Teacher
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FRAGNELLI Genni
(syllabus)
Functions and number sets Introduction: operations among sets. Function; domain, co-domain, 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. Right-side and left-side 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 anti-derivatives. 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.
(reference books)
Elementi di calcolo. Versione semplificata per i nuovi corsi di laurea di Paolo Marcellini, Carlo Sbordone Editore: Liguori Data di Pubblicazione: febbraio 2016 EAN: 9788820736651 ISBN: 8820736659
Books should be completed with the notes of the lessons. It is suggested not to take notes from Internet.
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