B5085 - Elements of Mathematics for Agricultural Science

Learning outcomes

At the end of the course, the student acquires both a good knowledge of the technical mathematical tools and their use and of the main basic methods and tools of the quantitative study of collective phenomena. He is therefore able to set and solve problems and assimilate new concepts from previous experience and knowledge. Furthermore, he is able to independently produce and process statistical data, developing the ability to interpret and critically evaluate statistical information.

Course contents

Mathematics

- Course presentation: contents, study materials, exercises, exams (0.5h)
- Algebra reminders: monomials, polynomials, algebraic fractions. (1h).
- Elements of combinatorial calculus: factorial, permutations, arrangements, binomial coefficients, combinations; applications to counting exercises. Notes on probability calculus. (3.5h).
- Powers with integer and rational exponent. Resolution of simple algebraic equations and inequalities: integer, fractional, rational, irrational. Systems of equations and inequalities (3h).
- Cartesian plane. Functions: definition, graph, examples of algebraic functions, domain and image set, injective, surjective, biunivocal, invertible functions; inverse function, composite function, increasing/decreasing function; even/odd function (5h).
- Analytical geometry: straight line, parabola, circumference, ellipse, hyperbola, functions studied and represented by referring them to the previous curves (4h).
- Logarithms. Exponential and logarithmic functions. Exponential and logarithmic equations and inequalities (4h).
- Limits: definition, calculation techniques and geometric meaning, asymptotes, notable limits, continuity of a function, points of discontinuity (5h).
- First derivative: definition and geometric meaning. Derivability of a function, points of non-derivability. Sufficient condition of derivability and classification of the points of non-derivability of a function. Rules for calculating a derivative (4h).
- Applications of the concept of Derivative to Economics: marginal cost, marginal utility. Logarithmic derivative and concept of Elasticity of a function (1.5h).
- Growth-decrease of a function; relative and absolute maxima and minima, horizontal inflections; second derivative, convexity-concavity of a function, inflection points (5h).
- Problems of optimization of functions with applications to economics (1.5h).
- Study of functions of one variable and representation in the Cartesian plane (5h).
- Primitives of a function, definition of indefinite integral, rules for the calculation of the primitives of a function. Riemann's definite integral: definition and theorems; calculation of areas with definite integrals (5h).
- Summary exercises on the study of functions of one variable with relative graph, on optimization problems and on the calculation of areas using definite integrals (4h).

Readings/Bibliography

-Handouts available in PDF format on Virtuale del Corso: all the lesson boards and exercises proposed with results.
-F.G. Alessio, C. de Fabritiis, c: Marcelli, P. Montecchiari, "Matematica Zero", Pearson;
-R. D'Ercole, "Precorso di Matematica" second edition, Pearson;
-C. Marcelli, "Analisi matematica 1" Exercises with reminders of theory, Pearson;
-M. Bramanti, F. Confortola, S.. Salsa, "Matematica per le Scienze", Zanichelli;
- M. Abate, "Metodi Matematici per l’economia e il management", Mc Graw Hill;
-D. Ritelli, M. Bergamini, A. Trifone, “Fondamenti di Matematica”, Zanichelli

Teaching methods

The teaching is divided into lectures and exercises in the classroom. Also as a consequence of the intensive nature of the lessons and their sequential structure, attendance is strongly recommended. During the course, examples from the sectors of animal husbandry, agronomy and agricultural engineering are taken into consideration.

Assessment methods

The learning assessment of the entire course will be done through a final exam that includes a written test containing exercises related to the Mathematics module (maximum score 75).
The detailed procedure for the proposed exercises will be required, complete with reasons for each answer. The number of exercises and the relative score may change based on the difficulty.
The duration of the test will be two hours and forty-five minutes.
The grade will be expressed in thirtieths and the written test will be considered passed if this grade is at least 18 out of 30 corresponding to 45 points out of 75 in the test.
PRAISE will be awarded to those who, in addition to earning 30, will answer an additional question included in the text of the written assignment.
The number of appeals is equal six: tree for the winter session, two for the summer session and one in the months of September.

Teaching tools

Blackboard; video projector; computer lab; Internet connection, "Virtuale" of unibo.

Office hours

See the website of Silvia Foschi