MATH 170 • Calculus for Scientists and Engineers II • Final

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

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

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Vector Functions and Curves

Domain of a Vector Function

Limit of a Vector Function

Derivative of a Vector Function

Integral of a Vector Function

Position, Velocity, Acceleration

Position, Velocity, Acceleration 2

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

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

Vector Valued Functions 1

Vector Valued Functions 2

Vector Valued Functions 3

Vector Valued Functions 4

Tangent Line to Vector Functions

Unit Tangent 1

Unit Tanget 2

Unit Tangent 3

Unit Tangent, Normal, Binormal

Arc Length 1

Arc Length 2

Arc Length 3

Curvature 1

Curvature 2

Arc Length, Curvature, Tangent

Integral of Vector Valued Functions

Position Vectors 1 : Velocity,Speed,Acceleration

Position Vectors 2 : Velocity,Speed,Acceleration

Position Vectors 3 : Velocity,Speed,Acceleration

Position Vectors 4: Velocity, Speed, Acceleration

Parametric Equation for Tangent Line

Parameterization of the Curves 1

Parameterization of the Curves 2

Parameterization of the Curves 3

Parameterization of the Curves 4

Parameterization of the Curves 5

Position Vectors 5: Velocity, Speed, Acceleration

Position Vectors 6: Velocity, Speed, Acceleration

Length of the Curves 1

Length of the Curves 2

Length of the Curve 3

Length of the Curve 4

Length of the Curves 5

Length of the Curves 6

Conservative Vector Fields

Line Integrals

Green's Theorem & Line Integrals

Green's Theorem & Line Integrals 2

Green's Theorem & Line Integrals 3

Introduction to Sequences

Bounded Sequences

Limit of a Sequence

Convergence of a Sequence

Recursive Sequences

Exam like Question 1-2

Series : Partial Sums

Geometric Series & Harmonic Series

Telescoping Series

The Nth-Term Test

Combining Series

The Integral Test

P test & Comparison Test 1

Comparison Test 2

The Limit Comparison Test 1

The Limit Comparison Test 2

The Ratio Test

The Root Test

Introduction to Absolute Convergence

Absolute Convergence Theorem

Introduction to Alternating Series Test

Alterneting Series and Conditional Convergence

Interval of Convergence

What is a Power Series?

Convergence of a Power Series

Convergence on Endpoints

Term by Term Differentiation

Finding a Power Series Expansion

Power Series with Different Centers

Taylor Series : Intuition

Taylor and Maclaurin Series

Taylor and Maclaurin Series 2

Finding a Taylor Series Expansion 1

Finding a Taylor Series Expansion 2

Applications of Taylor Series 1

Applications of Taylor Series 2

Taylor Polynomial 1

Taylor Polynomial 2

Radius of Convergence

Radius of Convergence

Radius of Convergence

Radius of Convergence

Interval of Convergence 1

Interval of Convergence 2

Taylor Series 1

Taylor Series 2

Taylor Series 3

Taylor Series 4

Taylor Series 5

Taylor Series 6

Taylor Series 7

Taylor Series 8

Taylor Polynomial 1

Taylor Polynomial 2

Taylor Polynomial 3

Taylor Polynomial 4

Taylor Polynomial (Spring 2023)

Limit with Taylor Series 1

Limit with Taylor Series 2

Limit with Taylor Series 3

Limit with Taylor Series 4

Limit with Taylor Series 5

Sequences

The Nth-Term Test 1

The Nth-Term Test 2

The Nth-Term Test 3

The Nth-Term Test 4

The Nth-Term Test 5

The Nth-Term Test 6

The Integral Test

Limit Comparison Test 1

Limit Comparison Test 2

Limit Comparison Test 3

Limit Comparison Test 4

Ratio Test 1

Ratio Test 2

Ratio Test 3

Ratio Test 4

Ratio Test 5

The Nth-Term Test & Root Test 1

Root Test 2

Alternating Series Test 1

Alternating Series Test 2

Alternating Series Test 3