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**Email:** bieselod@math.leidenuniv.nl (no longer valid)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