Bernd Schroeder

Single Variable Calculus Videos

 

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Electronic book available at Fountainhead Press

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

Introduction

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.

 

Derivatives

  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.

 

Sequences

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

 

Series

  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.