Books on calculus of variations and|or integral equations

Question

I want to find a good textbooks on calculus of variations and|or integral equations. It would be awesome if:

• the textbook has a lot of difficult exercises explained or has a problem book;
• it starts from the basis and goes to really difficult concepts;
• it has examples from such fields as electrodynamics or radiotechnics;

Thank you in advance :)

Answer 1

You might want to try "Calculus of Variations" by Gelfand and Fomin. From the author preface:

Our aim is to give a treatment of the ele­ments of the calculus of variations in a form which is both easily understandable and sufficiently modem. Considerable attention is devoted to physical applica­tions of variational methods, e.g., canonical equations, variational principles of mechanics and conservation laws.