Ordinary Differential Equations (ODE)
Sequences and series of functions. Fourier series. Properties. Punctual and uniform convergence of the Fourier series. Partial differential equations (PDE). Classification of PDE. First order equations. Characteristics method. Second order semi-linear equations. The wave equation. The method of separating variables. The Laplace and Poisson equations. The Heat equation. The Fourier Transform. Introduction to numerical methods for PDE.
• Iório, Valeria. EDP An undergraduate course. University Mathematical Collection, IMPA;
• Figueiredo, Djairo. Fourier analysis and partial differential equations. Rio de Janeiro: IMPA, 2003.
• Elsgoltz, L. Differential equations and Variational calculus. MIR Moscu.
• Courant, Richard. Differential and Integral Calculus. Nordeman;
• Iório, Rafael; Iório Valeria. Partial differential equations: An introduction. Euclid Project. IMPA;
• Boyce, W. Di Prima, R. Elementary Differential Equations and Boundary Value Problems. LTC
• Apostol, Tom. Mathematical analysis. Addison-Wesley Publishing;
• Iório, Valeria. Fourier series. Mat. Univ. 3 (1996) 92-111;