### Maths and Applied Maths 2 (MAM2)

Mathematics and Applied Mathematics 2 is made of 2 one-semester credits, MAM 201 and MAM 202.

##### MAM 201:

This first-semester credit consists of two courses:

Partial differentiation: directional derivatives and the gradient vector; maxima and minima of surfaces; Lagrange multipliers. Multiple integrals: surface and volume integrals in general coordinate systems. Vector calculus: vector fields, line integrals, fundamental theorem of line integrals, Green's theorem, curl and divergence, parametric curves and surfaces.

• ###### Ordinary Differential Equations:

First order ordinary differential equations, linear differential equations of second order, Laplace transforms, systems of equations, series solutions.

##### MAM 202:

This second semester credit consists of two courses:

• ###### Linear Algebra:

Linear spaces, inner products, norms. Vector spaces, spans, linear independence, basis and dimension. Linear transformations, change of basis, eigenvalues, diagonalization and its applications.

• ###### Introduction to analysis and algebra:

Set theory; mappings; binary operations; equivalence relations and order; groups; real numbers; open and closed intervals; sequences and series (convergence); functions of a real variable (continuity, limit); series of functions; Taylor series.

Throughout the year, there is an an additional, assignment based, introduction to mathematical programming.