Bernd Schroeder

Single Variable 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.


Video.    (45:06min, 102MB)               Slides.

Limits and Continuity

  1. Motivation.
    Video.  (10:22min, 14MB)                   Slides.
  2. Limits at a Point.
    Video.  (30:11min, 26MB)                   Slides.
  3. One Sided Limits.
    Video.  (21:50min, 20MB)                   Slides.
  4. Continuous Functions.
    Video.  (15:29min, 16MB)                   Slides.
  5. Intermediate Value Theorem.
    Video.  (20:34min, 23MB)                   Slides.
  6. Limits at Infinity.
    Video.  (22:42min, 22MB)                   Slides.



  1. Motivation.
    Video.  (29:27min, 29MB)                   Slides.
  2. Definition of the Derivative.
    Video.  (16:01min, 17MB)                   Slides.
  3. Differentiable Functions.
    Video.  (16:11min, 17MB)                   Slides.
  4. Mean Value Theorem.
    Video.  (18:02min, 20MB)                   Slides.
  5. Higher Derivatives.
    Video.  (20:42min, 24MB)                   Slides.


Differentiation Formulas

  1. Power Rule.
    Video.  (33:52min, 30MB)                   Slides.
  2. Graphing.
    Video.  (21:42min, 22MB)                   Slides.
  3. Optimization.
    Video.  (29:15min, 35MB)                   Slides.
  4. Product and Quotient Rule.
    Video.  (19:41min, 18MB)                   Slides.
  5. Chain Rule.
    Video.  (46:16min, 49MB)                   Slides.
  6. Derivatives of Trigonometric Functions.
    Video.  (21:54min, 25MB)                   Slides.
  7. Implicit Differentiation.
    Video. (15:09min, 15MB)                    Slides.
  8. Derivatives of Inverse Functions.
    Video. (18:37min, 18MB)                    Slides.


Modeling with Derivatives

  1. Optimizing Parameter Dependent Functions. (Snell's Law.)
    Video.  (18:46min, 21MB)                   Slides.
  2. Graphing Parameter Dependent Functions. (Sketching normal distributions. Note: Sigma is supposed to be positive throughout.)
    Video.  (20:37min, 22MB)                   Slides.
  3. Related Rates.
    Video. (11:58min, 16MB)                    Slides.
  4. L'Hospital's Rule
    Video. (28:04min, 25MB)                    Slides.
  5. Linear Approximations and Error Estimates.
    Video. (27:37min, 78MB)                    Slides.


Definite Integrals         Video. (61:23min, 70MB)                    Slides.


Integration Techniques

  1. Antiderivatives.
    Video.  (23:27min, 26MB)                   Slides.
  2. Substitution.
    Video.  (24:10min, 22MB)                   Slides.
  3. Integration by Parts. (Don't worry too much about the last example. It's deliberately ugly.)
    Video.  (36:30min, 36MB)                   Slides.
  4. Integration via Partial Fraction Decomposition
    Video.  (52:46min, 48MB)                   Slides.
  5. Substitutions x=h(v) (Trigonometric and Hyperbolic Substitutions)
    Video.  (38:08min, 41MB)                   Slides.
  6. Deciding Which Integration Method to Use
    Video.  (21:53min, 33MB)                   Slides.


The Fundamental Theorem of Calculus

  1. The Fundamental Theorem of Calculus - Antiderivative Form
    Video. (24:32min, 30MB)                    Slides.
  2. Computing Areas Under and Between Curves
    Video. (25:02min, 25MB)                    Slides.
  3. The Fundamental Theorem of Calculus - Derivative Form
    Video. (11:33min, 15MB)                    Slides.


Applications of Integration

  1. Volumes
    Video.  (32:40min, 56MB)                    Slides.
  2. Work
    Video.  (34:07min,36MB)                     Slides.
  3. Improper Integrals over Infinite Intervals
    Video.  (49:02min, 49MB)                    Slides.
  4. Improper Integrals Across Singularities
    Video.  (22:45min, 24MB)                    Slides.
  5. Centers of Mass of Linear Densities
    Video. Slides.


Numerical Methods

  1. Taylor Polynomials
    Video. (47:22min, 48MB)                    Slides.
  2. Numerical Integration
    Video. (76:07min, 82MB)                    Slides.
  3. Newton's Method
    Video. (20:20min, 20MB)                    Slides.


Introduction to Statistics - Continuous Distribution Functions

  1. Probability Functions
    Video. (37:31min, 42MB)                    Slides.
  2. Continuous Random Variables
    Video. (29:47min, 33MB)                    Slides.
  3. Widely Used Density Functions
    • Uniform Distribution
      Video. (  9:07min,  9MB)                    Slides.
    • Exponential Distribution
      Video. (14:44min, 17MB)                    Slides.
    • Normal Distribution
      Video. (27:37min, 30MB)                    Slides.
  4. Cumulative Distribution Functions
    Video. (19:31min, 27MB)                    Slides.
  5. Mean and Variance
    Video. (28:02min, 28MB)                    Slides.


Introduction to Statistics - Connecting Data and Theory

  1. Sample Statistics
    Video. (31:39min, 30MB)                    Slides.
  2. The Central Limit Theorem
    Video. (31:57min, 39MB)                    Slides.
  3. Large Sample Confidence Interval for the Mean
    Video. (16:41min, 18MB)                    Slides.



  1. Sequences
    Video. (38:57min, 40MB)                    Slides.
  2. Recursive Sequences
    Video. (22:09min, 25MB)                    Slides.



  1. Introduction to Series
    Video. (30:43min, 29MB)                    Slides.
    Alternative Introduction Without Using Integrals
    Video. (30:14min, 27MB)                    Slides.
  2. Tests for Convergence
    Video. (23:59min, 24MB)                    Slides.
  3. Power Series
    Video. (29:46min, 29MB)                    Slides.
  4. Multiplication and Division of Power Series
    Video. (14:49min, 14MB)                    Slides.
  5. More Tests for Convergence
    Video. (20:21min, 20MB)                    Slides.