96993 - Mathematics and Statistics (9 CFU)

Academic Year 2021/2022

Learning outcomes

On successful completion of the course, the student will have acquired the basic knowledge of calculus, linear algebra and geometry, essential to describe geological processes and to deal with other courses of the degree programme, especially those related to physics.

In particular, the student will be able to represent functions graphically, to apply one-variable and multivariable calculus, to compute solutions of first order differential equations, to perform operations on vectors and matrices, and to solve systems of linear equations and easy geometric problems on the plane and the three-dimensional space.

Course contents

  • Basic notions of combinatorics; lists, permutations and combinations.
  • Elements of linear algebra: vectors in the place and the three dimensional space, linear systems, linear applications, matrices, Gaussian elimination.
  • Equations of lines and planes, distance between point-line, point-plane, line-plane. Slop of a line.  
  • Real functions of a real variable: injectivity, surjectivity, monotony; graph of a function. Elementary functions : powers, polynomial, rational, logarithm, exponential, trigonometric functions and their graphs.
  • One-variable calculus: limits, continuity, derivatives, basic theorems and applications: tangents to curves, increasing and decreasing functions, convexity.
  • Integral calculus: definitions and properties; integration techniques (integration by parts, by substitution). Improper Integrals.
  • Differential equations. Methods to solve first order ODEs, of linear type or separate variables type.
  • First elements of differential calculus of several variables, partial derivatives, gradient and Hessian matrix, maxima and minima.

 

Readings/Bibliography

  • Bigatti, Robbiano. Matematica di base. Seconda edizione. Cea. Zanichelli.
  • Bramanti, Pagani, Salsa, Matematica. Calcolo infinitesimale e algebra lineare, Zanichelli.
  • Other documents available on Virtuale.

Teaching methods

Front lectures and exercise sessions.

Assessment methods

The course assessment consists of a written examination followed by an oral examination. The written part consists of a series of exercises and questions. The validity of the written exam is for all the sessions of 2021/22. The oral exam aims to test knowledge acquisition and to discuss exercises. The final mark is based on both parts of the examination. More precise information are on Virtuale.

Office hours

See the website of Riccardo Biagioli

See the website of Federico Plazzi