Introduction to Mathematical Analysis
The book begins at the level of an undergraduate student assuming only basic knowledge of calculus in one variable. It rigorously treats topics such as multivariable differential calculus, Lebesgue integral, vector calculus and differential equations. After having built on a solid foundation of topology and linear algebra, the text later expands into more advanced topics such as complex analysis, differential forms, calculus of variations, differential geometry and even functional analysis. Overall, this text provides a unique and well-rounded introduction to the highly developed and multi-faceted subject of mathematical analysis, as understood by a mathematician today.
In a single text, the student gets a glimpse of a big picture The treatment of mathematical analysis is rigorous and self-contained Can be used not only as a textbook for a course but also as a reference book for lecturers in analysis or mathematicians and scientists in general