What You Will Learn!
- Understand Vectors in the Plane
- Understand the Three Dimensional Coordinate System
- How to Plot Points in Three Dimensions
- Find the Magnitude of Vectors in Two Dimensions and Three Dimensions
- How to Find the Vector Given the Initial and Terminal Points
- How to Sketch a Vector in Standard Position
- Understand what a Unit Vector Actually Is
- How to Find a Unit Vector in the Direction of Another Vector
- How to Construct a Vector with a Given Magnitude in the Direction of Another Vector
- How to Find the Terminal Point of a Vector Given the Vector and its Initial Point
- How to Find a Unit Vector in the Direction Opposite of a Vector
- How to Compute the Dot Product
- How to Determine if Vectors are Orthogonal
- How to Find the Angle Between Two Vectors
- How to Compute the Dot Product Given the Magnitudes of Vectors and the Angle Between Them
- How to Find Two Vectors in Opposite Directions Orthogonal to a Given Vector
- Understand What Direction Cosines and Direction Angles Are
- How to Derive the Formulas for Direction Cosines and Direction Angles
- How to Find Direction Cosines
- How to Find Direction Angles
- How to Find the Cross Product
- How to Find a Unit Vector Orthogonal to Two Vectors
- How to Find the Distance Between Two Points in Space
- How to Find the Equation of a Sphere Given the Center and Radius
- How to Find the Equation of a Sphere Given the Endpoints of the Diameter
- How to Write the Equation of the Sphere in Standard Form by Completing the Square and Find the Center and Radius
- How to Derive the Formulas for the Parametric and Symmetric Equations of a Line in Space
- How to Find the Equation of a Line in Space Given a Point and a Parallel Vector
- How to Find the Equation of a Line in Space Passing through Two Points
- How to Find the Equation of a Line in Space Given a Point and a Parallel Line
- How to Find the Equation of the Plane Given a Point and a Normal Vector
- How to Find the Equation of a Plane Given Three Points
- How to Find the Equation of the Plane that is Parallel to the z-axis Given Two Points
- How to Find the Equation of a Plane Given a Point and a Line on the Plane
- How to Find the Equation of a Plane Given Two Points and a Perpendicular Plane
- Understand Cylindrical Coordinates and Why they Are Useful
- How to Convert from Cylindrical Coordinates to Rectangular Coordinates
- How to Convert from Rectangular Coordinates to Cylindrical Coordinates
- How to Convert Rectangular Equations to Cylindrical Equations
- How to Convert Cylindrical Equations to Rectangular Equations
- Understand Spherical Coordinates
- How to Convert Spherical Coordinates to Rectangular Coordinates
- How to Convert Rectangular Coordinates to Spherical Coordinates
- How to Convert Spherical Equations to Rectangular Equations
- How to Convert Rectangular Equations to Spherical Equations
- Understand Vector-Valued Functions
- How to Graph a Vector-Valued Function, Find the Orientation of the Graph, and Write it in Rectangular Form
- How to Represent Plane Curves as Vector-Valued Functions
- How to Represent Any Circle as a Vector-Valued Function
- How to Represent Any Ellipse as a Vector-Valued Function
- How to Represent Any Hyperbola as a Vector-Valued Function
- How to Evaluate Limits involving Vector-Valued Functions
- How to Determine the Intervals on which a Vector-Valued Function is Continuous
- How to Find the Derivative of a Vector-Valued Function
- How to Find the Second Derivative of a Vector-Valued Function
- How to Find the Intervals where a Vector-Valued Function is Smooth
- How to Solve Differential Equations with Vector-Valued Functions
- How to Evaluate Indefinite Integrals with Vector-Valued Functions
- How to Evaluate Definite Integrals with Vector-Valued Functions
- How to Find the Velocity, Speed, and Acceleration Given a Position Function as a Vector-Valued Function
- How to Find the Position Function Given the Velocity and Acceleration
- Understand the Unit Tangent Vector
- How to Compute the Unit Tangent Vector
- How to Find the Equation of a Tangent Line in Space
- Understand the Principal Unit Normal Vector
- How to Find the Principal Unit Normal Vector
- Understand Arc Length
- Understand the Arc Length Function
- How to Compute Arc Length
- Understand Curvature
- Understand the Curvature of a Circle Intuitively
- How to Compute the Curvature of a Circle
- How to Compute Curvature using Various Formulas
- Understand Functions of Several Variables
- How to Evaluate Functions of Several Variables
- How to Find the Domain and Range of Functions of Several Variables
- How to Find the Level Curves of a Function
- How to Find Limits for Functions of Several Variables
- How to Show a Multivariate Limit Does Not Exist
- How to Use Polar Coordinates to Evaluate Limits for Functions of Several Variables
- Understand Partial Derivatives
- How to Compute Partial Derivatives
- Understand the Notation for Higher Order Partial Derivatives
- How to Compute Higher Order Partial Derivatives
- How to Show a Function Satisfies Laplace's Equation
- How to Show a Function Satisfies the Heat Equation
- How to Show a Function Satisfies the Wave Equation
- How to Show a Function Satisfies the Cauchy Riemann Equations
- How to Compute the Total Differential
- How to Use the Total Differential To Approximate a Function of Several Variables
- Understand the Chain Rule for One Independent Variable
- How to use the Chain Rule to Find the Derivative in the One Independent Variable Case
- Understand the Chain rule for Two Independent Variables
- How to use the Chain Rule to Find the Derivative in the Two Independent Variable Case
- How to Find dy/dx using Calculus 3 Methods
- How to Differentiate Multivariable Functions Implicity
- Understand Directional Derivatives
- How to Compute Directional Derivatives
- Understand the Gradient
- How to Compute the Gradient
- How to Find the Maximum Value of the Directional Derivative
- How to Find a Unit Normal Vector Given a Surface
- Understand Tangent Planes and Normal Lines
- How to Find the Equation of a Tangent Plane and the Equation of the Normal Line
- How to use the Second Partials Test to Find Relative Extrema and Saddle Points
- How to Find the Minimum Distance from a Point to a Plane
- How to use Lagrange Multipliers to Find Relative Extrema
- How to use Lagrange Multipliers in the Case with Two Constraints
- How to Integrate Multivariable Functions with respect to One Variable
- Understand Iterated Integrals
- How to Evaluate Iterated Integrals
- How to Switch the Order of Integration in Iterated Integrals
- Understand Double Integrals
- How to Write Both Orders of Integration in Double Integrals
- Understand Triple Integrals
- How to Evaluate Triple Integrals
- Understand Vector Fields
- How to Determine if a Vector Field is Conservative
- How to Find the Potential Function for a Conservative Vector Field
- How to Compute the Divergence of a Vector Field
- How to Compute the Curl of a Vector Field
- How to Evaluate a Line Integral
- How to Evaluate the Line Integral of a Vector Field
- How to Evaluate a Line Integral in Differential Form
- How to Compute the Work Done by a Force Field
- Understand Projections
- How to find the Projection of u onto v
- How to find the Vector Component of u along v
Description
This Calculus 3 Course has hundreds of videos:)
Note: If you know some Calculus 1 you could probably jump in and complete a significant portion of this course without Calculus 2.
Basically just,
1) Watch the videos, and try to follow along with a pencil and paper, take notes!
2) Try to do the problems before I do them(if you can!)
3) Repeat!
Calculus 3 is an absolutely beautiful subject. I hope you enjoy watching these videos and working through these problems as much as I have:)
Note this course has lots of very short videos. If you are trying to learn math then this format can be good because you don't have to spend tons of time on the course every day. Even if you can only spend time doing 1 video a day, that is honestly better than not doing any mathematics. You can learn a lot and because there are so many videos you could do 1 video a day for a very long time. Remember that math can be challenging and time consuming, so if you just do a little bit every day it can make your journey much more enjoyable. I hope you enjoy this course and learn lots of mathematics.
Who Should Attend!
- Anyone Who Wants to Learn Calculus 3
