CSIR NET Physical Science Exam > CSIR NET Physical Science Videos > CSIR NET Crash Course for Physical Science > Residue and Its Type Residue at Simple Pole
Residue and Its Type Residue at Simple Pole Video Lecture | CSIR NET Crash Course for Physical Science - CSIR NET Physical Science
FAQs on Residue and Its Type Residue at Simple Pole Video Lecture - CSIR NET Crash Course for Physical Science - CSIR NET Physical Science
| 1. What is residue at a simple pole in complex analysis? |  |
Ans. The residue at a simple pole in complex analysis is the coefficient of the term with the power of -1 in the Laurent series expansion of a function around that pole.
| 2. How do you calculate the residue at a simple pole? | |
Ans. To calculate the residue at a simple pole, you can use the formula Res(f, z0) = lim(z->z0) (z-z0) * f(z), where f(z) is the function and z0 is the location of the simple pole.
| 3. What are the types of residues at a simple pole? | |
Ans. There are two types of residues at a simple pole - positive residue and negative residue. The positive residue occurs when the Laurent series expansion has a positive coefficient for the term with power -1, while the negative residue occurs when the coefficient is negative.
| 4. Can a function have more than one simple pole? | |
Ans. Yes, a function can have multiple simple poles. Each simple pole will have its own residue, which can be calculated separately using the residue formula.
| 5. How are residues at simple poles used in complex analysis? | |
Ans. Residues at simple poles are important in complex analysis for evaluating complex integrals using the residue theorem. By calculating residues at simple poles, one can simplify the integration process and solve complex problems efficiently.
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