Mathematical Analysis I

6 ECTS / Semester / Portuguese

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.



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


Associate Professor
Got her B.Sc. in Chemical Engineering from the University of Porto (1985), her M.Sc. (1986) and Ph.D. (1990) in Food Processing from the Ecole Nationale…
Invited Professor
Degree in Food Engineering (1998) from Universidade Católica Portuguesa.
Invited Professor
Licensed in Technological Physics Engineering by Instituto Superior Técnico and Master in Classical Studies at Coimbra University.