Infinitesimal Analysis

Code:

M217

Acronym:

M217

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2013/2014 - 1S

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

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:AST	16	Plano de Estudos a partir de 2008	2	-	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	46	Plano de estudos a partir de 2008	2	-	7,5	-
L:G	0	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:Q	0	Plano de estudos Oficial	3	-	7,5	-
MI:EF	25	Plano de Estudos a partir de 2007	2	-	7,5	-

Teaching language

Portuguese

Objectives

Introduction to methods of solving ordinary differential equations with emphasis on equations and systems of linear differential equations.
Integral over path and Surfaces. Integral theorems of Vector Analysis. path and Surfaces.

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 and Ricatti equations, Homogeneous equations. Integrating factors. 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.Euler Equations.
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". Systems of differential equations.The convolution integral.

Vector fields. Line integrals of scalar fields on the length of arc. Line integrals in the general case. Applications to physics. Line integrals of vector fields. Conservative field gradients and rotational fields. Simply connected domains. Test for independence of path.
Green theorem. Applications.

Parametrized surfaces in three-dimensional Euclidean space. Surface integrals of scalar functions. Surfaces. Area of a surface. Integral of a vector field on a surface. Divergence Theorem (Gauss) and Stokes' theorem.

Mandatory literature

Madureira Luísa; Problemas de equações diferenciais ordinárias e transformadas de Laplace. ISBN: 978-972-752-124-1
Marsden Jerrold E.; Vector calculus. ISBN: 7167-4992-0

Complementary Bibliography

Braun M.; Differential equations and their applications. ISBN: 0-387-90114-0
Bronson Richard; Moderna introdução às equações diferenciais
Swokowski Earl W.; Calculo com geometria analitica. vol. i. 2ª ed. trad. ISBN: 85-346-0308-1
Young Eutiquio C.; Vector and tensor analysis. ISBN: 0-8247-6671-7
Boyce William E.; Elementary differential equations and boundary value problems. ISBN: 0-471-31999-6
Marsden Jerrold; Calculus iii. 2nd ed. ISBN: 0-387-90985-0

Comments from the literature

Program given in lectures is the most important"bibliography"

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

designation	Weight (%)
Exame	100,00
Total:	100,00

Eligibility for exams

If the limit of absences is exceeded the student will not be admited access to examination, either in time or normal use (except for students exempted from frequency)

Calculation formula of final grade

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.

Minimum grade of second test  6 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.

Special assessment (TE, DA, ...)

According to the General Evaluation Rules

Classification improvement

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.