x
will do at least a modest amount of writing to answer the questions and explain
their findings. For instructors interested in a more conventional source of exercises,
consider the freely available text by Gilbert Strang of MIT, available in .pdf format
from the MIT open courseware site via http://gvsu.edu/s/bh.
• Graphics. As much as possible, we strive to demonstrate key fundamental ideas
visually, and to encourage students to do the same. Throughout the text, we use
full-color 1 graphics to exemplify and magnify key ideas, and to use this graphical
perspective alongside both numerical and algebraic representations of calculus.
• Links to Java Applets. Many of the ideas of calculus are best understood dynamically; java applets offer an often ideal format for investigations and demonstrations.
Relying primarily on the work of David Austin of Grand Valley State University
and Marc Renault of Shippensburg University, each of whom has developed a large
library of applets for calculus, we frequently point the reader (through active links
in the .pdf version of the text) to applets that are relevant for key ideas under
consideration.
• Summary of Key Ideas. Each section concludes with a summary of the key ideas
encountered in the preceding section; this summary normally reflects responses to
the motivating questions that began the section.
How to Use this Text
This text may be used as a stand-alone textbook for a standard first semester college
calculus course or as a supplement to a more traditional text. Chapters 1-4 address the
typical topics for differential calculus, while Chapters 5-8 provide the standard topics of
integral calculus, including a chapter on differential equations (Chapter 7) and on infinite
series (Chapter 8).
Electronically
Because students and instructors alike have access to the book in .pdf format, there are
several advantages to the text over a traditional print text. One is that the text may be
projected on a screen in the classroom (or even better, on a whiteboard) and the instructor
may reference ideas in the text directly, add comments or notation or features to graphs,
and indeed write right on the text itself. Students can do likewise, choosing to print only
whatever portions of the text are needed for them. In addition, the electronic version of
the text includes live html links to java applets, so student and instructor alike may follow
those links to additional resources that lie outside the text itself. Finally, students can have
1 To keep cost low, the graphics in the print-on-demand version are in black and white. When the text
itself refers to color in images, one needs to view the .pdf file electronically.
will do at least a modest amount of writing to answer the questions and explain
their findings. For instructors interested in a more conventional source of exercises,
consider the freely available text by Gilbert Strang of MIT, available in .pdf format
from the MIT open courseware site via http://gvsu.edu/s/bh.
• Graphics. As much as possible, we strive to demonstrate key fundamental ideas
visually, and to encourage students to do the same. Throughout the text, we use
full-color 1 graphics to exemplify and magnify key ideas, and to use this graphical
perspective alongside both numerical and algebraic representations of calculus.
• Links to Java Applets. Many of the ideas of calculus are best understood dynamically; java applets offer an often ideal format for investigations and demonstrations.
Relying primarily on the work of David Austin of Grand Valley State University
and Marc Renault of Shippensburg University, each of whom has developed a large
library of applets for calculus, we frequently point the reader (through active links
in the .pdf version of the text) to applets that are relevant for key ideas under
consideration.
• Summary of Key Ideas. Each section concludes with a summary of the key ideas
encountered in the preceding section; this summary normally reflects responses to
the motivating questions that began the section.
How to Use this Text
This text may be used as a stand-alone textbook for a standard first semester college
calculus course or as a supplement to a more traditional text. Chapters 1-4 address the
typical topics for differential calculus, while Chapters 5-8 provide the standard topics of
integral calculus, including a chapter on differential equations (Chapter 7) and on infinite
series (Chapter 8).
Electronically
Because students and instructors alike have access to the book in .pdf format, there are
several advantages to the text over a traditional print text. One is that the text may be
projected on a screen in the classroom (or even better, on a whiteboard) and the instructor
may reference ideas in the text directly, add comments or notation or features to graphs,
and indeed write right on the text itself. Students can do likewise, choosing to print only
whatever portions of the text are needed for them. In addition, the electronic version of
the text includes live html links to java applets, so student and instructor alike may follow
those links to additional resources that lie outside the text itself. Finally, students can have
1 To keep cost low, the graphics in the print-on-demand version are in black and white. When the text
itself refers to color in images, one needs to view the .pdf file electronically.