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freeCodeCamp

Calculus 2 - Full College Course

via freeCodeCamp

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Overview

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Video lecture series covering a standard second-semester college calculus curriculum. Topics include applications of integration (area between curves, volumes by revolution and cross-sections, arclength, work, average value), integration techniques (parts, trigonometric integrals and substitution, rational functions), improper integrals, L'Hospital's Rule, sequences and series with the full battery of convergence tests, power and Taylor series, and parametric equations with polar coordinates. Several results, including the Mean Value Theorem for Integrals, the limit comparison test and the ratio test, are proved. Intended for students who have completed a first calculus course in limits and derivatives.

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

Reviews

5.0 rating, based on 1 Class Central review

Start your review of Calculus 2 - Full College Course

  • Profile image for Feri Andana Putra
    Feri Andana Putra
    The 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.
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