Real Analysis An Undergraduate Problem Book for Mathematicians, Applied Scientists, and Engineers

Real Analysis: An Undergraduate Problem Book for Mathematicians, Applied Scientists, and Engineers is a classical Real Analysis/Calculus problem book. This topic has been a compulsory subject for every undergraduate studying mathematics or engineering for a very long time. This volume contains a huge number of engaging problems and solutions, as well as detailed explanations of how to achieve these solutions. This latter quality is something that many problem books lack, and it is hoped that this feature will be useful to students and instructors alike.

Features

• Hundreds of problems and solutions

• Can be used as a stand-alone problem book, or in conjunction with the author?s textbook, Real Analysis: An Undergraduate Textbook for Mathematicians, Applied Scientists, and Engineers, ISBN 9781032481487
• Perfect resource for undergraduate students studying a first course in Calculus or Real Analysis

• Contains explanatory figures, detailed techniques, tricks, hints, and ?recipes? on how to proceed once we have a calculus problem in front of us.

1. The Field of Real Numbers. 2. The Field of Complex Numbers. 3. Sequences of Real Numbers. Convergence. 4. Continuous Functions. 5. Differentiable Functions. 6. Riemann Integral. 7. Numerical Series. 8. Power Series. Function Sequences and Series.

Gustavo da Silva Araújo is an Assistant professor at the State University of Paraíba, Brazil. His primary research interests encompass real and complex analysis, the geometry of Banach spaces, operator theory, series and summability, mathematical inequalities, and lineability. He has authored several papers in these areas, and also serves as reviewer for many mathematics journals. He earned his Ph.D. in mathematics from the Federal University of Paraíba in 2016.

Gustavo A. Muñoz Fernández graduated in Mathematics from Universidad Complutense in 1994 and in Physics from UNED in 2001. He earned his Ph.D. in Mathematics from Universidad Complutense in 1999. Dr. Muñoz is currently the Academic Secretary of the Interdisciplinary Mathematics Institute (IMI) and a Full Professor at the Department of Mathematical Analysis and Applied Mathematics at Universidad Complutense. Dr. Muñoz has co-authored more than 70 publications including a research book and several textbooks. The scientific interests of Dr. Muñoz are related, mainly, to geometry of Banach spaces, polynomials in normed spaces and algebraic genericity (lineability).

María E. Martínez Gómez is currently an Assistant Professor at the Department of Applied Mathematics, Materials Science and Engineering and Electronic Technology, Rey Juan Carlos University (Spain). In 2017, she graduated in Mathematics from the Complutense University of Madrid (UCM) and defended her PhD Thesis in 2021. Her areas of expertise include Real and Convex Analysis and Set Theory.

Luis Bernal González graduated in 1980 from the Universidad de Sevilla, Spain. He obtained his Ph.D. in Mathematics from the same university in 1984. Dr. Bernal has been a permanent faculty member at Sevilla since 1980 and was promoted to associate professor in 1987, and to full professor in 2010. He was an invited speaker at the International Congress on Hypercyclicity and Chaos for Linear Operators and Semigrou