MAT 104E • Final • Mathematics II

Domain of Multivariable Functions

Level Curves

Level Curves and Level Surfaces

Graphs of Surfaces

Limits of Multivariable Functions 1

Limits of Multivariable Functions 2

Limits of Multivariable Functions 3

The Squeeze Theorem

Continuity of Multivariable Functions

Limits with Polar Coordinates

Limit Definition of Partial Derivative

Partial Differentiation Rules 1

Partial Differentiation Rules 2

Higher Order Partial Differentiation

Implicit Differentiation I

Implicit Differentiation II

Implicit Differentiation III

Implicit Higher Differentiation

Chain Rule 1

Chain Rule 2

Chain Rule 3

Equation of a Tangent Plane 1

Equation of a Tangent Plane 2

Horizontal Tangent Plane

Normal Vector to a Multivariable Function

Tangent Plane Approximation

Gradient Vector

Directional Derivative

Gradient and Directional Derivative

Extreme Values

Extreme Values on Restricted Regions 1

Extreme Values on Restricted Regions 2

Optimization With Lagrange Multipliers

Lagrange Multipliers Example-1

Lagrange Multipliers Example-2

Lagrange Multipliers Example-3

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

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 : Jacobian

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

Extremum

Extremum 2

Double Integral

Double Integral 2

Triple Integral - Polar

Triple Integral - Change order of Integration

Triple Integral - Spherical

Jacobian

Cylindrical to Spherical Coordinates