Calculus II - Older Playlist

Overview

This course covers Integration methods, polar curves, sequences/series, and vectors in Calculus II. The learning outcomes include understanding integration techniques, working with sequences and series, and applying vector concepts. The course teaches skills such as integration by parts, trigonometric integrals, series convergence, and vector operations. The teaching method involves video lectures and examples. The intended audience is students studying Calculus II or individuals interested in advanced calculus topics.

Syllabus

How to watch these videos.
Integration by Parts.
Trigonometric Integrals.
Trigonometric Substitution.
Trig Substitutions Part 2.
Partial Fractions Part 1.
Partial Fractions Part II.
Improper Integrals Part I.
Improper Integrals Part II.
Comparison Test for Integrals.
Arclength - Definition and Example.
Surface Area Part I: Revolving around the x-axis.
Surface Area Part II: Revolving around the y-axis.
Introduction to Sequences Part I: Definition, Examples, and Convergence.
Introduction to Sequences Part II: Computing limits.
Bounded and Monotonic Sequences.
Introduction to Series | Definition, Convergence, and Geometric Series.
Divergence Test for Series.
Algebraic Laws for Series.
Telescoping Series.
Integral Test - Bonus Example.
Integral Test for Series.
Using the Integral Test to Estimate Remainders of Series.
Comparison Test for Series.
Limit Comparison Test for Series.
Alternating Series | Definition and Convergence.
Alternating Series | Estimating Remainers.
Absolute and Conditional Convergence.
Ratio Test.
Root Test.
Introduction to Power Series.
Power Series | Determining endpoints of the interval of convergence.
Taylor Series Part I.
Tayor Series Part 2.
Getting new Taylor series from old ones.
Parametric Curves.
Tangents to Parametric Curves.
Area under a curve given parametrically.
Arclength of curves given parametrically.
Polar Coordinates.
Curve Sketching in Polar Coordinates.
Tangents to Polar Curves.
Equations in 3 Dimensions.
Introduction to Vectors.
The Cross Product.
Lines Three Ways.
Equation of a plane.
Example: Finding the equation of a weird plane.
Intersections of Planes.