Follows an advanced course in analysis (vector analysis, complex analysis and Fourier analysis) for engineering students, but can also be useful, as a complement to a more theoretical course, to mathematics and physics students. This title represents the theoretical aspects.

Vector Analysis: Differential Operators of Mathematical Physics; Line Integrals; Gradient Vector Fields; Green Theorem; Surface Integrals; Divergence Theorem; Stokes Theorem; Appendix; Complex Analysis: Holomorphic Functions; Complex Integration; Laurent Series; Residue Theorem and Applications; Conformal Mapping; Fourier Analysis: Fourier Series; Fourier Transform; Laplace Transform; Applications: ODE; Applications: PDE; Solutions to the Exercises: Differential Operators: Solutions; Line Integrals: Solutions; Gradient Vector Fields: Solutions; Green Theorem: Solutions; Surface Integrals: Solutions; Divergence Theorem: Solutions; Stokes Theorem: Solutions; Holomorphic Functions: Solutions; Complex Integration: Solutions; Laurent Series: Solutions; Residue Theorem: Solutions; Conformal Mapping: Solutions; Fourier Series: Solutions; Fourier Transform: Solutions; Laplace Transform: Solutions; ODE: Solutions; PDE: Solutions.