MATH 203 • Midterm II • Multivariable Calculus

Limit Definition of Partial Derivative

Partial Differentiation Rules 1

Partial Differentiation Rules 2

Higher Order Partial 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

Implicit Differentiation I

Implicit Differentiation II

Implicit Differentiation III

Implicit Higher Differentiation

Extreme Values

Exam like Question 1

Exam like Question 2

Exam like Question 3

Exam like Question 4

Extreme Values on Closed Regions 1

Extreme Values on Closed Regions 2

Exam like Question 1

Exam like Question 2

Exam like Question 3

Lagrange Multipliers I

Lagrange Multipliers II

Lagrange Multipliers with Two Constraints

Lagrange Multipliers Using Gradient

Optimization with Lagrange Multipliers 1

Optimization with Lagrange Multipliers 2

Optimization with Lagrange Multipliers 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

Reversing the Order of Integration 4

Sketching & Reversing the Order

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

Extreme Values 1

Extreme Values 2

Extreme Values 3

Extreme Values 4

Extreme Values 5

Extreme Values on Closed Region 1

Extreme Values on Closed Region 2

Extreme Values on Closed Region 3

Extreme Values on Closed Region 4

Extreme Values on Closed Region 5

Extreme Values on Closed Region 6

Lagrange Multipliers 1

Lagrange Multipliers 2

Lagrange Multipliers 3

Lagrange Multipliers 4

Lagrange Multipliers 5

Lagrange Multipliers 6

Lagrange Multiplier 7

Reversing the Order of Integration 1

Reversing the Order of Integration 2

Reversing the Order of Integration 3

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

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 1

Problem 2

Problem 3

Problem 4

Extremum Values

Lagrange Multipliers

Double Integral

Line Integral

Conservative Field

Surface Area and Volume

Lagrange Multiplier

Lagrange Multiplier

Lagrange Multiplier

Lagrange Multiplier

Lagrange Multiplier

Extreme Values on Closed Region

Extreme Values on Closed Region

Reversing the Order of Integration

Reversing the Order of Integration

Reversing the Order of Integration

Reversing the Order of Integration

Double Integral on Cartesian Coordinates

Double Integral in Polar Coordinates

Double Integral in Polar Coordinates

Double Integral in Polar Coordinates

Double Integral in Polar Coordinates

Double Integral on Cartesian Coordinates

Double Integral in Polar Coordinates