Subject: Mathematics II for Economics

Scientific Area:

Mathematics

80 Hours

Number of ECTS:

6 ECTS

Language:

Portuguese

# Overall objectives:

1 - Calculate integrals of real functions of a real variable ,using anti derivation , the method of integration by parts , the variable change method , the simplification of rational functions, the simplification of trigonometric functions. Know how to calculate areas using the concept of integral. Know how to solve improper integrals and study their convergence..
2 - To identify and solve various types of ordinary differential equations by variable separation methods , change of variable , variation of parameters , selection method to determine a particular solution .
3 - Know how to solve linear differential 1st order equations.
4 - Know how to solve some basic types of partial differential equations . Know how to use the method of separate functions.

# Syllabus:

1 - Primitives of real functions of one real variable: primitives such as anti-derivation; indefinite integral and properties; integrations immediately, almost immediately, by parts, by change of variable and rational functions. Definite integral. Fundamental theorem of calculus. Application of the concept of integral to the calculation of areas. The definition of improper integral.
2 - Historical introduction to the subject and generalities about differential equations; method of separable variables, substitution of a variable, linear differential equations of 1st order; 2nd order differential equations with constant coefficients; variation of constants method; solving linear differential equations of order n; systems of linear differential equations of 1st order .
3 - Partial differential equations. Equations of 1st and second order. The method of separate functions .

# Literature/Sources:

Piskounov N. , 1977 , Cálculo Diferencial e Integral , Lopes da Silva
Apostol Tom M. , 1983 , Cálculo , Reverté Ltda
Boyce, W. E. and DiPrima, R. C. , 1992 , Elementary Differential Equations and Boundary Value Problems, 5th Edition , Jonh Wiley & Sons
Braun, M. , 1993 , Differential Equations and Their Applications , Springer
Tiernet, J. A. , 1989 , Differential Equations , Wm. C. Brown Publishers
Phoebus J. Dhrymes , 2013 , Mathematics for Econometrics Phoebus J. Dhrymes Fourth Edition , Springer

# Assesssment methods and criteria:

Classification Type: Quantitativa (0-20)

Evaluation Methodology:
Lectures, problem solving and discussion sessions and presentation problems. Exercises. Study, research, problem solving. Two frequencies in normal season with 50% each in the final grade (to obtain approval the student must be evaluated in both frequencies). A resource examination where the student can make an overall examination or just the part corresponding to one of the frequencies. There will not be minimum to achieve in each partial evaluation, but students will be encouraged by teachers to develop a study throughout the semester. Every week, the student attendance to answer questions, will be equal to half hours of weekly contact.