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

This book is a collection of carefully selected problems in mathematical analysis, designed to achieve synergy between analytic geometry and algebra and promote mathematical creativity. It covers fundamental concepts seen in a first-year Calculus course, such as inequalities, point-set topology, limits of real-valued functions, differentiation, classical theorems of differential calculus, graphs of functions, and Riemann integrals and antiderivatives. Solutions are provided at the end of each chapter.

Format: Paperback / softback
Length: 220 pages
Publication date: 23 March 2023
Publisher: Springer Nature Switzerland AG

This book is a remarkable compilation of meticulously chosen problems in mathematical analysis, designed to achieve optimal synergy between analytic geometry and algebra while promoting mathematical creativity rather than mere repetitive techniques. Spanning eight chapters, this comprehensive work guides students through the fundamental principles of the subject, requiring a strong dose of imagination. Within its pages, all the essential concepts covered in a first-year Calculus course are explored. The problems touch upon various topics, including inequalities, elementary point-set topology, limits of real-valued functions, differentiation, classical theorems of differential calculus (Rolle, Lagrange, Cauchy, and lHospital), graphs of functions, and Riemann integrals and antiderivatives. Each chapter begins with a theoretical background, providing relevant definitions and theorems, followed by related problems. Formalism is kept to a minimum, and solutions are readily available at the end of each chapter. This book is an invaluable resource for instructors and students of Mathematical Analysis, Calculus, and Advanced Calculus, particularly targeting first-year undergraduates in Mathematics, Physics, and Engineering courses. It can also serve as a valuable supplement to any traditional textbook on these subjects.

Weight: 386g
Dimension: 156 x 234 x 17 (mm)
ISBN-13: 9783030918651
Edition number: 1st ed. 2022