Created on: August 6, 2010

Website Address: https://library.curriki.org/oer/Line-Integrals-II

TABLE OF CONTENTS

- Limits
- Derivatives
- The Chain Rule
- Derivatives of Special Functions
- Implicit Differentiation
- Minima and Maxima
- Optimization Problems
- Indefinite Integrals
- Definite Integrals
- Solids of Revolution
- Sequences and Series
- Polynomial Approximations
- Partial derivatives
- AP Calculus BC
- Partial Derivatives
- Double Integrals
- Line Integrals I
- Vectors
- Line Integrals II
- Green's Theorem
- L'Hospital's Rule

- Partial Derivatives
- Partial derivatives
- Partial Derivatives 2
- Gradient 1
- Gradient of a scalar field
- Divergence 1
- Divergence 2
- Divergence 3
- Curl 1
- Curl 2
- Curl 3

- Implicit Differentiation
- Implicit Differentiation (part 2)
- More implicit differentiation
- More chain rule and implicit differentiation intuition
- Trig Implicit Differentiation Example

- Introduction to definite integrals
- Definite integrals (part II)
- Definite Integrals (area under a curve) (part III)
- Definite Integrals (part 4)
- Definite Integrals (part 5)
- Definite integral with substitution
- Integrals: Trig Substitution 1
- Integrals: Trig Substitution 2
- Integrals: Trig Substitution 3 (long problem)
- Introduction to differential equations

- Using a line integral to find the work done by a vector field example
- Parametrization of a Reverse Path
- Scalar Field Line Integral Independent of Path Direction
- Vector Field Line Integrals Dependent on Path Direction
- Path Independence for Line Integrals
- Closed Curve Line Integrals of Conservative Vector Fields
- Example of Closed Line Integral of Conservative Field
- Second Example of Line Integral of Conservative Vector Field

path independence

This video provides an example of the work done by a vector field.

This video explores the effect on the previous line integral of reversing the parametrization of the path of the line.

This video establishes that the line integral is independent of path direction.

This video establishes that vector-valued functions, as opposed to scalar functions, are path direction dependent.

This video establishes the conditions for a line integral of a vector-valued function to be path-independent.

This video demonstrates that the line integral of a closed curve over a conservative vector field is 0.

This video provides an example illuminating the previous video.

This video provides yet another example of a line integral over a closed curve.