Multivariable Integral Calculus

Double Integrals

• Notes on Double Integrals (Paul's Online Notes)
• Notes on Iterated Integrals - Evaluating Double Integrals over a Rectangle (Paul's Online Notes)
• Notes on Evaluating Double Integrals over a General Region (Paul's Online Notes)
• Notes on Evaluating Double Integrals in Polar Coordinates (Paul's Online Notes)
• Videos on Double Integrals (Khan Academy)
• Video on Double Integrals - Basics (Patrick JMT)
• Video on Double Integrals - Over a general region (Patrick JMT)
• Video on Double Integrals - Changing Order of Integration (Patrick JMT)
• Video on Double Integrals using Polar Coordinates (Part 1 of 3) (Patrick JMT)
• Video on Double Integrals - Change of Variables (Part 1 of 2) (Patrick JMT)
• Video on Double Integrals (integralCALC)
• Video on Double Integrals to find the Area enclosed by Type 1 & 2 Regions (integralCALC)
• Video on Double Integrals to find Surface Area (integralCALC)
• Video on Converting Double Integrals using Polar Coordinates (integralCALC)
• Video on Sketching the Region of a Double Integral with Polar Co-ordinates (integralCALC)
• Video on Double Integrals with Polar Co-ordinates (integralCALC)
• Videos on Double Integrals - Introduction, Changing Order of Integration, Polar Coordinates, Change of Variables (MIT)

Triple Integrals

• Notes on Triple Integrals (Paul's Online Notes)
• Notes on Triple Integrals with Cylindrical Coordinates (Paul's Online Notes)
• Notes on Triple Integrals with Spherical Coordinates (Paul's Online Notes)
• Notes on Change of Variable (Paul's Online Notes)
• Notes on Surface Area (Paul's Online Notes)
• Notes on Change of Variables (Paul's Online Notes)
• Videos on Triple Integrals (Khan Academy)
• Video on Triple Integrals (Patrick JMT)
• Videos on Triple Integrals - Rectangular, Cylindrical & Spherical Coordinates (MIT)

Line Integrals

• Notes on Vector Fields (Paul's Online Notes)
• Notes on Line Integrals Part 1 -wrt Arc Length (Paul's Online Notes)
• Notes on Line Integrals Part 2 - wrt x and y (Paul's Online Notes)
• Video on Evaluating Line Integrals (Patrick JMT)
• Notes on Line Integrals of a Vector Field (Paul's Online Notes)
• Videos on Line Integrals (Khan Academy)
• Videos on Line Integrals in Vector Fields - Scalar Field Line Integral Independent of Path Direction, Vector Field L.I. Dependant on Path, Path Independence, Closed Curve L.I. of Conservative Vector Fields (Khan Academy)
• Notes on the Fundamental Theorem for Line Integrals (Paul's Online Notes)
• Video on the Fundamental Theorem for Line Integrals (Patrick JMT)
• Videos on Vector Fields & Line Integrals - Examples, Fundamental Theorem for Line Integrals, Conservative Fields, Gradient Fields, Potential Functions, Curl (MIT)

Conservative Vector Fields

• Notes on Conservative Vector Fields (Paul's Online Notes)
• Video on Conservative Vector Fields (Patrick JMT)
• Video on Finding Potential for a Conservative Vector Field (Patrick JMT)
• Video on Showing a Vector Field is a Conservative Vector Field (Patrick JMT)

 Green's Theorem

• Notes on Green's Theorem (Paul's Online Notes)
• Video on Green's Theorem (Patrick JMT)
• Videos on Green's Theorem - Proof & Example (Khan Academy)
• Video on Green's Theorem (integralCALC)
• Videos on Green's Theorem, Proof and Applications (MIT)

Curl & Divergence

• Videos on Curl (Khan Academy)
• Notes on Curl & Divergence (Paul's Online Notes)
• Video on The Jacobian (Patrick JMT)
• Video on Curl & Showing a Vector Field is Conservative (Patrick JMT)

Surface Integrals

• Video on Surface Integrals (Patrick JMT)
• Videos on Parameterizing a Surface (Khan Academy)
• Videos on Surface Integrals (Khan Academy)

 Coordinate Systems

• Video on Sketching Vector Fields (Patrick JMT)
• Video on Arc Length of a Vector Function (Patrick JMT)
• Video on Polar Co-ordinates (Patrick JMT)
• Video on Polar Co-ordinates - Finding Areas (Patrick JMT)
• Video on Polar Co-ordinates - Graphing (Patrick JMT)
• Notes on Arc Length of Vectors (Paul's Online Notes)
• Notes on Polar Coordinates (Paul's Online Notes)
• Notes on Cylindrical Coordinates (Paul's Online Notes)
• Notes on Spherical Coordinates (Paul's Online Notes)
• Video on Spherical Coordinates (integralCALC)