Infinitesimal Analysis

Code:

M217

Acronym:

M217

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2011/2012 - 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	14	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	33	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	32	Plano de Estudos a partir de 2007	2	-	7,5	-

Teaching language

Portuguese

Objectives

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.
Inverse function theorem and implicit function theorem and its main applications.

Skills:
Problem-solving skills. Theoretical understanding

Program

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

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	75,00
	Total:	-	0,00

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.

------------------------------------------
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, the final classification is obtained by the highest ranking achieved in the distributed evaluation and / or examination.

Examinations or Special Assignments

1st Test - November 19, 2011
2nd Test - December 17, 2011

Examination - regular season - January 27, 2012
Examination - the time of appeal - 11 February 2012

Special assessment (TE, DA, ...)

According to the General Evaluation Rules

Classification improvement

The classification can be improved by improving the outcome of the final exam, according to the rules of the University.

Observations

Bibliography:
-Calculus with Analytic Geometry (vol2) - Earl W. Swokowski-McGraw-Hill
- Differential Equations and Their Applications - M. Braun. Springer-Verlag
- Elementary Differential Equations and Boundary Value Problems - Boyce, W., DiPrima - RC, Rio de Janeiro: Books Scientific and Technical Publishing SA, 2002
- Modern Introduction to Differential Equations, Richard Bronson, Schaum, McGraw-Hill
- Issues of ordinary differential equations and Laplace transforms - Luísa Madureira (FEUP editions)
- Vector Calculus, Jerrold E. Marsden, Anthony Tromba - Freeman and Company
-Vector and Tensor Analysis - Eutyches C. Young - Marcel Dekker, Inc.


Jury of the discipline:

Maria Eugénia de Almeida César de Sá
Semyon Borisovich Yakubovich