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Calculus 3

Playlist:    • Calculus III - Multivariable Calculus  

Chapter 1: Parametric Equations and Polar Coordinates

1.1 Parametric Equations

Eliminating the Parameter    • Parametric Equations: Eliminating the Para...  
Sketching and Orientation    • Parametric Equations: Sketching and Orient...  
Finding the Slope of the Tangent Line    • Parameter Equations: Slope of the tangent ...  
Equation of a Tangent Line at a Point    • Parametric Equations: Equation of a Tangen...  

1.2 Polar Coordinates

Converting Rectangular to Polar Coordinates    • Polar Coordinates: Converting Rectangular ...  
Converting Equations to Rectangular Form    • Polar Coordinates: Converting Eq to Rect F...  
Identifying a Curve from a Polar Equation    • Polar Coordinates: Identifying a Curve fro...  

1.3 Polar Curves

Sketching and Identifying Curves    • Polar Curves: Sketching and Identifying Cu...  
Working with Cardioids    • Polar Curves: Working with Cardioids #calc...  

1.4 Tangent Lines and Arc Length for Parametric and Polar Curves

Tangent Line of a Parametric Curve    • Parametric Curves: Tanget Line of a Parame...  
Arc Length of a Polar Curve    • Polar Curves: Arc Length of a Polar Curve ...  
Arc Length Inside a Cardioid    • Polar Curves: Arc Length Inside a Cardioid...  
Setting Up Arc Length    • Polar Curves: Setting Up Arc Length #calcu...  

Chapter 2: Three-Dimensional Space; Vectors

2.1 Rectangular Coordinates in 3-Space

Finding Distance and Midpoint    • Rectangular Coordinates in 3 Space: Findin...  
Finding the Equation of a Sphere    • Rectangular Coordinates in 3-Space: Find t...  

2.2 Vectors

Finding Components and Magnitude    • Vectors: Finding Components and Magnitude ...  
Unit Vectors and Orthogonality    • Vectors: Unit Vectors and Orthogonality #c...  

2.3 Dot Products; Projections

Finding the Angle Between Vectors    • Vectors: Finding the Angle Between Vectors...  
Vector Projection    • Vectors: Vector Projection #calculus3  

2.4 Cross Products

Computing the Cross Product    • Vectors: Computing the Cross Product #calc...  
Area of a Triangle    • Vector Cross Products: Area of a Triangle ...  
Volume of a Parallelepiped    • Vector Cross Products: Volume of a Paralle...  

2.5 Parametric Equations of Lines

Finding Equations of a Line    • Parametric Equations of Lines: Finding Equ...  
Intersection of Two Lines    • Parametric Equations of Lines: Intersectio...  

2.6 Planes in 3-Space

Finding the Equation of a Plane    • Planes in 3 Space: Finding the Equation of...  
Plane Perpendicular to a Line    • Planes in 3-Space: Plane Perpendicular to ...  
Distance from a Point to a Plane    • Planes in 3 Space Distance from a Point to...  

2.7 Cylindrical and Quadric Surfaces

Identifying a Surface    • Cylindrical and Quadric Surfaces: Identify...  
Reducing to Standard Form    • Cylindrical and Quadric Surfaces: Reducing...  

Chapter 3: Partial Derivatives

3.1 Functions of Two or More Variables

Finding and Sketching the Domain    • Functions of Two or More Variables: Findin...  
Sketching Level Curves    • Functions of Two or More Variables: Sketch...  

3.2 Limits and Continuity

Showing a Limit Does Not Exist    • Limits and Continuity: Showing a Limit Doe...  
Continuity and Piecewise Functions    • Limits and Continuity: Continuity and Piec...  

3.3 Partial Derivatives

Finding First Partial Derivatives    • Partial Derivatives: Finding First Partial...  
Mixed Partial Derivatives    • Partial Derivatives: Mixed Partial Derivat...  
Mixed Partials Not Equal (Continuity Fails)    • Partial Derivatives: Mixed Partials Not Eq...  

3.4 Chain Rule

Single Parameter    • Chain Rule: Single Parameter #calculus3  
Multiple Parameters    • Chain Rule: Multiple Parameters #calculus3  
Implicit Partial Differentiation    • Implicit Partial Differentiation #calculus3  

3.5 Tangent Plane; Total Differentials

Finding the Equation of a Tangent Plane    • Finding the Equation of a Tangent Plane #c...  
Total Differentials (Numerical Approximation)    • Total Differentials #calculus3  

3.6 Directional Derivatives

Calculating a Directional Derivative    • Calculating a Directional Derivative #calc...  
Maximum Rate of Change    • Maximum Rate of Change #calculus3  
Zero Directional Derivative and Level Curves    • Zero Directional Derivative and Level Curv...  

3.7 Maxima and Minima of Functions of Two Variables

Classifying Critical Points    • Classifying Critical Points  
An Inconclusive Case (D = 0)    • Classifying Critical Points Case D = 0 #ca...  

Chapter 4: Multiple Integrals

4.1 Double Integrals in Rectangular Coordinates

Evaluating an Iterated Integral    • Double Integrals #calculus3  
Calculating Volume Over a Rectangle    • Calculating Volume Over a Rectangle #calcu...  

4.2 Double Integrals Over Non-rectangular Regions

Evaluating a Type I Integral    • Evaluating a Type I Integral #calculus3  
Reversing the Order of Integration    • Reversing the Order of Integration #calculus3  

4.3 Double Integrals in Polar Coordinates

Evaluating a Basic Polar Integral    • Evaluating a Basic Polar Integral #calculus3  
Region Above the x-axis    • Double Integrals: Area of a region #calculus3  

4.4 Triple Integrals in Rectangular Coordinates

Evaluating a Basic Triple Integral    • Evaluating a Basic Triple Integral #calculus3  
Volume of a Solid    • Triple Integral: Volume of a Solid #calculus3  

4.5 Triple Integrals in Cylindrical and Spherical Coordinates

Evaluating a Triple Integral in Spherical Coordinates    • Evaluating a Triple Integral in Spherical ...  
Volume of an Ice Cream Cone    • Volume of an Ice Cream Cone #calculus3