There are many introductory textbooks on the calculus of variations, but most of them go into far more mathematical detail that is required for MATH0043. If you'd like to know more of the theory, Gelfand and Fomin's Calculus of Variations is available in the library. A less technical source is chapter 9 of Boas Mathematical Methods in the Physical Sciences. There are many short introductions to calculus of variations on the web, e.g.