There are many types of software development that require high level mathematics such as graphics simulations and some types of machine learning.

We are helping people learn the mathematics they need by posting a series of college-level courses on the YouTube channel. Our latest free course is a complete 7-hour Calculus 2 course.

This  course was created by Dr. Linda Green who teaches at the University of  North Carolina at Chapel Hill. She has years of experience teaching Calculus 2 to undergraduate students.

Besides the video content, we have also included full course notes from Dr. Green as a link in the video description.

Below are all the Calculus 2 concepts you will learn about in this course.

  • Area Between Curves
  • Volumes of Solids of Revolution
  • Volumes Using Cross-Sections
  • Arclength
  • Work as an Integral
  • Average Value of a Function
  • Proof of the Mean Value Theorem for Integrals
  • Integration by Parts
  • Trig Identities
  • Proof of the Angle Sum Formulas
  • Integrals Involving Odd Powers of Sine and Cosine
  • Integrals Involving Even Powers of Sine and Cosine
  • Special Trig Integrals
  • Integration Using Trig Substitution
  • Integrals of Rational Functions
  • Improper Integrals - Type 1
  • Improper Integrals - Type 2
  • The Comparison Theorem for Integrals
  • Sequences - Definitions and Notation
  • Series Definitions
  • Sequences - More Definitions
  • Monotonic and Bounded Sequences Extra
  • L'Hospital's Rule
  • L'Hospital's Rule on Other Indeterminate Forms
  • Convergence of Sequences
  • Geometric Series
  • The Integral Test
  • Comparison Test for Series
  • The Limit Comparison Test
  • Proof of the Limit Comparison Test
  • Absolute Convergence
  • The Ratio Test
  • Proof of the Ratio Test
  • Series Convergence Test Strategy
  • Taylor Series Introduction
  • Power Series
  • Convergence of Power Series
  • Power Series Interval of Convergence Example
  • Proofs of Facts about Convergence of Power Series
  • Power Series as Functions
  • Representing Functions with Power Series
  • Using Taylor Series to find Sums of Series
  • Taylor Series Theory and Remainder
  • Parametric Equations
  • Slopes of Parametric Curves
  • Area under a Parametric Curve
  • Arclength of Parametric Curves
  • Polar Coordinates

We recommend you pull out some paper and a pencil and take physical notes – just like when you were back in a classroom.

This manual process of taking notes will help you better comprehend and  retain these concepts, since Dr. Green moves fast and covers a lot of  topics in a short time.

Check out our mathematics playlist if you want to brush up on the prerequisites such as Algebra, Precalculus, and Calculus 1.

You can watch the full course on the YouTube channel (7-hour watch).