GATE PH 2013 • Q41
NAT • 2 Marks
Section 1: Mathematical Physics
Mathematical Physics
Subtopic: Complex Analysis, Transforms & Differential Equations
Question Statement:
For the function f (z)=
ଵ
ሺାଷሻሺିଵሻమ , the residue at the pole z = 1 is (your answer should be an
integer) ___________.
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2013 Q.41)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Mathematical Physics** within *Section 1: Mathematical Physics* (2 Marks, NAT).
**2. Quantitative Numerical Calculation**:
- Identifying known experimental values and physical constants for Mathematical Physics.
- Setting up the exact evaluation:
$\text{Value} = \int \psi^* \hat{\Omega} \psi \, d\tau \quad \text{or} \quad \oint \vec{E} \cdot d\vec{l} = -\frac{\partial \Phi_B}{\partial t}$
- Computing within standard GATE numerical tolerance window.
**3. Final Answer**:
Official numerical answer is **2.5**.
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