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 h), where fundamental concepts are presented and some application examples are given, accompanied by tutorial classes, in which students solve exercises related to the CU.

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.
    
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 and complete.

Applications in different areas of Bioengineering.