Maths

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 area of ocean sciences;
4- Develop the capacity of reasoning in mathematics and the creativity and autonomy of thought.

1. Differential Calculus in R

1.1. Elementary concepts and generalities about real functions of a real variable; Limits and continuity; L'Hopital's rule;

1.2. The derivative function and its application in the study of monotonicity, determination of maxima, minima, and inflection points of a function;

1.3. Specific study of the behavior of exponential and logarithmic functions, focusing on the logistic function.

2. Integral Calculus in R

2.1 Primitive of a real function of a real variable;

2.2. The definite integral; The improper integral; Applications in mathematical models.

3. Matrices (up to 4x4) and Vectors in Space

3.1 Matrices and matrix operations; Calculation of the inverse matrix, using elementary operations;

3.2 Solving systems of linear equations;

3.3 Calculation of determinants, using Laplace's theorem; Use of the adjoint matrix in 3.4 the calculation of the inverse matrix;

3.5 Bases and linear independence;

3.6 Eigenvalues ​​and eigenvectors;

3.7 Elementary applications to ecological evolution models;

4. Differential Equations

4.1 Elementary concepts and generalities about ordinary differential equations;

4.2 Graphical and analytical study of the general and the particular solution of an ordinary differential equation;

4.3 Solution of ordinary differential equations up to the third order;

4.4 Applications in mathematical models applicable in marine sciences.

Classes with open discussion and dynamic problem-solving for practical application of the course contents.

- 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.
- 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.