Mathematics

Objectives

1. Understand the basic concepts and techniques of Differentiation in R, Integration in R, Ordinary Differential Equations and Theory of Matrices;

2. Combine the theoretical aspects studied with concrete applications;

3. Develop problem-solving ability through the study of mathematical models for certain real-life situations in the life sciences;

4. Develop the capacity of reasoning in mathematics and the creativity and autonomy of thought.

Program

1. DIFFERENTIATION IN R
1.1 Basic concepts
1.2 Overview of real functions
1.3 Limits and continuity
1.4 The derivative
1.5 Monotonicity and extrema
1.6 L´Hôpital´s rule
1.7 Applications
2. INTEGRATION IN R
2.1 Antiderivatives and indefinite integrals
2.2 Integration techniques
2.3 Definite integrals
2.4 Improper integrals
2.5 Applications
3. DIFFERENTIAL EQUATIONS
3.1 Definition and classification
3.2 General and particular solutions
3.3 First-order differential equations
3.4 Higher-order differential equations
3.5 Applications
4. MATRICES AND VECTORS
4.1 Definitions
4.2 Basic matrices operations. Inverse matrices
4.3 Systems of linear equations
4.4 Determinants
4.5 Vectors in space
4.6 Eigenvalues and eigenvectors
4.7 Applications

Teaching Methodologies

Lectures – The topics of this course will be presented using electronic means when appropriated.

Theoretical-practical classes – The topics will be discussed and developed by studying concrete applications, through the analysis of mathematical models and by solving problems and exercises.

The course will also benefit from the use of the learning management platform available at the University of the Azores, thus enhancing the performance of asynchronous activities.

Bibliography

H. Anton e C. Rorres, Elementary Linear Algebra - Applications Version, 9th Edition, John Wiley & Sons, 2005.

J. Berry, A. Norcliffe e S. Humble, Introductory Mathematics through Science Applications, Cambridge University Press, 1989.

M. Ferreira, Equações Diferenciais Ordinárias - Um primeiro curso com aplicações, Editora McGraw-Hill de Portugal, 1995.

D. Hughes-Hallett et al., Applied Calculus, 3rd Edition, John Wiley & Sons, 2006.

R. Larson e B. Edwards, Calculus - An Applied Approach, 7th Edition, Houghton Mifflin Company, 2006.

J. Stewart, Cálculo, Vol. I e II, 5ª Edição, Cengage Learning, 2005.