Lecture 17| Improper Integral using rectangular contour integration| Example 2|Theta Classes

In this lecture we are going to discuss second example related to rectangular contour while solving improper integral.So first we see that when integrand involves hyperbolic or periodic functions then we will use rectangular contour . After that we will find the poles of the function and locate them in z plane and then we will form a rectangle in such a way that only one pole lies within that and then we apply Cauchy Residue theorem. After that we will break our contour into four parts and solve each integral along particular path and see their value as R tends to infinity. And then after some calculation we will get our result. I am providing links of concepts which we used in solving the given improper integral: Multi valued function, Branch point and Branch cut :    • Branch Point and Branch Cut |Multi valued ...   Singularities and its types :    • Types of Singularity in complex analysis|I...   How to find poles :    • example of singularity in complex analysis...   Cauchy Residue Theorem and its proof :    • Cauchy residue theorem|Statement and Proof...   Finding residue at simple pole and pole of order m :    • Residue at a pole|residue at simple pole|r...   In case if any student finds any difficulty in understanding this lecture do mention it in comment section. Keep connected with ‪@thetaclasses‬ to study various topics of higher mathematics. Thank You.