Syllabus
1.- Integration in One Variable
1. The Riemann integral
2. Applications of the integral
3. Improper integration
4. Sequences of functions and
integration
2.- Integration in Several Variables
1. The n-dimensional Riemann
integral
2. Calculation of several variable
integrals
3.- Integrals Depending on a Parameter
1. Fundamental theorems
2. Integration by differentiating with
respect to a parameter
3. Applications: transforms and
convolutions
4.- Line and Path Integrals
1. Path integral of scalar fields and
line integral of vector fields
2. Green's Theorem
3. Characterization of gradients on the
plane
5.- Surface Integrals
1. Surface integrals of scalar and
vector fields
2. Stokes’s and Gauss’s Theorems
3. Characterization of gradients in the
space