Brief Calculus

This text fully embraces the "reform" being called for in calculus teaching and learning. All key concepts are presented following the Rule of Three: from a graphical, numerical, and algebraic viewpoint, encouraging students to visualise, verbalise and write. By always bringing these viewpoints to bear on each topic, the text presents a conceptual understanding of the calculus that is deep and flexible enough to accommodate the many diverse business and science applications presented. The graphing calculator is fully integrated to make these viewpoints and the applications more accessible. Features: * Technology is fully integrated throughout the text and is used to assist the students to think about the geometric and numerical meaning of calculus, without undermining the algebraic aspects. When applicable, examples are demonstrated with graphing calculators. In almost all cases, they represent opportunities for the instructor to have the students reproduce these screens on their graphing calculators, making the student an active partner in the learning process. * Procedures and definitions evolve from the investigation of section-opening applications.
These applications are extensive, varied, referenced, and realistic and allow topics to be taught using an investigative, exploratory approach. * Extensive exercises involving writing, exploration, and creativity are given to help students gain better problem-solving skills. Meaningful applications, drawn from a variety of fields, are given for all the mathematics that is presented to motivate the students. Many of the applications are referenced from the modern day journals and articles. * "Explorations", individual or group projects, and writing exercises present students with the opportunity to learn through their own investigations, explore their interests, and increase their communication skills, both inside and outside the classroom.