MATH 102 (Spring 24) • Multivariable Calculus • Final

Intuition: Double Integrals

Volume Calculation with Double Integration

Area Calculation with Double Integral

Sketching the Area of Integration 1

Sketching the Area of Integration 2

Sketching the Area of Integration 3

Reversing the Order of Integration 1

Reversing the Order of Integration 2

Reversing the Order of Integration 3

Reversing the Order of Integration 4

Sketching & Reversing the Integration Area

Cartesian to Polar Coordinates 1

Cartesian to Polar Coordinates 2

Polar to Cartesian Coordinates

Double Integrals in Polar Coordinates 1

Double Integrals in Polar Coordinates 2

Double Integrals in Polar Coordinates 3

Double Integrals in Polar Coordinates 4

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Reversing the Order of Integration 1

Reversing the Order of Integration 2

Reversing the Order of Integration 3

Reversing the Order of Integration 4

Reversing the Order of Integration 5

Double Integral 1

Double Integral 2

Area Between Curves in Polar Coordinates

Double Integral in Polar Coordinate 1

Double Integral in Polar Coordinate 2

Double Integral in Polar Coordinate 3

Double Integral in Polar Coordinate 4

Double Integral in Polar Coordinate 5

Double Integral in Polar Coordinate 6

Double Integral in Polar Coordinate 7

Double Integral in Polar Coordinate 8

Double Integral in Polar Coordinate 9

Double Integral in Polar Coordinate 10

Introduction to Triple Integrals

Triple Integrals 2

Triple Integrals 3

Important Functions and Their Graphs

Triple Integrals 4

Triple Integrals 5

Triple Integrals 6

Reversing the Order of Triple Integrals

Volume with Double or Triple Integral 1

Volume with Double or Triple Integral 2

Volume with Double or Triple Integral 3

Cylindrical Coordinates 1

Cylindrical Coordinates 2

Change of Variable in Triple Integrals

Change of Variable: Cartesian to Cylindrical

Triple Integral in Cylindrical Coordinates 1

Triple Integral in Cylindrical Coordinates 2

Triple Integral in Cylindrical Coordinates 3

Triple Integral in Cylindrical Coordinates 4

Triple Integral in Cylindrical Coordinates 5

Triple Integral in Cylindrical Coordinates 6

Spherical Coordinates 1

Spherical Coordinates 2

Change of Variable: Cartesian to Spherical

Triple Integral in Spherical Coordinates 1

Triple Integral in Spherical Coordinates 2

Triple Integral in Spherical Coordinates 3

Triple Integral in Spherical Coordinates 4

Triple Integral in Spherical Coordinates 5

Triple Integral in Spherical Coordinates 6

Triple Integral in Spherical Coordinates 7

Triple Integral in Spherical Coordinates 8

Choose your side 1: Spherical or Cylindrical

Choose your side 2 : Cylindrical or Spherical or Cartesian

Choose your side 3 : Cylindrical or Spherical or Cartesian

Choose your side 4 : Cylindrical or Spherical or Cartesian

Change of Variable - Double Integral

Triple Integral in Cylindrical Coordinates

Triple Integral in Cylindrical Coordinates

Double Integral & Triple Integral in Cylindrical Coordinates

Triple Integral in Spherical Coordinates

Triple Integral in Spherical Coordinates

Triple Integral in Spherical Coordinates

Triple Integral in Spherical Coordinates

Triple Integral in Cylindrical & Spherical Coordinates

Triple Integral in Cylindrical & Spherical Coordinates

Triple Integral in Cartesian & Cylindrical & Spherical Coordinates

Triple Integral in Cartesian & Cylindrical & Spherical Coordinates

Triple Integral in Cartesian & Cylindrical & Spherical Coordinates

Triple Integral in Cartesian & Cylindrical & Spherical Coordinates

Vector Functions and Curves

Domain of a Vector Function

Limit of a Vector Function

Derivative of a Vector Function

Integral of a Vector Function

Arc Length

Arc Length Parametrization

Line Integral 1

Line Integral 2

Line Integral 3

Line Integral 4

Line Integral 5

Vector Fields and Field Lines

Conservative Fields

Potential Function

Line Integrals of Vector Fields

Green's Theorem

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Conservative Field & Potential 1

Conservative Field & Potential 2

Conservative Field & Potential 3

Conservative Field & Potential 4

Conservative Field & Potential 5

Conservative Field & Potential 6

Conservative Field & Line Integral

Line Integrals 1

Line Integrals 2

Line Integrals 3

Line Integral 4

Line Integral 5

Line Integrals of Vector Fields 1

Line Integrals of Vector Fields 2

Divergence and Curl

Green's Theorem 1

Green's Theorem 2

Green's Theorem 3

Green's Theorem 4