# Calculus 3 with the Math Sorcerer

## What you'll 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

## Requirements

- Calculus 1 and Calculus 2
- Knowledge of Basic Calculus

## 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:)**

## Who this course is for:

- Anyone Who Wants to Learn Calculus 3

## Instructor

I was born on a small unnamed Island in the Pacific Ocean inhabited mostly by natives who practiced mathematics on a daily basis.

My mother was a witch who specialized in Calculus and my father was a warlock who was well versed in the dark arts of Algebra.

As I grew older so did my thirst for knowledge, and so I set out on a long voyage to improve my mathematical skills. I traveled the world for years and learned a great deal of mathematics, but it wasn't until I met that raging Hobbit that my true powers started to show.

I am here today to share my magical powers with you.

Come join on me on this journey as we explore the world of mathematics together.