Mathematical Analysis IV

Code:

EM224

Acronym:

AM4

Instance: 2003/2004 - 2S

Active?	Yes
Responsible unit:	Mathematics Section
Course/CS Responsible:	Mechanical Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
LEM	238	Plano de Estudos EM Oficial a partir de 2000	2	3	6	-
		Plano para Bachareis EM a partir 2000	1	3	6	-

Teaching language

Portuguese

Objectives

The objectives are that the students get reasoning capacity and learn essential mathematical concepts. Solid theoretical information is given with immediate exemplification like solving problems of differential equations or integration in surfaces.

Program

INTEGRAL CALCULUS

Line integral of scalar and vector functions. Independence of path. Work done by a force. Green’s Theorem.
Surface integral. Area of a surface, mass, center of gravity, centroid and moment of inertia. Flux integral. Theorems of Stoke´s and Gauss.

FOURIER ANALYSIS

Fourier Series. Euler formulas and “method of jumps”. Even and odd functions, half-range expansions. Approximation by trigonometric polynomials and minimum square error. Fourier Integral.

PARTIAL DIFFERENTIAL EQUATIONS

Equations of first order. General solution of linear equations. Surfaces orthogonal to a family of surfaces. Second order equations. Solution by the method of factorization for homogeneous partial differential equations with constant coefficients. The wave equation: D’Alembert solution and separation of variables. The heat equation.

Main Bibliography

Erwin Kreyszig, 'Advanced Engineering Mathematics' 7th Ed., John Wiley and Sons,1993.

Tom Apostol 'Calculus' vol II, Wiley

Análise Matemática IV, smat-demegi

Complementary Bibliography

Michael D. Greenberg, 'Advanced Engineering Mathematics'.
Wylie & Barrett, 'Advanced Engineering Mathematics'

Teaching methods and learning activities

theoretical and practical lessons. In the theoretical classes detailed exposition of the program is presented where deduction and abstraction is fundamental.
In the theoretical-practical classes the students are presented with problems to solve by themselves after examples are given.

Software

None

Evaluation Type

Distributed evaluation with final exam

Calculation formula of final grade

0.1*mini-test+0.9*exam

Examinations or Special Assignments

None