MATH 158 (Spring 24) • Calculus for Engineering II • Final

Domain of Functions

Level Curves

Limits of Multivariable Functions 1

Limits of Multivariable Functions 2

Limits of Multivariable Functions 3

Continuity of Multivariable Functions

Exam like Question 1

Exam like Question 2

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

Gradient Vector

Directional Derivative

Gradient and Directional Derivative

Limit of Multivariable Functions 1

Limit of Multivariable Functions 2

Limit of Multivariable Functions 3

Limit of Multivariable Functions 4

Limit of Multivariable Functions 5

Limit of Multivariable Functions 6

Limit of Multivariable Functions 7

Limit of Multivariable Functions 8

Limit of Multivariable Functions 9

Limit of Multivariable Functions 10

Limit of Multivariable Functions 11

Limit of Multivariable Functions 12

Continuity 1

Continuity 2

Definition of Partial Derivative 1

Definition of Partial Derivative 2

Definition of Partial Derivative 3

Continuity and Partial Derivative

Gradient and Directional Derivative 1

Gradient and Directional Derivative 2

Gradient and Directional Derivative 3

Gradient and Directional Derivative 4

Gradient and Directional Derivative 5

Gradient and Directional Derivative 6

Gradient and Directional Derivative 7

Higher Order Derivative 1

Higher Order Derivative 2

Higher Order Derivative 3

Higher Order Derivative 4

Partial Derivatives 1

Partial Derivatives 2

Chain Rule 1

Chain Rule 2

Chain Rule 3

Chain Rule 4

Chain Rule 5

Chain Rule and Higher Order Derivative

Chain Rule and Higher Order Derivative 2

Implicit Differentiation 1

Implicit Differentiation 2

Implicit Differentiation 3

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

Extreme Values 1

Extreme Values 2

Extreme Values 3

Extreme Values 4

Extreme Values 5

Extreme Values 6

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 Multipliers 7

Lagrange Multipliers 8

Lagrange Multipliers 9

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

Double Integrals in Polar Coordinates 1

Double Integrals in Polar Coordinates 2

Double Integrals in Polar Coordinates 3

Double Integrals in Polar Coordinates 4

Exam like Question 1

Exam like Question 2

Exam like Question 3

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Exam like Question 5

Exam like Question 6

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Exam like Question 10

Exam like Question 11

Exam like Question 12

Exam like Question 13

Exam like Question 14

Exam like Question 15

Exam like Question 16

Exam like Question 17

Exam like Question 18

Exam like Question 19

Exam like Question 20

Exam like Question 21

Reversing the Order of Integration 1

Reversing the Order of Integration 2

Reversing the Order of Integration 3

Reversing the Order of Integration 4

Double Integral 1

Double Integral 2

Double Integral 3

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

Double Integral in Polar Coordinate 11

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

Exam-like Question 1

Exam-like Question 2

Exam-like Question 3