Dive into a comprehensive 7-hour college-level Calculus 2 course, created by Dr. Linda Green from the University of North Carolina at Chapel Hill. Master advanced calculus concepts including area between curves, volumes of solids, integration techniques, improper integrals, sequences and series, Taylor series, parametric equations, and polar coordinates. Prerequisites include algebra, precalculus, and Calculus 1. Access detailed lecture notes and follow along with the structured course content, featuring 50 in-depth lessons. Develop a strong foundation in calculus through theoretical explanations, proofs, and practical problem-solving techniques. Ideal for students seeking a thorough understanding of Calculus 2 principles and applications.
Overview
Syllabus
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.
Taught by
freecodecamp
Related Courses
Related articles
Reviews
5.0 rating, based on 1 Class Central review
-
Feri Andana PutraThe course covers all the fundamental aspects of advanced calculus, including integral calculus, series, and differential equations. Topics such as integral techniques (substitution, integration by parts, etc.), convergence of series, and parametric equations are covered in detail. The course also delves into real-world applications, such as calculating volumes of solids of revolution, arc lengths, and areas in polar coordinates.
