Bernd Schroeder

Multivariable Calculus Videos


Curriculum Vitae
Class Materials
Research Interests



Electronic book available at Fountainhead Press

The videos were produced with Camtasia studio. The slides were produced with the LaTeX beamer package.


Vector Algebra

  1. Points and Figures in Three-Dimensional Space
    Video. (54MB, 47:42min)                      Slides.
  2. Vectors
    Video. (30MB, 32:05min)                      Slides.
  3. The Scalar Product
    Video. (21MB, 22:36min)                      Slides.
  4. The Vector Product/Cross Product
    Video. (40MB, 40:56min)                      Slides.


Calculus of Vector-Valued Functions

  1. Vector-Valued Functions/Parametric Equations
    Video. (78MB, 45:58min)                      Slides.
  2. Lines in Three-Dimensional Space
    Video. (23MB, 22:32min)                      Slides.
  3. Limits and Continuity for Vector-Valued Functions
    Video. (14MB, 13:07min)                      Slides.
  4. Derivatives and Integrals of Vector-Valued Functions
    Video. (41MB, 40:41min)                      Slides.
  5. Arc Length, Curvature, Components of Acceleration
    Video. (60MB, 70:17min)                      Slides.


Surfaces in Three-Dimensional Space

  1. Multivariable Functions
    Video. (89MB, 44:05min)                      Slides.
  2. Parametric Surfaces
    Video. (93MB, 43:50min)                      Slides.
  3. Planes
    Video. (65MB, 54:55min)                      Slides.
  4. Conic Sections and Quadric Surfaces
    Video. (97MB, 35:45min)                      Slides.
  5. Non-Rectangular Coordinate Systems
    Video. (40MB, 36:50min)                      Slides.
  6. Limits and Continuity for Multivariable Functions
    Video. (35MB, 29:00min)                      Slides.


Integration of Multivariable Functions

  1. Definite Integrals of Multivariable Functions
    Video. (67MB, 55:06min)                      Slides.
  2. Iterated Integrals and Fubini's Theorem
    Video. (42MB, 32:43min)                      Slides.
  3. Double Integrals over General Regions
    Video. (33MB, 36:14min)                      Slides.
  4. Triple Integrals over General Regions
    Video. (38MB, 38:30min)                      Slides.
  5. Double Integrals in Polar Coordinates
    Video. (40MB, 41:55min)                      Slides.
  6. Triple Integrals in Non-Rectangular Coordinate Systems
    Video. (42MB, 41:53min)                      Slides.


Differentiation of Multivariable Functions

  1. Partial Derivatives
    Video. (65MB, 47:15min)                      Slides.
  2. The Chain Rule
    Video. (52MB, 44:06min)                      Slides.
  3. Directional Derivatives and the Gradient
    Video. (80MB, 52:57min)                      Slides.
  4. Tangent Planes
    Video. (79MB, 60:05min)                      Slides.


Multivariable Optimization

  1. Relative Extrema of Multivariable Functions
    Video. (31MB, 30:02min)                      Slides.
  2. Absolute Extrema
    Video. (40MB, 40:50min)                      Slides.
  3. Lagrange Multipliers
    Video. (35MB, 28:38min)                      Slides.


Vector Fields

  1. Vector Fields
    Video. (52MB, 47:29min)                      Slides.
  2. Line Integrals of Vector Fields
    Video. (50MB, 51:47min)                      Slides.
  3. The Fundamental Theorem for Line Integrals
    Video. (37MB, 35:38min)                      Slides.


Change of Variables and Surface Area

  1. Surface Area of a Parametric Surface
    Video. (47MB, 45:01min)                      Slides.
  2. The Multivariable Change of Variable Formula
    Video. (58MB, 54:25min)                      Slides.


Vector Calculus

  1. Surface Integrals of Vector Fields
    Video. (85MB, 77:01min)                      Slides.
  2. The Divergence Theorem
    Video. (57MB, 55:18min)                      Slides.
  3. Curl and Stokes' Theorem
    Video. (69MB, 62:13min)                      Slides.
  4. Gradient, Divergence and Curl
    Video. (37MB, 30:30min)                      Slides.
  5. Green's Theorem
    Video. (25MB, 19:17min)                      Slides.