Applied Engineering Mathematics I

In the theoretical-practical classes and tutorials we use the lecture method during the explanation of theoretical issues, alternating with periods of individual work supervised by the teacher, where students have to solve exercises on the subject.

Objectives: Interpret real problems with an increasing autonomy; find and select relevant information from different sources of knowledge for solving problems.
Generic skills: Application of the knowledge and understanding; self-learning.
Specific skills: Use of the differential and integral calculus on IRn in several academic and applied problems in engineering; understanding and analyses of results.

1. Analytical geometry – Short overview on conics, vectors, lines and planes in space. Polar, cylindrical and spherical coordinates. Quadric surfaces.
2. Differential Calculus on IRn – Topology concepts. Real functions of several real variables (domain, limits, partial derivatives, Schwarz theorem, l inear approx imation and differentials, chain rule, implicit function, directional derivative, gradient vector and applications). Simple and conditional extremes of a real function (method of Lagrange multipliers).
3. Integral Calculus on IRn – Double and triple integrals (definition, geometric interpretation, calculus in Cartesian and other systems of coordinates, applications); Brief introduction to vector analysis (vector fields; line integrals; conservative fields; Green’s theorem).

NAO