A lista seguinte de aplicações está incluída no livro Elementary Linear Algebra with applications , Ninth Edition, by Howard Anton and Chris Rorres. Consiste de aplicações a várias áreas – Economia, Engenharia, Física, Ciência de Computadores, Ecologia, Sociologia, Demografia e Genética. As aplicações estão desenvolvidas  de forma independente umas das outras pelo que o aluno pode seleccionar as que mais o motivar e fazer um estudo independente.

Para obter uma cópia de cada uma das aplicações, o aluno deve contactar por mail
João Nuno Tavares .

Lista de temas:

1. CONSTRUCTING CURVES AND SURFACES THROUGH SPECIFIED POINTS

        In this section we describe a technique that uses determinants to construct
lines, circles, and general conic sections through specified points in the plane. The procedure is also used to pass planes and spheres in 3-space through fixed points.

2. ELECTRICAL NETWORKS

        In this section basic laws of electrical circuits are discussed, and it is shown how these laws can be used to obtain systems of linear equations whose solutions yield the currents flowing in an electrical circuit.

3. GEOMETRIC LINEAR PROGRAMMING

     In this section we describe a geometric technique for maximizing or minimizing a linear expression in two variables subject to a set of linear constraints.

4. THE EARLIEST APPLICATIONS OF LINEAR ALGEBRA

        Linear systems can be found in the earliest writings of many ancient
civilizations. We give some examples of the types of problems that they used to solve.

5. CUBIC SPLINE INTERPOLATION

        In this section an artist's drafting aid is used as a physical model for the
mathematical problem of finding a curve that passes through specified points in the plane. The parameters of the curve are determined by solving a linear system of equations.

6. MARKOV CHAINS

       In this section we describe a general model of a system that changes from state to state. We then apply the model to several concrete problems.

7. GRAPH THEORY

    In this section we introduce matrix representations of relations among members of a set. We use matrix arithmetic to analyze these relationships.

8. GAMES OF STRATEGY

        In this section we discuss a general game in which two competing players
choose separate strategies to reach opposing objectives. The optimal strategy of each player is found in certain cases with the use of matrix techniques.

9. LEONTIEF ECONOMIC MODELS

        In this section we discuss two linear models for economic systems. Some
results about nonnegative matrices are applied to determine equilibrium price structures and outputs necessary to satisfy demand.

10. FOREST MANAGEMENT

      In this section we discuss a matrix model for the management of a forest where trees are grouped into classes according to height. The optimal sustainable yield of a periodic harvest is calculated when the trees of different height classes can have different economic values.

11. COMPUTER GRAPHICS

        In this section we assume that a view of a three-dimensional object is displayed on a video screen and show how matrix algebra can be used to obtain new views of the object by rotation, translation, and scaling.

12. EQUILIBRIUM TEMPERATURE DISTRIBUTIONS

      In this section we shall see that the equilibrium temperature distribution within a trapezoidal plate can be found when the temperatures around the edges of the plate are specified. The problem is reduced to solving a system of linear equations. Also, an interactive technique for solving the problem and a “random walk” approach to the problem are described.

13. COMPUTED TOMOGRAPHY

        In this section we shall see how constructing a cross-sectional view of a human body by analyzing X-ray scans leads to an inconsistent linear system. We present an iteration technique that provides an “approximate solution” of the linear system.

14. FRACTALS

    In this section we shall use certain classes of linear transformations to describe and generate intricate sets in the Euclidean plane. These sets, called fractals, are currently the focus of much mathematical and scientific research.

15. CHAOS

        In this section we use a map of the unit square in the xy-plane onto itself to
describe the concept of a chaotic mapping.

16. CRYPTOGRAPHY

        In this section we present a method of encoding and decoding messages. We also examine modular arithmetic and show how Gaussian elimination can sometimes be used to break an opponent's code.

17. GENETICS

      In this section we investigate the propagation of an inherited trait in successive generations by computing powers of a matrix.

18. AGE-SPECIFIC POPULATION GROWTH

        In this section we investigate, using the Leslie matrix model, the growth over
time of a female population that is divided into age classes. We then determine the limiting age distribution and growth rate of the population.

19. HARVESTING OF ANIMAL POPULATIONS

     In this section we employ the Leslie matrix model of population growth to model the sustainable harvesting of an animal population. We also examine the effect of harvesting different fractions of different age groups.

20.  A LEAST SQUARES MODEL FOR HUMAN HEARING

        In this section we apply the method of least squares approximation to a model for human hearing. The use of this method is motivated by energy
considerations.

21. WARPS AND MORPHS

        Among the more interesting image-manipulation techniques available for
computer graphics are warps and morphs. In this section we show how linear transformations can be used to distort a single picture to produce a warp, or to distort and blend two pictures to produce a morph.