Objectives and competences

To know how to perform numerical calculations.
To derivate and integrate functions. To know how to solve differential 1st order equations.

Teaching Methodologies

Theoretical classes (1.5 hours each), where fundamental concepts are presented and some application examples are given, followed by
theoretical-practical classes, in which students solve exercises related to the subject.

Syllabus

1. Functions.
Functions: power module, polynomial, rational, exponential, logarithmic, trigonometric and inverse trigonometric.

2. Differential calculus. Basic derivation rules
Derivative of the inverse function
Derivatives of studied functions, referred in 1 Logarithmic derivation
Implicit differentiation Tangents to parametric curves
linear approximation of a function Indeterminate forms and L'Hopital’s rule
Monotony of a function. Critical points of a function. Relative extremes Concavity of a function. Inflection Points
1st derivate test. 2nd derivate test.
Theorem of the average of the differential calculation. Lagrange's theorem

3. Integral calculus
Primitive of a function. Indefinite integral
Integral curves of a function. Immediate primitive Integration by parts replacement and by parts Definite integral
Fundamental theorem of calculus Theorem of the average of integral calculus Area calculation.

4. Differential equations.
Separable equations of 1st order.
Linear equations of 1st order: homogeneous. Applications in different areas of Bioengineering.