Mathematics II

Recommended Prerequisites

Mathematics I.

Teaching Methods

Lectures and classes.

Learning Outcomes

Overall objectives
The main goal is to consolidate the application of mathematical methods for the common practice of analysis, linear algebra and geometry applied to Economics and Management.

Specific objectives
In this course we will
(i) study sequences e development series for functions;
(ii) graph surfaces and level curves;
(iii) interpret partial derivatives as rates of change;
(iv) solve constrained optimization problems and differential equations.

Generic competencies
The students should develop:
(i) capacity for analysis and synthesis;
(ii) basic general knowledge;
(iii) oral and written communication;
(iv) problem solving and capacity for applying knowledge in practice.   

Work Placement(s)

No

Syllabus

I - Infinite Series: sequences; convergence of series, geometric, telescopic and harmonic series; convergence tests for series of non-negative terms; alternating series; power series; Taylor and Maclaurin series.

II - Functions of  Several Variables: domain, range, level curves and graph of a function of two variables (surface); limits and continuity;  partial differentiation; linear approximation and plane tangent; differentials; composite function: chain rule, homogeneous functions, implicit differentiation; optimization, global (or absolute) maxima and minima, relative (or local) maxima and minima, constrained optimization, method of Lagrange multipliers, applications (consumer’s problem and producer’s problem).

III - Differential Equations: homogeneous and exact equations, integrating factors for first order differential equations; second-order linear differential equations with constant coefficients.  

Head Lecturer(s)

Jorge Manuel Silva Marques

Assessment Methods

Assessment
Frequency: 40.0%
3 intermediate tests : 60.0%

Bibliography

BREDA, Ana de Azevedo ; COSTA, Joana Nunes da - Cálculo com funções de várias variáveis. Lisboa : Editora McGraw-Hill de Portugal, 1996.

LARSON, Ron ; HOSTETLER, Robert P. ; EDWARDS, Bruce H. – Cálculo. 8ª ed.. São Paulo : McGraw-Hill Interamericana do Brasil, 2006. 2 vol.

LIMA, Teresa Pedroso de ; MARQUES, Jorge - Lições de Matemática II.Coimbra: Imprensa da Universidade de Coimbra, 2014.

MURTEIRA, J. M. Ruas ; SARAIVA, Paulo Manuel David Mota - Equações diferenciais ordinárias : introdução teórica exercícios e aplicações. Coimbra : Edições Almedina, 2010.

PIRES, Cesaltina - Cálculo para economistas. Lisboa : Editora McGraw-Hill de Portugal, 2001.

SILVA, Jaime Carvalho e - Princípios de análise matemática aplicada. Lisboa : Editora McGraw-Hill de Portugal, 1994.