Vectors and 3D Space

Vectors and 3D Space

Vectors Part 1

Vectors Part 2

Dot Product Part 1

Dot Product Part 2

Dot Product Part 3

Dot Product and Work

Cross Product Part 1

Cross Product Part 2

Triple Scalar Product

Cross Product and Torque

Lines and Planes in 3D Space Part 1

Lines and Planes in 3D Space Part 2

Distance between a Point and Plane

Explicitly Defined Surfaces and Quadric Surfaces

Coordinate Systems in 3D Space

Coordinate Systems in 3D Space Example Conversions

Parametric Curves in 3D Space

Graphing Parametric Curves in 3D Space

Calculus with Parametric Curves

Parametric Curves: Examples of Limits and Antiderivatives

Objects Moving through Space

Tangent and Principal Normal Vectors

Curve Length and Curvature

Curvature and the Circle of Curvature

Introducing Multivariable Functions

Limits of Multivariable Functions

Partial Derivatives

Multivariable Chain Rule and Implicit Differentiation

Implicit Differentiation

Gradient and Directional Derivatives

Tangent Planes and Normal Lines

Critical Points of Multivariable Functions

Classifying Critical Points using Eigenvalues of Hessian Matrix

Minimum Distance Example

Polynomial Interpolation and Regression

Method of Lagrange Multipliers

Additional Lagrange Multipliers Examples

Multivariable Functions

Newton’s Method for Optimization in Higher Dimensions (Project Preparation)

Gaussian Elimination

Matrix Algebra

Finding Matrix Inverses

Newton's Method

Newton's Method for Polynomials in Python

Sphere Finding with Multivariable Newton's Method

Lagrange Multipliers, Gradient, and Hessian Matrix

Double Integration

Volumes with Double Integrals

Setting up a Double Integral Example

Volume of a Solid using a Double Integral Example

Setting up a Double Integral to find the Volume between Surfaces Example

Swapping the Order of Integration for a Double Integral Example

Double Integrals using Polar Coordinates

The Gaussian Integral

Mass, Center of Mass, Moments of Inertia

Finding Surface Area using Double Integrals

Surface Area with a Double Integral Example

Triple Integrals

Triple Integrals in Spherical Coordinates

Change the Order of Integration for a Triple Integral Example

Volume using Triple Integral Cylindrical Coordinates Example

Change of Variables and Jacobian Determinant

Multiple Integration

Vector Analysis

Introduction to Vector Fields

Path Integrals

Independence of Path for Integrals in Conservative Vector Fields

Green's Theorem

Using Green's Theorem to Find the Area of an Ellipse

Parametric Surfaces

Surface Integrals

Divergence Theorem

Stokes's Theorem

Surface Integral Solved Three Ways (Formula, Divergence, Stokes)