THREE-DIMENSIONAL MODELING

Course objectives

Dublin Descriptors Knowledge and understanding: learning elementary techniques of the theory of integration and differential equations, and how to solve some basic examples; knowledge of basics of linear algebra and plane geometry with application to statistics. Applying knowledge and understanding: at the end of the course students will be able to compute simple integrals by parts or substitution, to solve simple differential equations and problems about lines and vectors in plane geometry, with some applications to statistics. Critical and judgmental skills: at the end of the course students will have learned the basic ideas of the theory of integration and of differential equations, and some algebraic and geometrical tools needed to understand and express basic concepts of physics and statistics in the appropriate mathematical language. Communication skills: ability of exposition with clarity, also in written form, of notions, theorems and methods learned during the course. Learning skills: the acquired knowledge will allow the students to undertake successfully the subsequent study of more technical notions of mathematical analysis, physics and statistics.

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PAOLO PIAZZA Lecturers' profile

Program - Frequency - Exams

Course program
- limits of functions and properties, notable limits, comparison criteria; - continuous functions, theorem on the existence of zeros and intermediate value; - derivatives and geometric meaning, rules of calculation, derivatives of elementary functions, derivatives of composite functions, l'Hopital's rule for indeterminate forms; - absolute and relative maxima and minima, higher-order derivatives, concavity and convexity; study of the graph of functions; - primitives and definite integrals, properties, methods of integration by parts and change of variable, calculation of areas; - differential equations: models that lead to these problems (e.g., the second law of dynamics, carbon-14 dating method, epidemiological models, Lotka-Volterra equations for the predator-prey model, etc.); - solving first-order ordinary differential equations in normal form: Cauchy's theorem, linear equations and equations solvable by separation of variables; - overview of second-order linear differential equations (Cauchy's problem and solution method, the harmonic oscillator) (5); - overview of functions of two variables, surfaces as graphs, partial derivatives, contour lines, gradient, examples (6).
Books
Dispense dei Proff. D'Ancona e Manetti (reperibili sulla pagina Web del Prof. Manetti) Angelo Guerraggio, Matematica per le Scienze, Pearson, seconda edizione. Marcellini-Sbordone: Elementi di Analisi Matematica uno (Liguori Ed.) Marcellini-Sbordone: Esercitazioni di Matematica primo volume (prima e seconda parte) (Liguori Ed.).
  • Academic year2025/2026
  • CourseNatural Sciences
  • CurriculumSingle curriculum
  • Year1st year
  • Semester2nd semester
  • SSDMAT/05
  • CFU5