MATH 170 • Tüm Sınavlar • Calculus for Scientists and Engineers II

Distance Between Points 1

Cosine Theorem in 3D & Euclidean N-Space

Vectors: Arithmetic, Parallelism and Unit Vector

Angles between Vectors: Dot Product

Vector Projection

Cross Product of Vectors

Applications of Cross Product

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

Plane Equations

Line Equations 1

Line Equations 2

Intersection of Planes

Intersection of Planes and Lines

Distance of a Point to Lines & Planes

Graphs of Surfaces

Exam like Question 1

Exam like Question 2

Exam like Question 3

Exam like Question 4

Exam like Question 5

Domain of Multivariable Functions

Level Curves

Level Curves and Level 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

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

Continuity 1

Continuity 2

Definition of Partial Derivative 1

Definition of Partial Derivative 2

Partial Derivative 1

Partial Derivative 2

Partial Derivative 3

Partial Derivative 4

Partial Derivative 5

Partial Derivative 6

Higher Order Differentiation 1

Higher Order Differentiation 2

Higher Order Differentiation 3

Higher Order Differentiation 4

Higher Order Differentiation 5

Tangent Plane 1

Tangent Plane 2

Tangent Plane 3

Tangent Plane 4

Tangent Plane and Normal Line 1

Tangent Plane and Normal Line 2

Chain Rule 1

Chain Rule 2

Chain Rule 3

Chain Rule 4

Chain Rule 5

Chain Rule 6

Chain Rule and Tangent Plane

Gradient Vector

Directional Derivative

Gradient and Directional Derivative

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

Optimization with Lagrange Multipliers 1

Optimization with Lagrange Multipliers 2

Lagrange Multipliers with Two Constraints

Gradient and Tangent Plane 1

Gradient and Tangent Plane 2

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

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

Introduction to Double Integrals

Sketching the Area of Integration I

Sketching the Area of Integration II

Reversing the Order of Integration I

Reversing the Order of Integration II

Reversing the Order of Integration III

Volume Calculation by Double Integrals

Exam like Question 1

Exam like Question 2

Cartesian to Polar Coordinates

Double Integrals in Polar Coordinates I

Double Integrals in Polar Coordinates II

Double Integrals in Polar Coordinates III

Volume Calculation using Polar Coordinates

Area Calculation using Polar Coordinates

Introduction to Triple Integrals

Triple Integration over Regions

Graphs of Important Surfaces

Volume by Triple or Double Integrals

Volume between Two Surfaces

Triple Integrals: Reversing the Order

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

Limits of Multivariable Functions

Limits of Multivariable Functions

Directional Derivatives

Critical Points (Max-Min and Saddle Points)

Lagrange Multipliers

Double Integral: Reversing the Order of Integration

Limits of Multivariable Functions

Limits of Multivariable Functions

Tangent Planes and Normal Lines

Extreme Values over Closed Regions

Double Integrals in Polar Coordinates

Limit of Multivariable Functions

Limit of Multivariable Functions

Limit of Multivariable Functions

Reversing the Order of Integration

Extreme Values

Directional Derivative

Double Integrals in Poolar Coordinates

Change of Variable: The Jacobian

Plane Equations

Limits of Multivariable Functions

Limits of Multivariable Functions

Directional Derivatives

The Chain Rule

Double Integrals in Cartesian Coordinates

Extreme Values over Closed Regions

Reversing the order of Integration

Double Integrals in Poolar Coordinates

Graphs and Surfaces in 3D

Domain of Multivariable Functions

The Limit of Multivariable Functions

The Limit of Multivariable Functions

Higher Order Partial Derivative

The Chain Rule

Critical Points (Max-Min and Saddle Points)

Extreme Values on Closed Region

The Lagrange Multipliers

Reversing the order of Integration

Double Integrals in Cartesian Coordinates

Double Integrals in Cartesian Coordinates

Double Integrals in Polar Coordinates

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

Convergence and Limit of Sequences

Monotonic Sequence Theorem

Recursive Sequences

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

Series: Partial Sums

Geometric Series

Harmonic Series

Telescoping Series

Operations in Series

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

The Nth-Term Test

The Integral Test

P Test

The Ratio Test

The Root Test

Direct Comparison Test

The Limit Comparison Test

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

Exam like Question 15

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