MVC

Table of Contents

• Pretty Curves

  • Trochoid
  • Cardioids and Friends
  • Epicycles
  • Epitrochoids
  • Lissajous
  • Cauchy MVT
  • Slicing a Cone
  • Conic Sections
  • Polar Conic Sections
  • Comparing conic sections in polar coordinates
  • Checking Conic Parameters connecting polar and Cartesian descriptions
  • General Quadratic in 2D
  • Twisted Cubic
  • Hyperbolic trig functions

• Series

  • Conditional Convergence
  • Zeno
  • Linearization improvement leads to Maclaurin series
  • Using Taylor even when Maclaurin converges everywhere
  • Substitutions in Power Series

• Fourier Series

  • Fourier Example
  • Fourier Products
  • Fourier Series
  • Fourier Products
  • Why Fourier Analysis
  • Building with Gaussian-derivative Wavelets

• Vectors

  • Calculating Distances in Flat Spaces
  • How could we multiply vectors?

• quadratic surfaces

  • Standard Forms of Quadratic Surfaces
  • General Quadratic Surfaces

• TNB

  • Tracing 3D Curves
  • Tracing Tangent Lines in 3D
  • TNB frame
  • TNB special case
  • Double Helix
  • Toroidal Spiral
  • Trefoil
  • Tracing 3D Curves
  • Projectile Launched downhill

• Limits and Partial Derivatives

  • Tracing Out Surfaces in 3D
  • Contours
  • Delta-Epsilon definition of limit in 2D
  • Partial Derivatives
  • Derivatives of 2D functions
  • 2D Extrema
  • Constrained Extrema
  • 2-constraint Lagrange
  • Better Horizontal Trace and Contour display

• Multiple Integrals

  • 2D Riemann Sum
  • Figuring out what to integrate to get an area in polar
  • Spherical Coordinates
  • Tracing out region of integration in spherical coordinates
  • dV in Spherical Coordinates
  • Double Integration in Polar Coordinates

• vector calculus

  • Cross-product
  • Computing Cross-Product
  • Moveable Hand for RHR
  • Vector Field
  • 3D vector field
  • Line Integral
  • Line Integral as defined by left side sum
  • Line integral through scalar field
  • Line integral through a vector field
  • Divergence and Curl of 2D vector field
  • Divergence and Curl of 3D vector field
  • Green's Theorem in 2D
  • Parametric Surfaces
  • Parametric surface with curved edges
  • Curl of vector field on a surface

• Friday Funday

  • Linear Nomograph

• 2nd Order Differential Equations

  • Linear Homogeneous 2nd Order Ordinary Diff. Eq. Examples