A proper understanding and feeling for the geometry of space of many dimensions. This permits a geometric approach to the calculus of several variables.

1. Set theoretic notation
2. Euclidian space
3. Linear transformations
4. Matrices
5. Quadradic forms
6. Two-variable cubic forms
7. Polynomial geometry

Developing some basic principles of differential calculus of several variables, with stress on the geometric viewpoint and the derivative as the best linear approximations to a given function.

1. Distance in Euclidian space
2. The derivative as tangent
3. Contours
4. Partial derivatives
5. Higher derivatives
6. Taylor series
7. Inverse/Implicit Function Theorem