100+1 Problems in Advanced Calculus: A Creative Journey through the Fjords of Mathematical Analysis for Beginners

This  book convenes a collection of carefully selected problems in  mathematical analysis, crafted to achieve maximum synergy between  analytic geometry and algebra and favoring mathematical creativity in  contrast to mere repetitive techniques. With eight chapters, this work  guides the student through the basic principles of the subject, with a  level of complexity that requires good use of imagination.

In  this work, all the fundamental concepts seen in a first-year Calculus  course are covered. Problems touch on topics like inequalities,  elementary point-set topology, limits of real-valued functions,  differentiation, classical theorems of differential calculus (Rolle,  Lagrange, Cauchy, and l’Hospital), graphs of functions, and Riemann  integrals and antiderivatives. Every chapter starts with a theoretical  background, in which relevant definitions and theorems are provided;  then, related problems are presented. Formalism is kept at a minimum,  and solutions can be found at the end of each chapter.

Instructors  and students of Mathematical Analysis, Calculus and Advanced Calculus  aimed at first-year undergraduates in Mathematics, Physics and  Engineering courses can greatly benefit from this book, which can also  serve as a rich supplement to any traditional textbook on these subjects  as well.