Since then, each century has demonstrated the power of calculus to illuminate questions inmathematics, the physical sciences, engineering, and the social and biological sciences.
This edition of Calculus continues our effort to promote courses in which understanding and computation reinforce each other. It reflects the input of users at research universities, four-year colleges, community colleges, and secondary schools, as well as of professionals in partner disciplines such as engineering and the natural and social sciences. Mathematical Thinking Supported by Theory and Modeling.
The first stage in the development of mathematical thinking is the acquisition of a clear intuitive picture of the central ideas.
In the next stage, the student learns to reason with the intuitive ideas in plain English. After this foundation has been laid, there is a choice of direction. All students benefit from both theory and modeling, but the balance may differ for different groups. Some students, such as mathematics majors, may prefer more theory, while others may prefermoremodeling. Sloane, MD. As instructors ourselves, we know that interactive classrooms and well-crafted problems promote student learning.
Since its inception, the hallmark of our text has been its innovative and engaging problems. These problems probe student understanding in ways often taken for granted. Praised for their creativity and variety, these problems have had influence far beyond the users of our textbook. Genres: Mathematics. The art of teaching, Mark Van Doren said, is the art of assisting discovery.
In this edition, as in the first six editions, I aim to convey to the student a sense of the utility of calculus and develop technical competence, but I also strive to give some appreciation for the intrinsic beauty of the subject. Newton undoubtedly experienced a sense of triumph when he made his great discoveries.
I want students to share some of that excitement. The emphasis is on understanding concepts. I think that nearly everybody agrees that this should be the primary goal of calculus instruction. In fact, the impetus for the current calculus reform movement came from the Tulane Conference in , which formulated as their first recommendation:.
The Rule of Three has been expanded to become the Rule of Four by emphasizing the verbal, or descriptive, point of view as well. In writing the seventh edition my premise has been that it is possible to achieve conceptual understanding and still retain the best traditions of traditional calculus.
The book contains elements of reform, but within the context of a traditional curriculum.
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