Code: | M2037 | Acronym: | M2037 |
Keywords | |
---|---|
Classification | Keyword |
OFICIAL | Mathematics |
Active? | Yes |
Responsible unit: | Department of Mathematics |
Course/CS Responsible: | Bachelor in Physics |
Acronym | No. of Students | Study Plan | Curricular Years | Credits UCN | Credits ECTS | Contact hours | Total Time |
---|---|---|---|---|---|---|---|
L:B | 0 | Official Study Plan | 3 | - | 6 | 48 | 162 |
L:CC | 0 | study plan from 2021/22 | 2 | - | 6 | 48 | 162 |
3 | |||||||
L:F | 51 | Official Study Plan | 2 | - | 6 | 48 | 162 |
L:G | 0 | study plan from 2017/18 | 2 | - | 6 | 48 | 162 |
3 | |||||||
L:Q | 0 | study plan from 2016/17 | 3 | - | 6 | 48 | 162 |
A. Ordinary Differential equations (ODE). Study of the initial value prolems (IVP) for some types of ODE.
1. Reference to the theorem on the existence and uniqueness of solutions of the IVP for C^1 systems of first order ODEs. Transformation of an arbitrary order system to a first order system.
2. Expliict Solutions of some ODE: scalar 1st order linear equations. separable equations, 1st order homogeneous equations, Bernoulli equations, Ricatti equations, exact differental equations.
3. Linear ODE with continupus coefficients. Existence and uniqueness theorems. Vector spaces of solutions of the associated homogeneous equations. Fundamental systems of solutions, order reduction method. In case of inear ODE with constant coefficients use of the zeros of the characteristic polynomial to compute a fundamental system of solutions Methods for determining particular solutions of the general equation: method of undetermined coefficients and variation of parameters. Exponential of a linear operator. Systems of linear ODE.
B.Vector Analysis
1. Paths in open domains of R^n. Line integrals. Vector fields. Gradient of a scalar function, gradient and conservative vector fields, Convex, star-shapeped sets. Conditions for a vector field to be a gradient vector field. Green's theorem.
2. Regular submanifolds of R^3: inverse image of a regular value of a scalar function, regular parametrizations, tangent and normal spaces at a point Orientation of a regular surface. Orientation of the boundary
3. Surface integrals of scalar functions, Surface area. Flux of a vector field along a surface. Stokes and Gauss theorems.
The lecture notes are also part of the "main bibliography".
Theoretical classes: Exposition of the program subjects. Exercise proposals.
Practical classes: Resolution of part of the proposed exercises and clarification
of doubts about solving problems and proposed work.
Autonomous theoretical and practical study is strongly encouraged.
designation | Weight (%) |
---|---|
Exame | 100,00 |
Total: | 100,00 |
designation | Time (hours) |
---|---|
Estudo autónomo | 114,00 |
Frequência das aulas | 48,00 |
Total: | 162,00 |
The final grade will be the grade obtained from the final exam rounded to the nearest integer.
Any type or special examination can be from one the following types: exclusively by an oral examination, only a written exam, one oral examination and a written exam.
The option for one of the alternatives is exclusively up to the jury of the curricular unit.