Mathematics III

Code:

LEC202

Acronym:

MATIII

Keywords
Classification	Keyword
OFICIAL	Mathematics and Informatics

Instance: 2007/2008 - 1S

Active?	Yes
Responsible unit:	Matematics and Informatics Group
Course/CS Responsible:	ECONOMICS

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
ECO	255	Official Curricular Structure since 2004	2	3		-

Teaching language

Portuguese

Objectives

Students who achieve a pass rate in this course are expected to be able to:
-calculate the definite and indefinite integral of a one-variable function;
-calculate the area of a planar region using simple and double integrals;
understand the meaning of a differential equation, calculate equilibria and study their stability;
-interpret the effect of a change in parameter values upon the equilibria and their stability;
-do qualitative analysis of a difference equation.

The learning process aims at the development of constructive criticism and the understanding of the relationship between different concepts and areas of knowledge.

Program

I. Simple integrals: definition, geometric meaning and their value. Areas of regions in the plane; extension to unbounded domains.

II. Double integrals: definition, geometric meaning and their value. Areas of regions in the plane.

III. Differential equations: existence and uniqueness of solutions; solution of simple differential equations; equilibria and their stability; qualitative analysis near hyperbolic equilibria; phase diagrams.

VI. Difference equations: introduction to qualitative analysis.

Main Bibliography

S. Castro Gothen, Apontamentos de apoio às aulas - disponíveis através do e-learning

F. Durão, 'Lições de Matemática -- Séries Numéricas e Integrais', Universidade Portucalense, Porto, 1992.

L. D. Hoffman e G. L. Bradley, 'Calculus -- for Business, Economics, and the Social and Life Sciences', Mc-Graw-Hill, New York, 1996.

Complementary Bibliography

J.E. Marsden e A.J. Tromba, 'Vector Calculus', W.H. Freeman and Company, San Francisco, 1976.

C. Pires, 'Cálculo para Economistas', McGraw-Hill, Lisboa, 2001.

Evaluation Type

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Subject Classes	Participação presencial	45,00
	Total:	-	0,00

Eligibility for exams

3 tests or one final exam. The tests represent, respectively, 30%, 20% and 50% of the final mark. The students pass if the average is greater or equal to 10, given that each individual mark is greater or equal to 6.

Calculation formula of final grade

Final mark = .3*(mark of 1st test)+.2*(mark of 2nd test)+.5*(mark of 3rd test)
or
Final mark = mark of the exam