Welcome to the International Metric Version of Essential Calculus: Early Transcendental Functions. For this metric version, the units of measurement used in most of the examples and exercises have been changed from U.S. Customary units to metric units. We did not convert problems that are specific to the U.S. Customary units, such as dimensions of a baseball field or U.S. postal rates. We are excited to offer you a new edition with more resources then ever that will help you understand and master calculus. This text includes features and resources that continue to make Essential Calculus: Early Transcendental Functions a valuable learning tool for students and a trustworthy teaching tool for instructors.
Essential Calculus: Early Transcendental Functions provides the clear instruction, precise mathematics, and thorough coverage that you expect for your course.
NEWBig Ideas of Calculus
We have added a new feature to help you discover and understand the Big Ideas of Calculus. This feature has three parts.
The Big Ideas of Calculus notes give you an overview of the major concepts of a chapter and how they relate to the earlier concepts you have studied. These notes appear near the beginning of a chapter and in the chapter review.
In each section and in the chapter review, make sure you do the Exploring Concepts exercises. These exercises will help you develop a deeper and clearer knowledge of calculus. Work through these exercises to build and strengthen your understanding of the concepts.
To continue exploring calculus, do the Building on Concepts exercises at the end of the chapter review. Not only will these exercises help you expand your knowledge and use of calculus, they will prepare you to learn concepts in later chapters.
The exercise sets have been carefully and extensively examined to ensure they are rigorous and relevant and to include topics out users have suggested. The exercises are organized and titled so you can better see the connections better see the connections between examples and exercises. Multi-step, real-life exercises reinforce problem-solving skills and mastery of concepts by giving you the opportunity to apply the concepts in real-life situations.
A bulleted list of learning objectives provides you with the opportunity to preview what will be presented in the upcoming section.
Theorems provide the conceptual framework for calculus. Theorems are clearly stated and separated from the rest of the text by boxes for quick visual reference. Key proofs often follow the theorem and can be found in appendix A.
As with theorems, definitions are clearly stated using precise, formal wording and are separated from the text by boxes for quick visual reference.
Explorations provide unique challenges to study concepts that have not yet been formally covered in the text. They allow you to learn by discovery and introduce topics related to ones presently being studied. Exploring topics in this way encourages you to think outside the box.
These hints and tips reinforce or expand upon concepts, help you learn how to study mathematics, caution you about common errors, address special cases, or show an alternative solution to an example. We have added several new Remarks to help students who need more in-depth algebra support.
UPDATED Historical Notes and Biographies
Historical Notes provide you with background information on the foundations of calculus. The Biographies introduce you to the people who created and contributed to calculus. We have added several new biographies.
Throughout the book, technology boxes show you how to use technology to solve problems and explore concepts of calculus. These tips also point out some pitfalls of using technology.
How Do You See It? Exercise
The How Do You See It? exercise in each section presents a problem that you will solve by visual inspection using the concepts learned in the lesson.
Carefully chosen applied exercises and examples are included throughout to address the question, “When will I use this ?”These applications are pulled from diverse sources, such as current events, world data, industry trends, and more, and relate to a wide range of interests. Understanding where calculus is (or can be) used promotes fuller understanding of the material.
Putnam Exam Challenges
Putnam Exam questions appear in selected sections. These actual Putnam Exam questions will challenge you and push the limits of your understanding of calculus.
Table of Contents
1. Limits and Their Properties
3. Applications of Differentiation
5. Applications of Integration
6. Integration Techniques and Improper Integrals
7. Infinite Series
8. Parametric Equations, and Polar Coordinates
9. Vectores and the Geometry of Space
10. Vector-Valued Functions
11. Functions of Several Variables
12. Multiple Integration
13. Vector Analysis
Appendix A. Proofs of Selected Theorems (Online)*
Appendix B. Integration Tables
Appendix C. Precalculus Reviews (Online)*
Appendix D. Rotation and the General Second-Degree Equation (Online)*
Appendix E. Complex Numberss (Online)*
Appendix F. Business and Economic Applications (Online)*
Answers to Selected Exercises