Base Knowledge
Knowledge of Mathematical Analysis I (1st semester).
Teaching Methodologies
In theoretical lessons a theoretical exposition of each subject is made. In theoretical-practical lessons the resolution of application exercises are made. In laboratory classes is used Matlab.Evaluation: A kind of continuous evaluation is optional. It consists of two Theoretical-Practical tests (T1, T2) and two laboratory tests (PL1, PL2) during the semester. Also approval in mini-testes is mandatory (minimum of 2.6 points) for T1 and (minimum of 0.9 points) PL1. The final mark is T1+T2+PL1+PL2, where each T1, T2 is worth 10 and each PL1, PL2 is worth 2. There is also the option to perform Final Exam with worth of 20 points.
Learning Results
The teaching of mathematics should facilitate mathematical communication, reflective thinking, the application of mathematical techniques to problem solving, critical analysis of the results obtained, in other worlds interdisciplinary. One of the goals of Calculus II is to provide the basic fundamentals of mathematical methods usually applied in engineering, used by different course units in Mechanical Engineering Degree.
Program
1. Curves and Surfaces – Quadric Surfaces; polar coordinates, cylindrical coordinates and spherical coordinates.
2. Functions of Several Variables – Understanding topology in Rn ; domains, graphs and level curves, limits, continuity, partial derivatives, higher order partial derivatives, differentiability, directional derivatives, gradient and tangent plane, linear approximation and differentials, maximum and minimum of functions: free and conditional extrema. Using Matlab in some subjects covered.
3. Double integrals – Definition and calculation of the double integral, double integrals in polar coordinates, applications of double integral to calculate the areas of three-dimensional surfaces, volumes of solids, centers of mass and moment of inertia. Using Matlab in some subjects covered.
4. Series – Numerical series, geometric series, telescoping series, Dirichlet series; properties of numerical series; necessary condition for convergence. Taylor series.
Internship(s)
NAO