This course extends the ideas of calculus learnt in earlier courses to two and higher dimensions, showing how to calculate integrals and derivatives in higher dimensions and exploring special relationships between integrals of different dimensions. It also extends calculus to functions of one complex variable. 

Key Topics:

1. Taylor polynomials of two and three dimensions. Time derivatives in plane polar, cylindrical and spherical coordinates.
2. Line integrals.
3. Double and triple integrals.
4. Surface and volume integrals.
5. Divergence theorem in simple applications.
6. Stokes' and Green's theorem in simple applications.
7. Complex arithmetic and functions of a complex variable.
8. Laurent and Taylor series.
9. Evaluating complex and improper integrals using the Residue Theorem.