 Mathematical Analysis III C

5004

Department

Departamento de Matemática

6.0

Teacher in charge

Ana Maria de Sousa Alves de Sá, José Maria Nunes de Almeida Gonçalves Gomes

5

70

Português

Objectives

We define as main objectives:

1) Basic notions on numerical and power series.

2)  Learning of basic tools for solving first order differential equations (linear equation, separable equation, exact differential equation) as well as of fundamental theoretical results (Picard’s Existence and Uniqueness Theorem). Knowledge of classical applications and acquisition of modelling skills of certain problems using differential equations.

3) Learning of basic tools for solving higher order differential equations (Variation of constants method, Judicious Guessing Method, Laplace Transform). Knowledge of classical applications of second order differential equations.

4) Learning of basic Fourrier Analysis and its applications to Partial Differential Equations.

Prerequisites

Knowledge of he contents of a first year academic courses on Linear Algebra and  Calculus.

Bibliography

Campos Ferreira, J. - Introdução à Análise Matemática, Edições da Fund. C. Gulbenkian.

Braun, Martin - Differential Equations and their Applications, Springer-Verlag.

Edwards, Jr; Penney, David - Elemetary Differential Equations (with boundary valur Problems), Prentice Hall.

Figueiredo, Djairo - Análise de Fourier e Equações Diferenciais Parciais, IMPA projeto Euclides.

Teaching method

Teaching Method bases on conferences a n problems solving sessions with the support of a personal attending schedule.

Evaluation method

Important:

In order to be evaluated, the student must attend at least to 2/3 of the problem solving sessions.

Evaluation Methods.

1-Continuous evaluation

The continuos evaluation consists on three tests during the semester. One of the tests may be improved in the final examination date. The final grade is the average of the grades of the three tests. The student is aproved if the final grade is greater or equal than 9,5.

Each test lasts for 1h 30min.

2-Final exam evaluation.

The student is aproved if the grade of the final exam is greater or equal than 9,5.

The final exam lasts for 3h.