A: Check McGraw-Hill Education India (the publisher) or Amazon Kindle . Do not pay for "premium PDF access" on shady websites; those are scams. The Verdict: To PDF or Not to PDF? The search for the "Veerarajan T. Engineering Mathematics for First Year PDF" is a rite of passage for engineering freshers. While the free PDF is a quick fix, it comes with quality and ethical compromises.
A: No. The book is self-contained. Every odd-numbered problem usually has a worked-out example earlier in the chapter. The even-numbered ones are for practice.
Methods for solving first-order ODEs (Linear, Bernoulli, Exact) and higher-order linear ODEs with constant coefficients. The "Method of Undetermined Coefficients" is explained via exhaustive examples.
This is the golden chapter. Characteristic equations, Eigenvalues, Eigenvectors, Cayley-Hamilton theorem, and Diagonalization. Veerarajan provides a "trick box" for solving 3x3 matrices quickly.