Teacher

MUGNAI Dimitri
(syllabus)
Functions and number sets Introduction: operations among sets. Function; domain, codomain, image and graph of functions. Injective, surjective, inverse function and composition. Increasing and decreasing, odd and even functions, Number sets N, Z, Q, R.
Elementary functions Review on lines, parabolas, exponential, logarithmic and trigoniometric functions. Absolute value. Neighborhood of a real number.
Limit and continuity Finite and infinite limit; sign permanence theorem. Rightside and leftside limit. Existence and uniqueness of the limit. Comparison theorem. Algebra of limits and indeterminate forms. Infinite and infinitesimal. Vertical, horizontal and oblique asymptote. Continuous functions. Weierstrass theorem. Intermediate value theorem. Intermediate zero theorem.
Derivatives Definition of derivative and its geometric interpretation. Calculation of derivatives. Differentiability and continuity. Point of non differentiability. Higher derivatives. Rolle's and Lagrange's theorem. De L’Hôpital's theorems. Taylor's theorem and McLaurin's expansion. Fermat's theorem. Maximum and minimum points. Convexity and concavity. Inflection point. Study of a function.
Integral Definition of indefinite integral and its properties. Straightforward antiderivatives. Integration by parts. Integration by substitution. Definite integral and its properties. The fundamental theorem of calculus. generalized integral. Area.
Differential Equations Differential Equations: an introduction. Differential Equations of first and second order and Cauchy problems. Separate variables differential equations. Malthus model; bacterial growth; epidemic diffusion; radioactive decay. Logistic growth. Time of the crime.
(reference books)
"Elementi di Calcolo. Versione semplificata per i nuovi corsi di laurea"
di Paolo Marcellini e Carlo Sbordone
Liguori Editore.
