Calculus 2 videos

Accumulations of change introduction

Approximation with Riemann sums

Summation notation review

Riemann sums in summation notation

Defining integrals with Riemann sums

Fundamental theorem of calculus and accumulation functions

Interpreting the behavior of accumulation functions

Properties of definite integrals

Fundamental theorem of calculus and definite integrals

Reverse power rule

Indefinite integrals of common functions

Definite integrals of common functions

Proof videos

Integrating with u-substitution

Integrating using long division and completing the square

Integrating using trigonometric identities

Trigonometric substitution

Integration by parts

Integrating using linear partial fractions

Improper integrals

Differential equations introduction

Verifying solutions for differential equations

Sketching slope fields

Reasoning using slope fields

Approximation with Euler’s method

Separation of variables

Particular solutions to differential equations

Exponential models

Logistic models

Average value of a function

Straight-line motion

Non-motion applications of integrals

Area: vertical area between curves

Area: horizontal area between curves

Volume: squares and rectangles cross sections

Area: curves that intersect at more than two points

Volume: triangles and semicircles cross sections

Volume: disc method (revolving around x- and y-axes)

Volume: disc method (revolving around other axes)

Volume: washer method (revolving around x- and y-axes)

Volume: washer method (revolving around other axes)

Arc length

Calculator-active practice

Parametric equations intro

Arc length: parametric curves

Second derivatives of parametric equations

Vector-valued functions

Planar motion

Polar functions

Area: polar regions (single curve)

Area: polar regions (two curves)

Arc length: polar curves

Calculator-active practice

Convergent and divergent infinite series

Infinite geometric series

nth-term test

Integral test

Harmonic series and p-series

Comparison tests

Alternating series test

Ratio test

Absolute and conditional convergence

Alternating series error bound

Taylor and Maclaurin polynomials intro

Lagrange error bound

Power series intro

Function as a geometric series

Maclaurin series of eˣ, sin(x), and cos(x)

Representing functions as power series

Telescoping series

Proof videos