Calculus Fall 2014

Here are the course materials for Calculus, taught at Leiden University College the Hague in Fall 2014.

Lecturer: Owen Biesel
Email: (no longer valid)

Course documents

Helpful links

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Potential Final Session Topics

  • Taylor’s theorem: how to know when derivative approximations are good enough.
  • Integration by parts: another tool for integrating a large class of elementary functions.
  • One-forms: what dx and dy really are.
  • Weird functions.
  • Infinity and the Hyperreal Numbers.
  • Total Derivatives and the Multivariable Chain Rule.
  • Integration in Polar Coordinates and Normalizing the Normal Distribution.

Session notes

  • August 26: What is a Derivative? pdf
  • August 28: Derivatives of Sums and Products. pdf
  • September 2: Derivatives of Rational Functions and Exponentials. pdf
  • September 4: Inverse Functions, Derivatives, and the Natural Logarithm. pdf
  • September 9: Derivatives of Trigonometric Functions. pdf
  • September 11: The Chain Rule. pdf
  • September 16: Integrals and Antiderivatives. pdf
  • September 18: Integration by Substitution. pdf
  • September 23: Extremization; Partial Derivatives. pdf
  • September 25: Extremization with Multiple Variables. pdf
  • September 30: Calculating Areas with Integrals. pdf
  • October 2: Multivariable Integration. pdf
  • October 7: Differential Equations pdf
  • October 9: Special Topic: Total Derivatives