Calculus 2

Welcome to Calculus 2, the second part of Single Variable Calculus. This course covers all of integral calculus, starting with Riemann Sums and ending with Series and Sequences.

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Lectures

Areas and Integrals

Area
Riemann Sums
The Definite Integral
Properties of Integrals
Fundamental Theorem of Calculus 1
Fundamental Theorem of Calculus 2
Indefinite Integrals
Net Change Theorem
U-Substitution Method for Indefinite Integrals
U-Substitution Method for Definite Integrals

Applications of Integrals

Area Between Curves for y=f(x)
Area Between Curves for x=f(y)
Volume by Disc Method I
Volume by Disc Method II
Volume by Cylindrical Shells
Average Value and MVT for Integrals

Integration Techniques

Integration by Parts
Trigonometric Integrals I
Trigonometric Integrals II
Trigonometric Substitution
Partial Fractions
Integration Strategies
Improper Integrals

Parametric Equations and Polar Coordinates

Arc Length in Cartesian Coordinates
Arc Length in Parametric Equations
Area in Polar Coordinates
Arc Length in Polar Coordinates

Sequences and Series

Sequences
Series – Convergence and Divergence
Series – Integral Test
Series – Comparison Test
Alternating Series
Series – Absolute Convergence Test
Series – Ratio Test
Series – Root Test
Series – Strategies
Power Series
Generating Functions
Taylor Series
Maclaurin Series

Exercise Videos

U-Substitution Method for Indefinite Integrals
U-Substitution Method for Definite Integrals
(Challenging) Area Between Curves

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