Ordinary Differential Equations (ODE)

Basic information


60 hours


Calculus in several Variables, Linear Algebra.


Modeling with ordinary differential equations (ODEs). First-order ODE solution methods. Second order linear equations. Coefficients method to be determined, parameter variation method. Applications. Existence and uniqueness of solutions. Numerical methods. ODE systems, stability. Solution of linear ODE systems. Matrix exponential. Phase portrait, equilibrium points and stability of linear systems. Nonlinear systems: phase portrait, balance points and stability. Ecological models based on ODEs; predator-prey systems, species competition.


Teaching Plan



•    Calculus II, James Stewart. Pioneira / Thompson, 2006;
•    Elementary Differential Equations and Boundary Value Problems, W. E. Boyce and R.C.Di-Prima. LTC. 2006;
•    Differential Equations. An introduction to modern methods and applications, J. Brannan and W. E. Boyce. John Wiley & Sons, Inc. (Digital), 2011.


•    Differential Equations, Dennis Zill; Michael S Cullen, Pearson Makron Books;
•    An introduction to ordinary differential equations, James Robinson. Cambridge University Press, 2004;
•    Differential Equations Applied, Djairo Figueiredo and Aloísio Freiria Neves. University Mathematical Collection, IMPA, 2014;
•    Linear Algebra, Elon Lages Lima. University Mathematical Collection - IMPA, 2012;
•    Differential equations and Variational calculus, Elsgoltz, L. MIR. Moscu, 1986.