recommandation of books

leon1127

I am a big application guy. I am trying to find some book with a lot of applications, proofs, and examples. I am able to read undergraduate real analysis and matrix algebra text. Recently, I am working on Calculus of Variation, Differential Equations and Exterior Differential Forms. Moreover, I want to prepare for my postgraduate work for next year, thus I am wishing if anyone could give me some recommandation on:

Introduction of Optimization
Introduction of Linear Control
Introduction of PDE
Introduction of Stochastic Calculus in Fianace
Introduction of Time Series Analysis
Introduction of Mathematical Foundations of Option Pricing
Advance Variational Calculus
Advance Exterior Differential Forms
Advance Financial Mathematic
Advance ODE (heavy emphasis on Existence and Uniqueness)
Advace Mathematical Economics (Anything beyond the use of elementary Calculus)

If needed, I can give further informations for each topic.

Any though will be truely appreciated.