# Calculus 2

## Differential Equations

Separable Differential Equations & Growth and Decay Model

More Solving Separable Differential Equations

Half Life Carbon 14 Dating Exponential Decay

Solving First Order Linear Differential Equations 3 Examples

Homogeneous Differential Equations First Order3 Examples

## Area Between Curves

Area Between 2 Curves using Vertical and Horizontal Representative Rectangles

Area Under a Curve & Definite Integrals with TI NSPIRE

## Volume of Solid of Revolution

Volume of Solid of Revolution Disk Method and Washer Method

Volumes of Solids with Known Cross Sections 3 Examples

Volume of Solid of Revolution Shell Method 3 Examples

## Arc Length of a Curve Area of Surface of Revolution

Arc Length of a Curve ( Smooth Curve ) 5 Examples

Arc Length Disc Method Related Rates

Area of a Surface of Revolution

## Review of Basic Integration Rules L'Hopital's Rule

Review of Basic Integration Rules - 6 Examples

L'Hopital's Rule Lesson 8 Examples (includes small correction)

L'Hopital's Rule and Continuity at a Point to Solve for Two Unknowns

## More Applications of Integration

Work Done by a Variable Force 7 Examples

Work Done by a Variable Force Empty a Tank

Theorem of Pappus to find Volume of Revolution

Center of Mass in a 1 and 2 Dimensional System

Center of Mass in a Planar Lamina Centroid 3 Examples

Fluid Pressure & Fluid Force 4 Examples

## Integration by Parts

Integration by Parts 6 Examples LIATE

Integration by Parts 2 Times 2 Examples

Integration by Parts Tabular Method TIC TAC TOE

## Integration: Trigonometric Integrals

Trigonometric Integrals Powers of Sine and Cosine 5 Examples

Trigonometric Integrals Powers of Tangent and Secant 5 Examples

Integration using Trigonometric Substitution 4 Examples

Definite Integration Trigonometric Substitution

Integrating Inverse Trigonometric Functions Trig Substitution

Partial Fractions Integration 3 Examples

## Sequences and Series

Integral Test for Series Convergence or Divergence 4 Examples

p Series Test for Convergence or Divergence

Direct Comparison Test for Series 3 Examples

Limit Comparison Test for Series 3 Examples

Alternating Series Test and Estimating Series Sum w/ Maximum Error

Alternating Series Estimation Theorem

Ratio Test for Convergence of Series

Root Test for Convergence of a Series

Taylor Polynomials & Estimation Error, Lagrange Remainder

Interval of Convergence of Power Series (3 Examples)

Differentiation and Integration of a Power Series

Power Series Representation of Functions

Taylor Series & Maclaurin Series

Maclaurin Series, Interval of Convergence, Alternating Series Error Theorem

Taylor Polynomials and Lagrange Error Calculus BC (4 Parts)

## Polar Curves

Graphing Polar Equations, Test for Symmetry & 4 Examples

Slope and Tangent Line to Polar Curves

Area of Polar Curves, Slope of Polar Curve, Related Rates

## Parametric Equations

Introduction to Parametric Equations

Parametric Equations Eliminating Parameter T

Derivative of Parametric Equations

Tangent Lines to Parametric Curves

Arc Length of a Parametric Curve

# Vectors

Position Vector, Velocity Vector, Net Change Theorem AP Exam Style