Mehdi Rahmani-Andebili - Practice Problems, Methods, and Solutions

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Calculus is one of the most important courses of many majors, including engineering and science, and even some of the non-engineering majors like economics and business, which is taught in the first semester at universities and colleges all over the world. Moreover, in many universities and colleges, precalculus is a mandatory course for the under-prepared students as the prerequisite course of calculus.

Unfortunately, some students do not have a solid background and knowledge in math and calculus when they begin their education in universities or colleges. This issue prevents them from learning other important courses like physics and calculus-based courses. Sometimes, the problem is so escalated that they give up and leave university or college. Based on my real professorship experience, students do not have a serious issue to comprehend physics and engineering courses. In fact, it is the lack of enough knowledge of calculus that hinders their understanding of calculus-based courses. Therefore, this textbook, along with the other one (Calculus: Practice Problems, Methods, and Solutions, Springer, 2020), has been prepared to help students succeed in their major.

Both textbooks include basic and advanced problems of calculus with very detailed problem solutions. They can be used as practicing textbooks by students and as a supplementary teaching source by instructors. Since the problems have very detailed solutions, the textbooks are useful for under-prepared students. In addition, the textbooks are beneficial for knowledgeable students because they include advanced problems. In the preparation of problem solutions, effort has been made to use typical methods to present the textbooks as an instructor-recommended one. By considering this key point, both textbooks are in the direction of instructors lectures, and the instructors will not see any untaught and unusual problem solutions in their students answer sheets.

To help students study the textbooks in the most efficient way, the problems have been categorized in nine different levels. In this regard, for each problem, a difficulty level (easy, normal, or hard) and a calculation amount (small, normal, or large) have been assigned. Moreover, in each chapter, problems have been ordered from the easiest one with the smallest amount of calculations to the most difficult one with the largest amount of calculations. Therefore, students are advised to study the textbooks from the easiest problem and continue practicing until they reach the normal and then the hardest one. On the other hand, this classification can help instructors choose their desirable problems to conduct a quiz or a test. Moreover, the classification of computation amount can help students manage their time during future exams and instructors assign appropriate problems based on the exam duration.