Engineering Mathematics 4 By Kumbhojkar Edition -
Why it fails: Kumbhojkar’s theoretical explanations are concise, sometimes too concise. The real learning is in the 10+ solved examples that follow each theorem. Fix: Read the theorem once, then immediately do Example 1 and 2. Refer back to theory only if stuck.
This section is the book’s strongest practical asset. Kumbhojkar avoids excessive measure theory and focuses on application-driven problems.
Q.3
a) Find the analytic function $f(z) = u + iv$ given that $u = x^2 - y^2 + xy$.
[06 Marks] engineering mathematics 4 by kumbhojkar edition
b) Evaluate $\int_C \fracz+4z^2+2z+5 , dz$ where $C$ is the circle $|z| = 2$ using the Cauchy Residue Theorem.
[06 Marks]
c) Find the image of the infinite strip $1 < x < 2$ under the transformation $w = \frac1z$.
[06 Marks] The book includes 5 full solved university papers
OR
Q.4
a) If $f(z)$ is an analytic function, prove that:
$$ \left( \frac\partial^2\partial x^2 + \frac\partial^2\partial y^2 \right) |f(z)|^2 = 4 |f'(z)|^2 $$
[06 Marks] engineering mathematics 4 by kumbhojkar edition
b) Evaluate $\oint_C \frace^2z(z-1)(z-2) , dz$ where $C$ is $|z| = 3$.
[06 Marks]
c) State Cauchy’s Integral Formula. Evaluate $\int_C \fracz^2z-2 , dz$ where $C$ is the circle $|z| = 3$.
[06 Marks]
The book includes 5 full solved university papers (typically Mumbai University). Time yourself for 3 hours. Use Kumbhojkar’s notation style—it is exactly what examiners want to see.