Mathematical Analysis II

The purpose of the volume is to provide a support textbook for a second lecture course on Mathematical Analysis, along the lines of the Programme Specifications for mathematical teaching recently adopted by European universities. The contents are organised to suit, in particular, students of Engineering, Computer Science and Physics, all areas in which mathematical tools play a crucial role. The basic notions and methods concerning integral and differential calculus for multivariable functions, series of functions and ordinary differential equations are presented in a manner that elicits critical reading and prompts a hands-on approach to concrete applications. The pedagogical layout echoes the one used in the companion text Mathematical Analysis I. The book's structure has a specifically-designed modular nature, which allows for great flexibility in the preparation of a lecture course on Mathematical Analysis. The style privileges clarity in the exposition and a linear progression through the theory. The material is organised on two levels. The first, reflected in this book, allows students to grasp the essential ideas, familiarise with the correspond-ing key techniques and find the proofs of the main results. The second level builds upon online complementary notes that enable the strongly motivated reader to explore further into the subject; pointers to this material are disseminated in the treatise. Definitions are enriched by many examples, which illustrate the properties discussed. A host of solved exercises complete the text, at least half of which guide the reader to the solution.