The objective of this course is to give students an understanding of basic calculus as well as to enable them to approach problems from a mathematical perspective.
teacher profile teaching materials
Programme
Numbers (naturali, integers, rationals, reals). Functions, their graphs. Injective, monotone, periodic functions. Composition and inversion of functions. Interpretation of the graph of a function. Elementary functions. Sequences and limits. Examples. Operations on limits, sum product and composition. Orders of magnitude. Some notable limits. Continuous functions. Differentiable functions. Geometric interpretation of the derivative. Derivative of elementary functions. Derivative of the product, sum, composition of functions. Second derivatives. Maxima and minima. Rolle and Lagrange theorems. Monotone functions. Theorem de l'Hopital. Taylor formula. Primitives and basic properties. Integration by parts and substitution. Rational functions. Riemann integrability. Differential equations. Vector spaces.Core Documentation
Marcellini-Sbordone Elementi di Matematica, Esercitazioni di Analisi MatematicaReference Bibliography
Apostol, Calculus Benedetto, Degli Espositi, Maffei: Matematica per le scienze della vitaType of delivery of the course
Lessons + exercises.Attendance
Following in person is highly recommended.Type of evaluation
The exam consists of a written test and an oral confirmation interview. The written test focuses on carrying out exercises of a similar type to those seen in class. It is possible to bring notes and a NON graphing calculator. The oral exam is used to verify the knowledge of the bases of mathematical reasoning as well as of the definitions used in carrying out the exercises. teacher profile teaching materials
Programme
Numbers (natural, integers, rationals, reals). Functions, their graphs. Injective, monotone, periodic functions. Composition and inversion of functions. Interpretation of the graph of a function. Elementary functions. Sequences and limits. Examples. Operations on limits, sum product and composition. Orders of magnitude. Some notable limits. Continuous functions. Differentiable functions. Geometric interpretation of the derivative. Derivative of elementary functions. Derivative of the product, sum, composition of functions. Second derivatives. Maxima and minima. Rolle and lagrange theorems. Monotone functions. Theorem de l'Hopital. Taylor formula. Primitives and basic properties. Integration by parts and substitution. Rational functions. Riemann integrability. Differential equations. Vector spaces.Core Documentation
Marcellini-Sbordone Elementi di Matematica, Esercitazioni di Analisi MatematicaReference Bibliography
Apostol, Calculus Benedetto, Degli Espositi, Maffei: Matematica per le scienze della vitaType of delivery of the course
lesson + exercisesAttendance
Following in person is highly recommendedType of evaluation
The exam consists of a written test and an oral confirmation interview. The written test focuses on carrying out exercises of a similar type to those seen in class. It is possible to bring notes and a NON-graphing calculator. The oral exam is used to verify the knowledge of the bases of mathematical reasoning as well as of the definitions used in carrying out the exercises.