Calculus and Analytic Geometry : For Engineering Technology

This book is an outgrowth of our Technical Mathematics with Calculus. It is intended for students enrolled in an engineering technology curriculum. The material is presented under the assumption that the student has a working knowledge of college-level algebra and trigonometry. The primary objective of a technical calculus book is to relate mathematical concepts to practical engineering technology problems. We have attempted to attain this goal by using physical problems that are well within the scope of the beginning student as a springboard to mathematical concepts. Our approach is exemplified in Chapters 2 and 6 in connection with the concepts of the derivative and the definite integral, respectively. Both chapters are designed to lead the student to the desired mathematical concept by identifying the common thread in several apparently unrelated physical problems. For example, in Chapter 2, the similarity in the solutions to the slope of a tangent line, the velocity of a particle, and the current in a circuit is used to motivate the definition of the derivative. The scope of topics covered in the text is standard for technical calculus books. Algebraic functions are discussed in the preliminary chapters and are followed by the transcendental functions. Selected topics from differential equations and infinite series are presented in the concluding chapters. Analytic geometry is presented as it is needed to facilitate an understanding of calculus applications. Except in Chapters 1 and 11, the two subjects are interwoven. The conic sections of Chapter 11 can be taught at any time after Chapter 1 is covered, but they are delayed in the arrangement of topics to allow earlier coverage of the transcendental functions. The book is designed to satisfy the needs of a two semester course; however, those desiring a one-semester coverage of calculus will find the first seven chapters ideal for this purpose. The presentation features a variety of learning aids. Numerous worked examples are included in each section, many of which have step-by-step comments to lead students through the solution. Because repetition is an important part of the learning process, we have included an abundant supply of graded problems in the end-of-section exercise sets. In addition, each chapter concludes with a set of review exercises. Exercises with application to a specific technology are 'called-out' with a distinctive logo. (A key to the application symbols follows the Table of Contents.) Answers to the odd-numbered exercises are provided at the end of the book. Comment and Warning statements are included throughout the book to alert the student to important ideas and processes and to warn of common pitfalls. Also, many of the mathematical procedures are presented in an easy-to-follow, step-by-step format. These procedural steps are boxed - as are key formulas, equations, and definitions - for emphasis and for easy reference. An additional learning aid is the Glossary of Important Terms at the back of the book. ...