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This textbook covers key topics of Elementary Calculus through selected exercises, in a sequence that facilitates development of problem-solving abilities and techniques. It opens with an introduction to fundamental facts of mathematical logic, set theory, and pre-calculus, extending toward functions, limits, derivatives, and integrals. Over 300 solved problems are approached with a simple, direct style, ordered in a way that positively challenges students and helps them build self-confidence as they progress. A special final chapter adds five carefully crafted problems for a comprehensive recap of the work.
The book is aimed at first-year students of fields in which calculus and its applications have a role, including Science, Technology, Engineering, Mathematics, Economics, Architecture, Management, and Applied Social Sciences, as well as students of Quantitative Methods courses. It can also serve as rich supplementary reading for self-study.
List of contents
Preface.- Preliminaries.- Functions.- Limits.- Derivatives.- Integrals.- Brief recap.- Solutions.- Appendix A: Pyramid and inequality.- Appendix B: Sources.- Index.
About the author
Edmundo Capelas de Oliveira is a Professor and Researcher at the Department of Applied Mathematics at the Institute of Mathematics, Statistics and Scientific Computing, State University of Campinas (Unicamp), Brazil. He got his PhD in Physics (1982) from the same university, and did post-doc studies (in 1991 and 1995) at the Università degli Studi di Perugia, Italy. In 2012, he was distinguished by Unicamp with the First Award for Undergraduate Teaching Incentive for outstanding teaching skills at the undergraduate level. He authored "Solved Exercises in Fractional Calculus" (2019) and co-authored "The Many Faces of Maxwell, Dirac and Einstein Equations: A Clifford Bundle Approach" (2016), both published by Springer. His research interests lie in fractional calculus, differential equations, and special functions.
Bárbara de Holanda Maia Teixeira is an Architect. During her undergraduate studies at the State University of Campinas (Unicamp), Brazil,she took part in an academic exchange at the Pontifical Catholic University of Chile, where she volunteered as a teacher of mathematics for students of high school level. Back in Brazil, she worked as a teaching assistant for the Calculus discipline at the UNICAMP.
Report
"Mastering Calculus through Practice offers a large number of challenging exercises, as well as complete solutions to these problems. ... for someone who has seen the material before and is looking to strengthen (or, indeed, master) the material, working through these problems could prove beneficial." (John Ross, MAA Reviews, June 20, 2022)
