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