I want to study path dependent options for which I am following the book Paul Wilmott on Quantitative finance.But here I dont find the detailed explanations or derivations for the various PDEs .So is there any other reference which has these in details
Is not total clear to me what you are looking for - but I would say Wilmott's book is probably the most accessible reference for various forms of path-dependent options in PDE setting, so you're already in the right place IMHO.
However I would add to this two other texts:
Hull's futures, options and other derivatives. The chapters on FDM are clear and practical on implementation considerations. Implement an American option pricer in FDM (explicit and implicit). You'll learn a lot in "the doing"
Wilmott himself wrote a paper on cliquet options in PDE, including UVM modeling and code in VBA. This appeared in a Risk paper "Cliquet Options and Volatility Models"
Personally I would go through these exercises, implement them yourself. Wilmott's book will then make a ton of sense thereafter.