences
(3:30:38) Geometric Series
(3:43:32) The Integral Test
(3:56:48) Comparison Test for Series
(4:03:29) The Limit Comparison Test
(4:09:24) Proof of the Limit Comparison Test
(4:16:00) Absolute Convergence
(4:25:03) The Ratio Test
(4:30:22) Proof of the Ratio Test
(4:39:34) Series Convergence Test Strategy
(4:50:26) Taylor Series Introduction
(5:02:28) Power Series
(5:05:42) Convergence of Power Series
(5:21:07) Power Series Interval of Convergence Example
(5:30:46) Proofs of Facts about Convergence of Power Series
(5:36:19) Power Series as Functions
(5:43:36) Representing Functions with Power Series
(5:52:07) Using Taylor Series to find Sums of Series
(6:02:18) Taylor Series Theory and Remainder
(6:15:38) Parametric Equations
(6:27:06) Slopes of Parametric Curves
(6:32:47) Area under a Parametric Curve
(6:38:07) Arclength of Parametric Curves
(6:45:20) Polar Coordinates
I hope I had this video last year...
Nothing but respect for you guys.
Is this sufficient for engineering
@@kuruvakoushik7613 I don't don't Calc 3 is a requirement for most engineering degrees but it does depend on the school. I'd ask your advisor if you're in school or your peers if you're going about this without college
Free Code Camp? more like F R E E C O L L E G E
Literally, I learn more here than in college
Yeah, no joke. I'm gonna use this video to prepare myself a bit for my real Calculus II course. I'm terrified.
@@gold4963 My son is in highschool in India he is passionate about STEM I just wanted to ask is Calculus 2 & 3 taught in American Collages or its a highschool level course?
@@smritiverma4600 it depends some people decide to only get to pre calc in or even just algebra 2 in high school while me an overachiever went for calc BC and is now driving toa college to get higher levels of calc done so really its just if you want to
Lmao
❤ Found the refresher I need before tackling the actuarial exams after 25 years of not doing math. Thank you!!!
did you pass?
I would love to see a course on Advanced Probabilities and Statistics one day, especially covering topics like Random Processes, Markov Chains etc. Like someone pointed out in another comment, a course on Linear Algebra too would be really nice. Besides that thanks for everything 💓
Coundnt agree more
They made a Linear Algebra course...ruclips.net/video/JnTa9XtvmfI/видео.html
It’s like Christmas for math majors
@@aubreyjohnson2551 💯🥳
bruh i’ll go straight to this after finishing calculus 1. thank you very much for this!
how's the update!??!?! :DDD
@@nobivy3524 I can give you mine. Learning Calc 1 and 2 on my own to skip college classes. I am applying and likely taking the placement test in the near future. Have been practicing, watching, and could not thank enough for these videos and Pauls's Online Notes. He provides example problems on his website and has explanations also.
My Calculus 2 met for 60 hours 40 minutes. It was hard. Calculus 3 was three-dimensional geometry, and I gave up. The benefit of RUclips is the professor doesn't have to take attendance, say what problems to do for homework, ask and answer questions, and give tests and review for them. It would be interesting to know what percent of an average college course is spent on things other than teaching.
This is far better than that which is being taught at my college. Thank you!
India?
@@devjoshi7062 I am from U.S. but the calc 3 class in my college is useless. Professor is going so fast she is doing integration by parts in her head and I can't even keep up.
@@daemonzap1481 Does anyone give her feedback?
@@DP-ot6zf most professors are stubborn
I am learning this in 12th
Imagine how good I would be in literally everything by now if instead of overwhelming myself in college with professors who cant teach I just took a year off and studied by myself
you need dedication though, no bsing around
Professor Linda Green, thank you for an incredible explanation and analysis of Calculus Two, a Full College Course. Everything in Calculus Two was explained and covered in full detail from start to finish. Th examples, problems and proofs are very helpful for all students taking Calculus Two worldwide. I took Calculus Two at the old Catonsville Community College in Catonsville, Maryland in the mid 1980's and I am still learning about topics /materials about Calculus that was not taught to me in a fourteen-week Semester.
⭐️ Course Contents ⭐️
⌨️ (0:00:00) Area Between Curves
⌨️ (0:11:11) Volumes of Solids of Revolution
⌨️ (0:21:33) Volumes Using Cross-Sections
⌨️ (0:31:34) Arclength
⌨️ (0:39:50) Work as an Integral
⌨️ (0:51:30) Average Value of a Function
⌨️ (0:59:05) Proof of the Mean Value Theorem for Integrals
⌨️ (1:04:55) Integration by Parts
⌨️ (1:13:03) Trig Identities
⌨️ (1:25:01) Proof of the Angle Sum Formulas
⌨️ (1:29:37) Integrals Involving Odd Powers of Sine and Cosine
⌨️ (1:36:21) Integrals Involving Even Powers of Sine and Cosine
⌨️ (1:44:59) Special Trig Integrals
⌨️ (1:47:36) Integration Using Trig Substitution
⌨️ (1:56:21) Integrals of Rational Functions
⌨️ (2:03:59) Improper Integrals - Type 1
⌨️ (2:10:13) Improper Integrals - Type 2
⌨️ (2:14:20) The Comparison Theorem for Integrals
⌨️ (2:19:43) Sequences - Definitions and Notation
⌨️ (2:31:05) Series Definitions
⌨️ (2:39:41) Sequences - More Definitions
⌨️ (2:46:06) Monotonic and Bounded Sequences Extra
⌨️ (2:49:46) L'Hospital's Rule
⌨️ (2:57:02) L'Hospital's Rule on Other Indeterminate Forms
⌨️ (3:06:48) Convergence of Sequences
⌨️ (3:30:38) Geometric Series
⌨️ (3:43:32) The Integral Test
⌨️ (3:56:48) Comparison Test for Series
⌨️ (4:03:29) The Limit Comparison Test
⌨️ (4:09:24) Proof of the Limit Comparison Test
⌨️ (4:16:00) Absolute Convergence
⌨️ (4:25:03) The Ratio Test
⌨️ (4:30:22) Proof of the Ratio Test
⌨️ (4:39:34) Series Convergence Test Strategy
⌨️ (4:50:26) Taylor Series Introduction
⌨️ (5:02:28) Power Series
⌨️ (5:05:42) Convergence of Power Series
⌨️ (5:21:07) Power Series Interval of Convergence Example
⌨️ (5:30:46) Proofs of Facts about Convergence of Power Series
⌨️ (5:36:19) Power Series as Functions
⌨️ (5:43:36) Representing Functions with Power Series
⌨️ (5:52:07) Using Taylor Series to find Sums of Series
⌨️ (6:02:18) Taylor Series Theory and Remainder
⌨️ (6:15:38) Parametric Equations
⌨️ (6:27:06) Slopes of Parametric Curves
⌨️ (6:32:47) Area under a Parametric Curve
⌨️ (6:38:07) Arclength of Parametric Curves
⌨️ (6:45:20) Polar Coordinates
Godspeed to everyone watching the entire video before the exam. May the grading curve be with you.
Please please please please please make a calculus 3 full course video. This video would've been a godsend last semester
^^
Hi there,
she's already done calc 3.
Here is her Channel
ruclips.net/video/oyM6ETt-gKY/видео.html
Thank you! I just got into calculus and I'm really struggling because I'm only an eighth grade. This video really helped.
My study's timestamps
. Day one (7:33) (21:24)
. Day two (31:58) (39:51) (51:31)
. Day three (59:07) (1:04:57)
. Day four (1:13:06) (1:25:04)
. Day five (1:36:27)
. Day six (1:38:17) (1:41:00)
. Day seven (1:45:00)
. Day eight (1:47:50)
. Day nine (1:48:23) (1:56:28)
. Day ten (2:04:00)
. Day eleven (2:05:57) (2:10:15)
. Day twelve (2:14:24)
. Day thirteen (2:19:46)
. Day fourteen (2:21:45) (2:26:07)
. Day fifteen (2:31:15)
. Day sixteen (2:39:51)
. Day seventeen (2:50:05)
. Day eighteen (2:57:07)
. Day nineteen (3:01:58)
They say day nineteen is the hardest
What could have possible occured on day 19 to cause such abrupt abscence
Really appreciate this video. Helped me refresh on Calc 2 since I took a few years off school to work after getting my associates.
i feel like my university intentionally makes these concepts harder. like we're being taught the same things but at the same time, the problems they give us are expert lvl problems. even my TA's struggle to solve them sometimes
AP Calc BC = Calculus 1 + Calculus 2 on this channel. Thanks so much!!
What a great work you all are doing for us thanks a lot you all.
You get big success in your goals.
my calc 2 final is in 4 days and it will be a 3 hour long paper. Thank you for this video i hope i can finish my revision in two days
Good luck on your test today homie
Let me know how it went
@@AmmoBops Thanks, it wasn't the best cuz the questions were super hard for me. Hopefully i can pass it
this video is a blessing, thank you for this!
these explanations are brilliant... thank you so much
23:21
1:13:15
1:56:54
2:10:00
2:39:15
3:07:06
This is so cool. Getting ready foe the differential equations video 🤘
This should be paid, thank u very very very very MUCH. SO HELPFUL
can't believe all this is for free, many thanks!
1:19:00
2:12:10
2:39:53
3:43:50
I’m sooooo….glad I’m done with Calculus. Cal 3 was my last math course.
In connection to the integral calculus, recently it was published a book about MIT integration bee, under the title " MIT Integration Bee, Solutions of Qualifying Tests from 2010 to 2023"
You can simply find it!
omg THE POWER I have! I'm unstoppable!
People in comment section getting full marks in college semester by just watching a video its a good video to clear the basics but for my country not enough to qualify even college entrance exam 😭
U r right i can understand from where r u india like me or china
mistake at 2:30:32 (maybe?)
for E, n=3 shouldn't be (-6)/(25) whereas it should be (-8)/(25)
Yeah, it should be 2^n, not 2n
Finish learning calculus in -+ 18 hours...
My brain : It's spicy...
OMG I LOVE YOU GUYS! , WHENS CALC 3 COMING OUT?
@@masternobody1896 By standard, it goes up to Calculus 3 but it all depends on the college. Generally cal3 covers Ordinary differential equations and things like Laplace Transform. Some might have multivariable calculus (vector analysis) included in cal3 or a whole new course.
@Aryan Naidu it is on Linda Green's channel: ruclips.net/p/PLAEgL_CQRjwTF3iqXIUKZvnaLHnZav0bv
Well I watched this from sequences and onward in hopes to pass my Calc 2 exam. Let's see what happens!
what happend
@@Moecodess I ended up passing the class but I failed the final for sure. Basically, the final was extremely heavy on understanding series and sequences using the different strategies given. You really got to understand those in-depth to pass. I was pretty much good on all the physics applications. Parametric equations and polar coordinates also got me on the final. Honestly, the best thing to do is start early on notes and homework and just do the class that way. I feel this video left a lot of gaps of understanding, especially in applying the series and sequences.
I just finished the calc 1 video, I'm getting ready for another all nighter.
How was it? Im currently doing calc2 at univ and my calc1 is weak so im planning to watch the calc1&2 playlist
@@kaelart5876 to clear all your doubts, it was worth it, unless you feel like you're learning enough in class (in which case it's wasting your time). Otherwise, you can save a LOT of study time by watching this and taking notes, I did.
@@juandanielcastanierrivas9545 thanks man i've barely learned anything in class so im gonna invest my time on this one this week. good luck to the two of us
Wish I knew this before, just finished eng calculus 2 last term hahaha (just ended a few weeks ago)
My calc prof: "They call it Calc 2 because you have to take it twice"
Yall are awesome! Is calc 3 dropping anytime soon?
ruclips.net/p/PLAEgL_CQRjwTF3iqXIUKZvnaLHnZav0bv
I love how there is a kitchen background noise for some of the lecture snippets😂btw very helpful video 🙏🏻
Oh I love Dr. Green! Shes my Cal 2 instructor
Have my final tomorrow, watching this as a final review. Wish me luck
How was your final? Hope u did very well...✊🏽
I have my final tomorrow...😬
how did u do
i am pretty sure if you guys collaborate with Khan Acdemy,you could make a video like:learn 1st to 12th grade math in 200 hours with practise material and stuff.
One of the best channels!
We are thankful to English people for giving free course of calculus .Thanks for their generosity.
Just when I thought Calculus 1 wasn't enough, comes Calculus 2
Dayum!!
Thanks for making these videos .... Put all graduation topics Maths like
Integral , calculus, real analysis ,vector calculus so on,.....
방학 이야기
지난 학기가 끝나고 3주 동안의 방학이 있었습니다. 저는 그 방학에 고향에 갔다 왔습니다.
고향에 있는 언니가 결혼을 해서 꼭 가야 했습니다. 고향에 가기 전에 저는 남대문 시장에
가서 언니의 결혼 선몰을 샀습니다. 언니가 좋아하는 화장품과 예쁜 가방을 골랐습니다.
언니는 그 결혼 선물을 받고 아주 좋아했습니다. 언니가 결혼을 방학에 하지 않았으면
저는 결혼식을 볼 수 없었을 겁니다.
고향에 있는 동안 정말 행복한 시간을 보냈습니다. 부모님과 이야기도 많이 하고 할아버지
댁에도 갔습니다. 한국에서는 먹을 수 없는 고향 음식도 많이 먹었습니다. 또 그동안 못
만난 친구들도 만나서 근처에 있는 바다에도 놀러 가고 등산도 같이 갔습니다. 그러는
동안 시간이 정말 빨리 갔습니다.
새 학기는 월요일부터 시작되었는데 저는 지난 주 수요일 밤에 한국에 돌아왔습니다.
고향에 더 있고 싶었지만 다음 학기를 준비하려고 일찍 돌아왔습니다. 나흘 동안 방
청소도 하고 한국어 공부도 했습니다. 고향에서 오랫동안 한국말을 하지 않아서 한국말을
많이 잊어버렸습니다. 그래서 초급 2반 수업이 시작되기 전에 지난 학기에 배운 것을
복습했습니다. 이번 학기 동안 한국어 공부도 열심히 하고 새로 만난 친구들과 잘 지내고
싶습니다. 이번 학기에도 재미있는 일이 많이 있으면 좋겠습니다.
Guys
We need linear algebra
Likes please!!
Also thanks FCC for your works its amazing and helping a lot of students around the world, I always struggled with math specially calculus 2 I failed at it for 3 times! I got it in the end
FreeCodeCamp now has a 12 hour Linear Algebra Course
@@joeyGalileoHotto thx
2:49:36 I believe this is wrong. It is not bounded by -4. If n--> 0 we get a large negative number
The sequence value keep decreasing but will not reach 0, if you want to check this just take lim(x→∞) of (x - 5)/x^2, which is 0
saving this vid to slam it the day before my final
Thank you so much please do a calculus 3 video!
ruclips.net/p/PLAEgL_CQRjwTF3iqXIUKZvnaLHnZav0bv
@@timvansurksum Thank you so much!
@@sushantguha407 no problem
@@sushantguha407 what are you studying?
Watching this so I can walk into my calc ii class next year having already taken calc ii 🤷♂️
Legends know that this is reuploaded.
why?
@@weirdscintillatingvedios2122 idk that lol
@@weirdscintillatingvedios2122 There was some sort of minor fix.
Indeed. In the original video, Beau misspoke and said "in this 5 hour video..." but the video is 7 hours long, so we thought this would cause confusion. So we re-uploaded.
And?
I needed this in 2015...
so ımma use this comment as a time stamp. thx for this incredible lesson!
50.13 first day.
Note To Zack: 1:04:56 - Integration by Two Parts
Super, thank you !
Note: At 1:20:41, the professor makes a small error while flipping signs on the angle difference formulas.
Area between gaps ( 20:05 )
me finishing cal1 with more then 80% by watching the cal1, now im here for cal 2!
you guys study this in college? I’m a junior in high school, and this is my math exam portion!!
This is a lie bc calc 2 isn’t taught in high school lmfao
@@juyeon5855 I’d like you to visit Indian high schools
@@juyeon5855 I teach calculus 2 in high school. It's called AP Calculus BC.
@@michaelcheverie7579 BC doesn’t cover all of calculus 2 though. At least in my state we don’t.
So if you are already doing this in high school what type of maths will you guys do in college? Calculus 3 and 4? Does that even exist? Lmao
HAPPY FINALS EVERYONE!
Hi!
Really enjoyed this review course(full course) as I did the previous one (cal 1).
Will there be one for vector calculus in the future (cal 3)?
Wounderful thanks👍
POV: You finished your first engineering semester and you’re watching Calc 2 videos during winter break to get ahead…
correct
@@Julio-re8em can comfirm
Me rn lol
I passed Cal 2 with an A+ but I'm watching to warm up during the winter break for Cal III lol
@@NemoTheGlover ruclips.net/video/0yebWTXixnE/видео.html
Thanks 👍🏻.It makes me relex
I cant believe i survived all this looking back at my engineering undergrad
This is such a cool resource, could you make one for Differential Equations?
yes and calc 3!!
I hope to I hope to continue to present these lectures, as they are wonderful, and benefit from the study in them, and I fully rely on them. I hope to continue to present on other topics continuously.
she doesnt explain many of the steps but still a good general big picture type of video
5:57:44
Thank you so much!
Im crying.
Ох ребята, сколько же годной информации на Вашем языке... На русском языке такой доступности нет, к сожалению. Учу английский.
At 1:20:50 , should we have dropped the negative sign on the sin(-B)? I feel like we dealt with that by making the cos(A)sin(-B) ==> -cos(A)sin(B)
yes. it was a typo. she forgot to drop the - sign.
I'm looking this comment :))
Now i'm waiting for Calculus 3 : )
^^
She's already done Calc 3. Here is her Channel
ruclips.net/video/oyM6ETt-gKY/видео.html
Awesome! Thank you!
Is this a good introduction to calculus 2? Recently finished calculus 1.
I failed last semester, and I feel like the professor I have this semester doesn't teach too well. It was the only option I had this time around so I'm thinking of just watching this instead.
More self studying is always the solution
Maybe it's because I'm not from the States, but I learnt all this in Calculus I. I suppose Calculus II in my country is equivalent to Calculus III? I studied all this in the first year of my degree.
Did you study series in Calculus I? I'm from Brazil - the part of Integrals we study in Calculus I (at least at UnB), but all of series is related to Calculus II
@@gabrielciriatico6464 Yes, I studied both numerical and functional series. I think it was distributed as:
Calculus I: one variable analysis and series.
Calculus II: multivariable analysis.
(I don't know if they are called exactly like that in English, I'm translating directly from Spanish)
At 39:50, why the work is about distance, not about time.
Work is force with respect to distance while impulse is force with respect to time.
Can't see it to small but it looks like a good video .Y need more spaceing.
Integrate; dx/(2+cos x)^2
Ya know after seeing this I think I’ll just stick to my pre calculus for now thank you very much😅
Now I'm just waiting for the grad courses vids
questions examples are highschool level of calculus.Could you please add more complex questions that would help our midterms?
Paul's online notes provide great calc 1, 2, 3, and differential equation practice questions and notes.
It's awesome 👍🏻👍🏻