MATH 203 • Final • Multivariable Calculus

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

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

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

Triple Integrals in Cylindrical Coordinates

Triple Integrals in Cylindrical Coordinates

Triple Integrals in Spherical Coordinates

Triple Integrals in Spherical Coordinates

Triple Integrals in Spherical Coordinates

Spherical Coordinates or Cylindrical Coordinates ?

Spherical Coordinates or Cylindrical Coordinates ?

Spherical Coordinates or Cylindrical 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

Surface Integrals I

Surface Integrals II

Surface Integrals III

Flux Integrals I

Flux Integrals II

Flux Integrals III

Green's Theorem

Exam like Question 1

Exam like Question 2

Exam like Question 3

Exam like Question 4

Exam like Question 5

Exam like Question 6

Exam like Question 7

Exam like Question 8

Exam like Question 9

Exam like Question 10

Exam like Question 11

Exam like Question 12

Exam like Question 13

Exam like Question 14

Conservative Field & Potential 1

Conservative Field & Potential 2

Conservative Field & Potential 3

Conservative Field & Potential 4

Conservative Fields, Potentials and Line Integrals (Important)

Line Integrals 1

Line Integrals 2

Line Integrals 3

Line Integrals 4

Line Integrals 5

Line Integrals of Vector Fields 1

Line Integrals of Vector Fields 2

Line Integrals of Vector Fields 3

Divergence and Curl

Surface Integral 1

Surface Integral 2

Surface Integral 3 (Important)

Surface Integral 4 (Important)

Green's Theorem I

Green's Theorem II

Green's Theorem III

Green's Theorem (Fall 2022)

Problem 1

Problem 2

Problem 3

Problem 4

Lines

Volume

(Hidden) Directional Derivative

Unit Vector, Curvature and Torsion

Area

Line Integral

(Hidden) Double Integral

Volume

Surface Integral

Arc Length of Vector Functions

Arc Length of Vector Functions

Arc Length of Vector Functions

Equation of a Plane

Limit of Multivariable Functions

Limit of Multivariable Functions

Multiple Choice: Limit of Multivariable Functions

Multiple Choice : Partial Derivative

Multiple Choice : Higher Order Derivative

Multiple Choice : The Chain Rule

Multiple Choice : Extreme Values - Saddle Points

Gradient, Directional derivative, Maximum Rate of Increase

Lagrange Multipliers

Reversing the Order of Integration

Double Integrals in Poolar Coordinates

Triple Integrals in Cylindrical Coordintes

Conservative Field and Potential Function

Change of Variable: The Jacobian

Change of Variable: The Jacobian