Features of the Book:
• Concept development flows from simple settings to general results
• Differential Equations and integration are used to motivate and guide the development of the concepts
• Simple functions are used to approximate functions and antiderivatives.
• The definite integral is defined using simple function approximation
• The derivative form of the Fundamental Theorem of Calculus is proven rigorously independent of the Mean Value Theorem.
• Our approach allows Fourier Series to be included without adding to the length or difficulty of a standard calculus course
• Every group of four sections is devoted to a single main theme, which allows instructors the freedom to design the course to suit their individual needs.
• Themes are eventually developed graphically, numerically and analytically
• Every fourth section is a "Pause" that reconsiders the material in the previous three sections from a different perspective
• The concepts introduced in each group of four sections are summarized in a rigorous listing of key definitions and theorems after each "Pause".
• After each summary, there is a self-test that allows the student to determine how well they have acquired the material to that point
• Individual sections are readable, thus permitting students to study calculus by marking key ideas with a highlighter and making notes in the margins
• Each section is written as a tutorial for the exercises that follow
• Included in the exposition are short, simple exercises designed to reinforce the reading. Thus, requiring the students to read the text involves little more than assigning the in-text exercises as part of the overall problem set.
• The in-text exercises are simple enough to be answered orally, thus generating class discussion and providing a tool for designing lectures.
• The use of technology is carefully interwoven into topics where it is either a tool widely used by scientists, mathematicians or engineers, or where it aids in the discovery or comprehension of a concept.
• Data sets and simple curve-fitting are incorporated throughout the textbook
• The graded problem sets drill the techniques encountered in the section, whether they are graphical, numerical or analytical.
• Applications are developed from a mathematical viewpoint with references to other fields so that they do not seem contrived and out of context.
• The Next Step sections are short essays that elaborate on themes introduced in the text. The AWrite to Learn@ assignments that follow afford the student an opportunity to learn through writing and to develop technical writing skills.
• Advanced contexts and in-depth exercises are included at the end of the "Next Steps" as a tool to challenge better students.
• The quotient rule is introduced a section after the product rule so that students do not confuse the signs of the two.
• Proofs are included for all the theorems except for the Mean Value Theorem (Because an actual proof of the Mean Value Theorem requires the Heine-Borel theorem or its equivalent, it is developed intuitively and without proof).

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