Single Variable Integral and Differential Calculus in a Nutshell with Elements of Critical Thinking

Ranis Ibragimov and Pirooz Mohazzabi
University of Wisconsin-Parkside, WI, USA

Series: Mathematics Research Developments
BISAC: MAT005000



Volume 10

Issue 1

Volume 2

Volume 3

Special issue: Resilience in breaking the cycle of children’s environmental health disparities
Edited by I Leslie Rubin, Robert J Geller, Abby Mutic, Benjamin A Gitterman, Nathan Mutic, Wayne Garfinkel, Claire D Coles, Kurt Martinuzzi, and Joav Merrick


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This book presents a variety of calculus problems concerning different levels of difficulty with technically correct solutions and methodological steps that look also correct, but that have obviously wrong results (like 0 = 1). Those errors are aimed to be resolved by applying critical thinking (i.e., reasonable, reflective, responsible, and skillful thinking). This book is structured in such a way that finding a problem for a given solution with the wrong answer requires a proper diagnosis by asking the right questions, which is one of the first steps to critical thinking. The objective of this book is to motivate students to identify various strategies and to develop criteria for choosing a suitable strategy to resolve obvious errors or illogical statements.


Chapter 1. Introduction

Chapter 2. Limits, Continuity and Derivatives

Chapter 3. Derivative and Di¤erentiation

Chapter 4. Applications of Derivative

Chapter 5. Integration


Keywords: Critical thinking; Mathematical Modeling

This book is meant for Calculus students and instructors.

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