Covering foundational concepts in mathematical analysis, this textbook guides students through essential topics from natural numbers to advanced theorems like Stokes-Cartan. It is designed for the first two years of study, ensuring a comprehensive understanding of the subject. The clear explanations and structured approach make it an invaluable resource for learners aiming to build a solid mathematical foundation.
A Promenade Along the Marvelous Theory of Integration
The book offers an accessible introduction to the Kurzweil-Henstock integral, presenting a clear and straightforward theory suitable for beginners. It emphasizes the integral's generality compared to the Lebesgue integral in R, making it a valuable resource for students looking to deepen their understanding of advanced calculus concepts. The course aims to equip readers with foundational knowledge and insights into this broader approach to integration.
An Invitation to the Search of Periodic Solutions for Second Order Ordinary Differential Equations
This book provides an up-to-date description of the methods needed to face the existence of solutions to some nonlinear boundary value problems. All important and interesting aspects of the theory of periodic solutions of ordinary differential equations related to the physical and mathematical question of resonance are treated. The author has chosen as a model example the periodic problem for a second order scalar differential equation. In a paedagogical style the author takes the reader step by step from the basics to the most advanced existence results in the field.