MATH 170 • Final • Calculus for Scientists and Engineers II

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

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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

Convergence and Limit of Sequences

Monotonic Sequence Theorem

Recursive Sequences

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Series: Partial Sums

Geometric Series

Harmonic Series

Telescoping Series

Operations in Series

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The Nth-Term Test

The Integral Test

P Test

The Ratio Test

The Root Test

Direct Comparison Test

The Limit Comparison Test

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Introduction to Absolute Convergence

Absolute Convergence Theorem

Alternating Series Test I

Alternating Series Test II

Conditional Convergence

Absolute or Conditional or Divergent

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

Triple Integrals: Cartesian Coordinates

Triple Integrals: Cartesian Coordinates

Triple Integrals: Spherical Coordinates

Triple Integrals: Cartesian Coordinates

The Line Integrals

Vector Fields & Divergence

Taylor Series Expansion

Convergence Tests for Infinite Series

Radius and Interval of Convergence

Limit of Sequences

Convergence Test for Series

Convergence of Series

Convergence of Series

Absolute & Conditional Convergence

Length of a Curve

Reversing the Order of Integration

Volume by Triple Integrals

Volume by Double Integrals

Triple Integrals in Spherical Coordinates

Triple Integrals in Cylindrical Coordinates

Gradient of Vector Field

Line Integrals

Line Integrals

Green's Theorem