Mathematics I

Recommended Prerequisites

Mathematics A or Mathematics B  (High school)

Teaching Methods

Lectures will be theoretical and practical. Theoretical lectures will be expositive, using the means and technology available at the classrooms. Practical lectures will mainly consist on solving problems in order to apply and consolidate the theoretical knowledge. Students must participate effectively and have a critical attitude regarding the development of their autonomy.

Evaluation: General regime (final exam - 100%) or mixed regime (final exam – 50%; 2 intermediate tests – 30%; assignments – 20%)

Learning Outcomes

Overall objectives

The main goal is to provide the basic fundamentals of the mathematical methods for the common practice of analysis, linear algebra and geometry applied to Economics and Management.

Specific objectives

Represent and interpret graphs of functions; Interpret derivative as rate of change; Solve optimization problems; Study models of exponential and logistic growth; Find areas using definite integrals; apply the Gauss algorithmic process used in solving linear systems.

Generic competencies

Capacity for analysis and synthesis; Basic general knowledge; Oral and written communication in your native language; Problem solving; Capacity for applying knowledge in practice.

Specific competencies

Express mathematical concepts clearly and objectively, exercise logical-deductive method, develop intuition and geometric approach of concepts and methods, develop analysis ability, formulate and solve problems, know and apply all topics to economics and management.

Work Placement(s)

No

Syllabus

I - Functions of one real variable: functions and graphs; arithmetic and composition of functions; inverse function; elementary functions and graphs (polynomials, rationales, irrationals, trigonometric, inverse trigonometric, exponentials, logarithms, hyperbolic sine, hyperbolic cosine); limits and continuity; derivatives and applications; antiderivatives.

II - Differential equations of the first order and mathematical modelling: separable, linear and Bernoulli type; initial value problems.

III - Integral calculus: definite integral; fundamental theorem of calculus; integration by parts and integration by substitution; improper integrals; area between graphs; applications.

IV - Matrices and Determinants and Systems of linear equations: vectors and matrices; operations for

vectors and matrices; determinants of arbitrary order; general properties of determinants; solving systems of linear equations by Gauss elimination and Cramer rule; rank of a matrix; inverse of a matrix.

Head Lecturer(s)

Jorge Manuel Silva Marques

Assessment Methods

Mixed Regime
Assignments : 20.0%
2 intermediate : 30.0%
Exame final: 50.0%

General regime
Exam: 100.0%

Bibliography

LIMA, Teresa Pedroso, Lições de Álgebra Linear, Coimbra, Imprensa da Universidade de Coimbra, 2010.

SILVA, Jaime Carvalho, Princípios de Análise Matemática Aplicada, Lisboa, Editora McGraw-Hill de Portugal, 1994.

SYDSAETER, knut; HAMMOND, Peter J. — Essential mathematics for economic analysis. Harlow: Pearson Education, 3rd ed., 2008.

ZILL, Dennis G., A first course in differential equations with modeling applications, 7th ed., Pacific Growe, Brooks/Cole, 2001.