The Lebesgue Integral (Cambridge Tracts in Mathematics) Book

I'm using this book as well as two other books on Engineering Mathematics by B.S Grewal and Michael Greenberg.
According to me this is a great book to learn D.E. and vector calculus and the book is very good as it has covered all the necessary topics with practical examples(I like this feature).

But I would say if you have weak basic concepts then go for B.S Grewal and Michael Greenberg before coming on to this books as this book do not cover all the basic concepts and contains very less solved problem.

But,Yes,everything is explained with clarity and cover a lot of advanced approaches.

You can also use this book if you are preparing for Gate,but I recommend using other books as well,for better understanding,but if you don't want to brawl your brain than this book is enough.