Teacher
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Chiaretti Mauro
(syllabus)
Integer, Rational and Real Numbers. Equalities and Inequalities. Proportions and Percentages. Powers and Roots with Integer or Rational Exponent. Logarithms and Exponentials.
The Cartesian Plane. The Straight Line in the Cartesian Plane.
Goniometry: Goniometric Functions and their Properties. Trigonometry: Right Triangles, Triangles: Sine Theorem and Carnot's Theorem.
Algebraic, Irrational, Goniometric, Logarithmic, Exponential Equations and Inequalities. The Absolute Value.
Functions: Definitions and Properties. Functions of a Real Variable. The Elementary Functions.
Limits. Properties of Limits. Calculation of Limits. Continuous Functions.
Derivatives. The Derivative of a Function. Operations with Derivatives: Derivation of Sum, Product, Quotient of Functions. Derivative of a Composition. Derivative of the Inverse Function. Derivation rules. Theorems of Rolle, Cauchy and Lagrange. De l'Hôpital's theorem.
Graph of a function. Maximum, Minimum and Horizontal Inflections. Growth and Decrease. Concavity and Convexity. Inflection Points. Asymptotes.
Integrals. The Definite Integral. Properties of the Integral and the Average Value. The Fundamental Theorem. Indefinite Integral. Elementary Integrals. Integration by Parts. Integration by Substitution. Integration of Rational Functions.
Elements of linear algebra. Vectors: Sum, Difference, Scalar Multiplication, Scalar Product and Vector (Cross) Product. Matrices. Matrix Operations: Sum and Difference, Scalar Multiplication, Matrix Multiplication.
Linear Systems. Determinants. Cramer's Theorem. System with parameters. Matrix Rank. Rouché-Capelli’s Theorem.
(reference books)
D’Ancona, Piero; Manetti, Marco: Istituzioni di Matematiche
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