Knowledge and understanding:
At the end of this course the student should know the essential definitions and results in analysis in several variables, and he should be able to grasp how these enter in the solution of problems.
Applying knowledge and understanding:
The student should be able to apply the forementioned notionsto solve medium level problems, and to understand how they will be used in a more applied context.
The student should be able to evaluate coherence and correctness of the results obtained by him or presented him.
The student should be able to communicate in a clear and precise way, also in a context broader than mere calculus.
Analysis in one real variable; Linear algebra and geometry
Course contents summary
Essential graphs; curves; differentiability; free and constrained extrema; linear differential equations; integrals (hints); sequences and series of functions (hints).
Essential graphs: lines, planes, sphere, ellipsoid, paraboloid, hyperboloid.
Curves: speed, length.
Free and constrained extrema, Lagrange multipliers.
Linear differential equations: first and second order.
Sequences and series of functions (hints).