Features of the Book:

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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