## Syllabus

Topics will include:

**Differentiation**

- Brief survey of Euclidean Geometry, scalar and vector products.
- Multivariate Functions: graphical representation (surfaces), continuity.
- Differentiation in two and three dimensions: partial derivatives, directional derivatives.
- Gradients, tangent lines and planes.
- Extremal problems.
- Lagrange Multipliers and constraints.
- Higher order derivatives and Taylor's Theorem.
- The Implicit Function Theorem, the Inverse Function Theorem.

**Integration**

- Brief survey of one dimensional integration.
- Integration in two dimensions: Cartesian, polar.
- Fubini's Theorem.
- Integration in three dimensions: Cartesian, cylindrical, spherical.
- Change of Variables: the Jacobian.
- Geometrical applications: solid volumes, surface area, center of mass.

**Vector analysis**

- Vector valued functions.
- The divergence and the curl of a vector field.
- Line integrals in two and three dimensions.
- Green's Theorem (in two dimensions).
- Surface integrals.
- Divergence Theorem (Gauss' Theorem).
- Stokes' Theorem.