Handbook

Understand the basic concepts of linear algebra, and recognise and manipulate elements of vector spaces;

Formulate and solve equations involving vectors and matrices, including for three-dimensional geometry;

Identify and evaluate improper integrals;

Solve simple first and second order differential equations, and formulate them for applications to physical systems;

Compute Taylor series expansions, with remainder, for functions of one variable;

Apply Taylor series and l'Hopital's rule to compute limits;

Understand and compute the convergence properties of infinite series;

Provide written reports that contain complete mathematical arguments;

Understand the concept of mathematical proof and the difference between proof by construction and proof by induction;

Prove elementary theorems by induction and by construction.