Calculus 2 - Full College Course

Learn Calculus 2 in this full college course. This course was created by Dr. Linda Green, a lecturer at the University of North Carolina at Chapel Hill. Check out her YouTube channel: https://www.youtube.com/channel/UCkyLJh6hQS1TlhUZxOMjTFw ⭐️ Prerequisites ⭐️ 🎥 Algebra: https://www.youtube.com/watch?v=LwCRRUa8yTU 🎥 Precalculus: https://www.youtube.com/watch?v=eI4an8aSsgw 🎥 Calculus 1: https://www.youtube.com/watch?v=HfACrKJ_Y2w ⭐️ Lecture Notes ⭐️ 🔗 Calculus 2 Notes: http://lindagreen.web.unc.edu/files/2020/08/courseNotes_m232_2018F.pdf ⭐️ 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 ❤️ Support for this channel comes from our friends at Scrimba – the coding platform that's reinvented interactive learning: https://scrimba.com/freecodecamp