Differential Equations

Code:

M222

Acronym:

M222

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2012/2013 - 2S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:AST	1	Plano de Estudos a partir de 2008	3	-	7,5	-
L:B	0	Plano de estudos a partir de 2008	3	-	7,5	-
L:CC	0	Plano de estudos de 2008 até 2013/14	3	-	7,5	-
L:F	0	Plano de estudos a partir de 2008	3	-	7,5	-
L:G	3	P.E - estudantes com 1ª matricula anterior a 09/10	3	-	7,5	-
		P.E - estudantes com 1ª matricula em 09/10	3	-	7,5	-
L:M	99	Plano de estudos a partir de 2009	2	-	7,5	-
L:Q	0	Plano de estudos Oficial	3	-	7,5	-
PGMP	0	PE da PG em Matemática para Professores	1	-	7,5	-

Teaching language

Portuguese

Objectives

 Introduction to methods of solving ordinary differential equations with emphasis on equations and systems of linear differential equations.

Learning outcomes and competences

Problem-solving skills. Theoretical understanding.

Working method

Presencial

Program

Differential equations. 1st-order equations: Separable Equations, Exact equations, linear and Bernoulli equations Integrating factors.Ricatti Equations.

 Linear equations. Existence and uniqueness theorems. Theory of solutions of linear equations.General solution of linear equation. Equations with constant coefficients. Solutions of the homogeneous equation. Methods for determining particular solutions of the general equation: method of undetermined coefficients and variation of parameters.
Ordinary and singular points of equations of non-constant coefficients. Resolution by power series in the neighbourhood of ordinary points.
Laplace transforms. Transforms of some functions. Properties. Inverse Laplace transform. Heaviside function and its transform. Solving differential equations with discontinuous 2 th member. The Delta- Dirac "function". The convolution integral. Systems of differential equations.

 

Mandatory literature

Luísa Madureira; Problemas de Equações Diferenciais e Transformadas de Laplace, EdiçõesFEUP (Important , first and above all :Program given in lectures)

Complementary Bibliography

Earl W. Swokowski; Cálculo com Geometria Analítica (vol2) , McGraw-Hill
M. Braun; Differential Equations and Their Applications , Springer-Verlag
Boyce, W., DiPrima; Equações Diferenciais Elementares e Problemas de Valores de Contorno, Rio de Janeiro: Livros Técnicos e Científicos Editora S.A, 2002

Teaching methods and learning activities

* Lectures:
Exposure of the material of the program and resolution of exercises.
* Pratical Classes:
Resolution, by the students, of the proposed exercises and answering questions about the resolution of problems and proposed work.

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Attendance (estimated)	Participação presencial	85,00
Tests/Exam	Exame		100,00
	Total:	-	100,00

Eligibility for exams

Eligibility for exams

There wil be two components of assessment:
• Continuous Evaluation (optional): based on test results and itcan be corrected by the assessment practices in the classroom (including level of participation and performance in class) *.
• final written exam with a total duration not exceeding 3 hours
-.-.-.-.-.-.-.-.-.-.-.-.-.-
The evaluation will be done through two tests required and the final exam.
Admission to the second test will be conditional upon a minimum grade of 8.0 values.
The tests may replace the exam.
The notice of exemption will not necessarily be the arithmetic mean of test scores *
The student with a grade exceeding eighteen values in tests or final examination may eventually be subjected to an extra proof.

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If the limit of absences, the student is not often running out of access to examination, either in time or normal use (except for students exempted from frequency)

Calculation formula of final grade

For students under normal conditions with access to examination and which have succeeded the distributed evaluation( score above or equal to 10/20), the final classification is obtained by the highest ranking achieved in the distributed evaluation and / or examination.

Special assessment (TE, DA, ...)

According to the General Evaluation Rules