Quantitative Methods II

Mathematics A of the 12th year of schooling

Quantitative Methods I

Teaching will have two components: exposure of subjects and resolution of exercises in class.

The GEOGEBRA application will be used to support problem solving.

There will also be the possibility for students to have work sessions and/or clarification of doubts.

•Study important topics in the areas of interest of the Accounting Course from the point of view of
applications;
•Provide knowledge of the wide variety of problems that can be formulated and solved with
use of mathematical concepts and results, as well as techniques based on them;
• Articulate subjects and emphasize practical examples, with a view to developing capacity
criticism and a better perception and consolidation of the subjects;
•Develop mental and analytical reasoning and calculation in order to create resolution skills
autonomous of problems and stimulate the search and formulation of others;
• Develop skills to, with opportunity, apply the subjects taught to problems
related to the specific areas of training during the course;
•Develop, in general, skills for the exercise of the future profession.

1. Real functions of two real variables

1.1 Elementary definitions

1.2 Derivatives and Differentials. Calculation of approximate values

1.2.1 Partial derivatives

1.2.2 Differentials

1.3 Calculation of extremums

1.3.1 Calculation of extremants inside a set: Lagrange multipliers method

1.4 Applications in the economic context

2. Primitives

2.1 Immediate Primitives

2.2 Primitives by parts

2.3 Primitives by replacement

2.4 Primitives by decomposition into rational fractions

3. Differential equations

3.1 Differential equations, solution of a differential equation and initial value problems.

3.2 Solving differential equations for separable variables

3.3 Resolution of 1st order linear differential equations.

3.4 Applications to the accounting and management area

3.4.1 Exponential growth model

3.4.2 Logistic equations.

4. Definite integrals

4.1 Definition, geometric interpretation and properties.
4.2 Fundamental theorem of calculus
4.3 Trapezoid Rule
4.4 Calculation of areas
4.5 Improper integrals of the 1st kind

4.6 Applications to the areas of accounting and management.

NAO

Fundamental:

. Carvalho, M. Quantitative Methods II (LCA), ISCAC – IPC, 2023 

Complementary:

– Bennett, J., Briggs, W., Using & Understanding Mathematics_ A Quantitative Reasoning Approach, Pearson (2015)

– Breda, A.d´A., Costa, J.N., Cálculo com Funções de Várias Variáveis, McGraw-Hill, 1996.

– Caraça, B. , Fundamental Concepts of Mathematics, Ed. Gradiva, 1998 (2nd ed.).

– Goldstein, L.J., Lay, D.C., Schneider, D.I., Applied Mathematics: Economics, Management and Accounting, 8th ed, Bookman (2000).

 –  Harshbarger, R. J. and Reynolds, J. J., Mathematical Applications for the Management, Life, and Social Sciences, 11th edition, Cengage Learning Brooks Cole, 2016.

– Sydsæter, K., Hammond P., with Strøm, A., Essential mathematics for economic analysis, 4th ed., Pearson Education Limited (2012)

– Weir, M.D. , Hass, J. , Thomas, G. B. , Thomas’ Calculus: Early Transcendentals , 12th ed, Pearson Education (2010)