https://betterexplained.com/articles/intuitive-arithmetic-with-complex-numbers/

# Category Archives: Calculus III

# Fundamental Theorem of Line Integrals

Part 1

Part 2

Closed path/curve

Source; James Sousa on youtube

# Line Integrals

IN 2D

IN3D

OF VECTOR FIELDS

IN DIFFERENTIAL FORM

Source: James Sousa on youtube

# Recall: Converting from Cartesian to Parametric Form

# Finding a Potential for a Conservative Vector Field

source: patrickjmt on youtube

source: James Sousa on youtube

# Sketching in 3D

# Defining a Smooth Parameterization of a Path

source: James Sousa on youtube

# Vector Fields (Divergence, Curl, Conservative Test)

Introduction

http://demonstrations.wolfram.com/3DVectorFields/

Divergence of a Vector Field

Curl of a Vector Field

Conservative Vector Fields

source: James Sousa on youtube

# Jacobian – Change of variables in Integrals

Double Integral: Change of Variables Using the Jacobian

Example of a Change of Variables for a Double Integral: Jacobian

Triple Integrals: Change of Three Variables Using the Jacobian

source: James Sousa on youtube

# Triple Integrals and Volume using Spherical Coordinates

Introduction:

Examples:

Source: James Sousa

http://tutorial.math.lamar.edu/Classes/CalcIII/SphericalCoords.aspx

Manipulation Demo:

http://mathinsight.org/applet/spherical_coordinates

http://mathinsight.org/spherical_coordinates

source: Nykamp DQ, “Spherical coordinates.” From *Math Insight*. http://mathinsight.org/applet/spherical_coordinates