 # Integrated Master in Pharmaceutical Sciences

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## Learning outcomes

To teach basic linear algebra and calculus concepts with the aim of understanding the applications to pharmaceutical sciences, solving problems and comunicate mathematical concepts in a logical way.

## Syllabus

I. Basic notions and generalities about functions.
Significative numbers and scientific notation. Algebraic Functions (polynomials and rational fractions). Transcendental functions (exponential, logaritm, inverse trigonometric functions, hyperbolic functions). Linearization of curves.
II. Real elementary differential and integral calculus
Derivatives, Theorems of Rolle, Lagrange and its consequences; Cauchy rule. Antiderivatives, integral and its geometric meaning, Mean Value Theorem, indefinite integral, areas and geometric interpretation of integrals.
III. Elementary differential equations
Definition, first order linear differential equations and of separable variables, applications to pharmacokinetics and to chemistry kinetics.
IV. Elementary linear algebra
Vector calculus, inner and outer, product, linear systems, operations with matrices, determinants, eigenvectors and eigenvalues, matrix diagonalization and its applications.

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