Applied Mathematics I

Knowledge compatible with the Mathematics A program of portuguese secondary education.

Expository method combined wikh solving exercises.

Providing mathematical knowledge that is essential for students’ performances in future subjects of the course, namely:

– the study of real-valued functions of one real variable

– the calculation of derivative functions

– the calculation of indefinite integrals

– solving differential equations

– the calculation of integrals of real-valued functions of one real variable.

Presenting some practical applications for these subjects, in the area of ​​management, such as the calculation of variation rates, the determination of growth or degrowth intervals of a function, the optimization of functions, the calculation of a cost function model, having been given a model of the marginal cost function, the calculation of areas of bidimensional regions, etc.

Encouraging the implementation of analytical and deductive methods in the analysis and resolution of specific problems and stimulating the application of the syllabus to other areas, especially those included in the respective curriculum, such as management.

I. Differential calculus of real functions of real variable
1. General concepts
2. Limits and continuity
3. Exponential and logarithmic function
4. Derivative of functions
5. Examples.
II. Integral calculus of real functions of real variable:
1. Indefinite integral
1.1. Anti derivatives
1.2. Integration by parts
1.3. Integration by partial fractions
1.4. Integration by substitution
1.5. Examples
2. Differential equations
2.1. General definitions
2.2. Separable equations
2.3. First order linear differential equations
2.4. Examples
3. Definite and improper Integrals
3.1 Definitions and geometric interpretation of definite integral
3.2 Conditions of existence and properties of the definite integral
3.3 Fundamental theorem of calculus
3.4 Riemann sum approximation formula
3.5 Calculation of areas in the plan
3.6 Improper integrals
3.7 Examples

NAO

1- T. Apostol, Cálculo (vol.1), Ed. Reverté, 1983

2- F. R. Dias Agudo, Análise Real, volume 1, Escolar Editora, 1989

3- A. Azenha, M. A. Jerónimo, Cálculo Diferencial e Integral, Ed. MacGraw-Hill, 1995

4- B. Jesus Caraça, Conceitos Fundamentais da Matemática, Ed. Gradiva, 1998 (2ª ed.)

5- M. Carvalho, Matemática Aplicada I, Licenciatura em Gestão de Empresas, ISCAC, 2011

6- J. Campos Ferreira, Análise Matemática, Fundação Gulbenkian, 6ª ed., 1995

7- J. Campos Ferreira, Elementos de Lógica Matemática e Teoria de Conjuntos, IST, 2001

8- L.J. Goldstein, D.C. Lay e D.I. Schneider, Matemática Aplicada: Economia, Administração e Contabilidade, Bookman, Porto Alegre, 8ª Edição, 2000

9- C. Neves, Cálculo Integral, ISCAC, 2006/2007

10- A. Franco de Oliveira, Lógica e Aritmética, Ed. Gradiva, 1996

11- J. Sousa Pinto, Tópicos de Matemática Discreta, Universidade de Aveiro, 1999

12- S.T. Tan, Matemática Aplicada à Administração e Economia, Pioneira – Thomson Learning, São Paulo, 5ª Edição, 2001.

Support material:

Will be available on Nonio:

• the theoretical notes
• the practical sheets and respective solutions
• the form
• the tests carried out in previous academic years.