MATEMATICA M - Z

At the end of the course, the student will acquire basic concepts of calculus. Will also be able to apply elementary calculus to biology, chemistry and pharmaco-kinetics applications.

Pre-Knowledge. Basic knowkledge of elementary algebra and set. Scientific notation; Trigonometry; Elements of Analytic Geometry.

Set Theory (module 1)

Logic and Set Theory. Definition of sets; membership; cardinality. Logic: propositions, predicates and operators. Operations between sets (Identity Boolean; Read De Morgan);

Set theory; Definitions. Membership; Cardinality; Basic Sets Operations; Boolean identities; De Morgan laws.

Set of Numbers. Natural numbers; Rational numbers. Real numbers, Intervals, upper and lower bounds; maximum and minimum; Cartesian products and their representation in R^2 and R^3.

Theory of functions (module 2) -

Functions: definition; domain, codomain, image and graph; Injective, Surjective and bijective functions; Function composition; Inverse function; Monotonic functions; Absolute Maximum and minimum of a function; Numerical sequences;

Limits and Derivative, (module 3) -

Limits of numerical sequences and functions: limit point of a set. Limits of numerical sequences and related theorems. Limits of functions : definitions and related theorems. Continuous functions and related theorems; Discontinuous functions; Derivatives of a function and related theorems (Lagrange, Rolle, Cauchy and De Hopital theorems); Graph of a function.

Integrals and Differential equations (module 4) -

Integrals. Elements of measure theory; Definition of definite integral; Theorems on definite integrals; Indefinite integrals; Integrals of elementary functions; Elements of integration methods.

Differential Equations. First order differential equations. Examples in biology, chemistry and pharmaco-kinetics.

1. Metodi e Modelli Matematici, S.Motta e M.A.Ragusa, CULC (2011)
2. Elementi di Logica - Domenico Zambella - Dip.di Matematica, Politecnico di Torino, Quaderno # 19 - Settembre 2003.