DERIVATIVES (colored)

DERIVATIVES (colored)This is an introductory book on mathematical analysis covering derivatives and their applications. The student should already be familiar with the concept of functions and limits in order to succeed in learning the material in this book. This book is divided into two chapters, structured as follows:¨ Chapter 1 covers differentiation. The first section of this chapter provides a basic introduction to derivatives with the help of tangents and velocity. In the second section, we discuss techniques of differentiation which will be vital in the remaining part of the book. The last section discusses further rules of differentiation of elementary functions.¨ Chapter 2 builds on the material of the previous chapter and covers applications of derivatives. Sections discuss the applications in calculation of limits, analyzing functions, optimization problems, and curve plotting in order.With the help of illustrations and pictures, visualization of the material is effectively improved to aid in students' understanding, especially the examples and the graphs. The book follows a linear approach, with the material in the latter sections building on concepts and math covered previously in the text. For this reason, there are several self-test 'Check Yourself ' sections that check students' understanding of the material at key points. 'Check Yourself ' sections include a rapid answer key that allows students to measure their own performance and understanding. Successful completion of each self-test section allows students to advance to the next topic. Each section is followed by a number of exercises. Many of the problems reflect skills or problem-solving techniques encountered in the section. All of these problems can be solved using skills the student should already have mastered. Each chapter ends with review materials, beginning with a brief summary of the chapter highlights. Following these highlights is a concept check test that asks the student to summarize the main ideas covered in the chapter. Following the concept check, review tests cover material from the chapter. Read more