Here are the course materials for Calculus, taught at Leiden University College the Hague in Fall 2014.
Lecturer: Owen Biesel
Email: bieselod@math.leidenuniv.nl (no longer valid)
Course documents
Helpful links
- Desmos Graphing Calculator
- Inverse Functions Explanation
- 3D function grapher
- Another explanation of multivariable stationary points.
- Extra practice with integrating exponential functions.
- More examples of double integrals
Have a helpful link to share? Let me know!
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