University Calculus: Early Transcendentals plus Pearson MyLab Math 4th Edition

Book Preface

University Calculus: Early Transcendentals, Fourth Edition in SI Units, provides a streamlined treatment of the material in a standard three-semester or four-quarter STEM-oriented  course. As the title suggests, the book aims to go beyond what many students may have  seen at the high school level. The book emphasizes mathematical precision and conceptual  understanding, supporting these goals with clear explanations and examples and carefully  crafted exercise sets.

Generalization drives the development of calculus and of mathematical maturity and  is pervasive in this text. Slopes of lines generalize to slopes of curves, lengths of line segments to lengths of curves, areas and volumes of regular geometric figures to areas and  volumes of shapes with curved boundaries, and finite sums to series. Plane analytic geometry generalizes to the geometry of space, and single variable calculus to the calculus  of many variables. Generalization weaves together the many threads of calculus into an  elegant tapestry that is rich in ideas and their applications.

Mastering this beautiful subject is its own reward, but the real gift of studying calculus is acquiring the ability to think logically and precisely; understanding what is defined,  what is assumed, and what is deduced; and learning how to generalize conceptually. We  intend this text to encourage and support those goals.

New to This Edition

We welcome to this edition two new co-authors: Christopher Heil from Georgia Institute  of Technology and Przemyslaw Bogacki from Old Dominion University. Heil’s focus was  primarily on the development of the text itself, while Bogacki focused on the MyLab™ Math course.

Christopher Heil has been involved in teaching calculus, linear algebra, analysis, and  abstract algebra at Georgia Tech since 1993. He is an experienced author and served as a  consultant on the previous edition of this text. His research is in harmonic analysis, including time-frequency analysis, wavelets, and operator theory.

Przemyslaw Bogacki joined the faculty at Old Dominion University in 1990. He has  taught calculus, linear algebra, and numerical methods. He is actively involved in applications of technology in collegiate mathematics. His areas of research include computeraided geometric design and numerical solution of initial value problems for ordinary differential equations.

This is a substantial revision. Every word, symbol, and figure was revisited to ensure  clarity, consistency, and conciseness. Additionally, we made the following text-wide  changes:
• Updated graphics to bring out clear visualization and mathematical correctness.
• Added new types of homework exercises throughout, including many that are geometric in nature. The new exercises are not just more of the same, but rather give different perspectives and approaches to each topic. In preparing this edition, we analyzed  aggregated student usage and performance data from MyLab Math for the previous  edition of the text. The results of this analysis increased both the quality and the quantity of the exercises.
• Added short URLs to historical links, thus enabling students to navigate directly to online information.
• Added new annotations in blue type throughout the text to guide the reader through the  process of problem solution and emphasize that each step in a mathematical argument is rigorously justified.

New To MyLab Math
Many improvements have been made to the overall functionality of MyLab Math since  the previous edition. We have also enhanced and improved the content specific to this text.
• Many of the online exercises in the course were reviewed for accuracy and alignment  with the text by author Przemyslaw Bogacki.
• Instructors now have more exercises than ever to choose from in assigning homework.
• The MyLab Math exercise-scoring engine has been updated to allow for more robust  coverage of certain topics, including differential equations.
• A full suite of Interactive Figures have been added  to support teaching and learning. The figures are designed to be used in lecture as well as by students  independently. The figures are editable via the freely  available GeoGebra software.
• Enhanced Sample Assignments include just-in-time  prerequisite review, help keep skills fresh with spaced
practice of key concepts, and provide opportunities to  work exercises without learning aids (to help students  develop confidence in their ability to solve problems independently).
• Additional Conceptual Questions augment the text  exercises to focus on deeper, theoretical understanding of the key concepts in calculus. These questions were written by faculty at Cornell University under an NSF grant. They are also assignable through Learning Catalytics.
• This MyLab Math course contains pre-made quizzes to assess the prerequisite skills  needed for each chapter, plus personalized remediation for any gaps in skills that are  identified.
• Additional Setup & Solve exercises now appear in many sections. These exercises  require students to show how they set up a problem, as well as the solution itself, better  mirroring what is required of students on tests.
• PowerPoint lecture slides have been expanded to include examples as well as key  theorems, definitions, and figures.
• Numerous instructional videos augment the already robust collection within the course.  These videos support the overall approach of the text—specifically, they go beyond  routine procedures to show students how to generalize and connect key concepts