Calculus II

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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