# Differential Calculus (Guichard)

Differential calculus is concerned with the study of the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus.

## Differential Calculus (Guichard)

David Guichard is a professor of mathematics in the department of Mathematics and Computer Science at Whitman College. His research interests are combinatorics and graph theory.

Books Authored by David Guichard

Post date: 20 Jul 2016
A textbook introduction to combinatorics and graph theory.

Post date: 20 Jul 2016
A textbook introduction to combinatorics and graph theory.

Post date: 09 Nov 2009
This is a freely available calculus book, covering a fairly standard course sequence: single variable calculus, infinite series, and multivariable calculus. There is no chapter on differential equations.

Post date: 09 Nov 2009
This is a freely available calculus book, covering a fairly standard course sequence: single variable calculus, infinite series, and multivariable calculus. There is no chapter on differential equations.

## Calculus

From the MAA review of this book: “The discussions and explanations are succinct and to the point, in a way that pleases mathematicians who don’t like calculus books to go on and on.”

The book covers the standard material in a calculus course for science and engineering. The size of the book is such that an instructor does not have to skip sections in order to fit the material into the typical course schedule. The single variable material is contained in eleven chapters beginning with analytic geometry and ending with sequences and series. The multivariable material consists of five chapters and includes with the vector calculus of in two and three dimensions through the divergence theorem. The book ends with a final chapter on differential equations.

There are sufficiently many exercises at the end of each sections, but not as many as the much bigger commercial texts. Also available are WeBWorK problem sets keyed to the sections of the text. Some students and instructors may want to use something like a Schaum’s outline for additional problems.

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## Existing Free (or Very Low Cost) Calculus Texts

One of the overwhelming things about the Internet (to me, at least) is just trying to keep track of what’s out there. With this post, I invite readers to contribute to a list of free (and where fitting, open) calculus texts that are available on the web I’ve added two that are very low cost (under $20 per student). If people want to offer testimonials or other observations in the comments, that would be especially appreciated. As noted in an earlier post, there are a couple of calculus texts posted online as part of the American Institute of Mathematics’s Open Textbook Project (those by Strang and Guichard, respectively). Again, Strang’s book is free, but not open, while Guichard’s is open. Here are some others. The first two have some modest costs associated with them the remaining ones are all free. None of these, to my knowledge, is open source. • David Massey, Worldwide Differential Calculus. Massey is the founder of the Worldwide Center of Math I believe that originally, this text was free. Massey now charges$10 for the .pdf, or $30 for a bound copy. In reviewing earlier versions (when it was posted online), I was struck by how complete the text is (differential calculus is 565 pages!), and how vast the included resources are for students, with even lengthy video tutorials. So not free, but not$189.95 either. Massey’s site has a growing collection of similar books.
• David Smith and Lang Moore, Calculus: Modeling and Application. I was (am) a huge fan of the print version (1st edition) of this text. Smith and Moore have converted the text to an entirely .html platform. Now hosted and endorsed by the MAA, schools can purchase a license agreement to gain access to the full text online for their students. From the order form on the page, it costs roughly $15-$20 per student, depending on the number of students enrolled. This is a great, low-cost alternative, and again the text and materials are extremely high quality. I’m not as big a fan of the .html format and how each link leads to a new window, but I do see advantages of this format.
• Miklos Bona and Sergei Shabanov, Concepts in Calculus I. “From the University of Florida Department of Mathematics, this is the first volume in a three volume presentation of calculus from a concepts perspective.” The other two volumes (for integral and multivariable calculus) are available from the Florida Digital Repository. At under 200 pages, this is a nice, comprehensive introduction to standard concepts in calculus. Exercises are included. Text is free and in .pdf format. (As an aside, the Florida Digital Repository seems to be one of the better online “warehouses” for free texts with a reasonably good search feature.)
• William Smith, The Calculus. Free, but copyrighted (the author doesn’t want any of the text even copied to other locations). The typesetting is poor and hard to read online, and the text has two unusual features (as noted by the author): (a) proofs for everything are included, and (b) the text introduces ideas in one and two variables simultaneously.
• Dan Sloughter, Difference Equations to Differential Equations. Clearly the author has more in mind than calculus, but there’s quite a lot of calculus content available the table of contents is presented in html, with the links leading the reader to .pdf files that are essentially short individual chapters. Sloughter also offers Yet Another Calculus Text, written from the perspective of the hyperreal numbers.
• Jerome Keisler has a text that seems similar in spirit to Sloughter’s, using infinitesimals, titled Elementary Calculus: an Infinitesimal Approach.
• Paul Garrett, Calculus Refresher. A brief (approximately 80 page) review of some key calculus ideas (with some exercises). This book seems designed for students who’ve had calculus and need some review, rather than for students encountering the ideas for the first time.

What am I missing? Are there other good texts out there that people have used? Testimonials for any of the above?

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### BC Open Textbook Project: Calculus (guichard), DiffEq (Trench)

Two open source textbook authors that many in this group are familiar with sent me announcements recently (see below). Looks like the folks at Simon Frasier are seeing if there is a viable business in offering print-on-demand versions of popular open source texts. They've branded the effort BCCampus.

The BC Open Textbook Project is offering print copies of the book (Calculus, Guichard et al) in color cheaply:

I imagine it's a bit out of date, and probably only single-variable, but the price is amazing if it's any good.

My "Elementary Differential Equations with Boundary Value Problems" is now available by print on demand from BCcampus on

which is funded by the British Columbia (Canada) Ministry of Advanced Education. The price: Approximately $27 for black and white or$83.00 for color. BCcampus derives no profit from this and I receive no royalties. Unfortunately, this isn't likely to appeal to US institutions because of the cost of shipping for example, \$52.00 to my New Hampshire address.

## Whitman Calculus

This free online calculus textbook was written by David Guichard, professor of mathematics at Whitman College, with material from Neal Koblitz (University of Washington) and H. Jerome Keisler. It has been in continuous use at Whitman since 2006. It has also been used at Manhattanville College, Northern Arizona, UC Riverside, UNC Asheville, University of Kentucky, University of Minnesota, Western Connecticut State and Westmont College.

The authors encourage feedback from students and educators and have been constantly updating this text. It had last been updated February 15, 2015, when I was writing this post in March of that same year.

It does include an answer key for selected exercises making it a good calculus textbook choice for self-study or homeschool students. It would appear that the text could be used for at least three semesters of calculus – a great cost-savings for students.

This mulivariable calculus online textbook is available freely from the website or your can purchase a printed copy at Lulu.

### Chapter Titles from Whitman Calculus Online Textbook

1. Analytic Geometry
2. The Derivative
3. Rules for Finding Derivatives
4. Transcendental Functions
5. Curve Sketching
6. Applications of the Derivative
7. Integration
8. Techniques of Integration
9. Applications of Integration
10. Polar Coordinates, Parametric Equations
11. Sequences and Series
12. Three Dimensions
13. Vector Functions
14. Partial Differentiation
15. Multiple Integration
16. Vector Calculus
17. Differential Equations
19. Appendix B: Useful Formulas

Another member of the mathematics faculty at Whitman has worked up some additional exercises that can be downloaded in a .tar format.

## MATH 223: Calculus III

We will be using a free online textbook for this course. Click the link below to get the book and view other resources, such as a Students Solution Manual. I recommend using the downloadable pdf version, but there is also an online web-based version.

Another quality, free online textbook that has nice interactive features is Calculus, by David Guichard and friends , chapters 12-16.

In previous semesters, I have also used Calculus, by Stewart or Thomas' Calculus, by Weir and Hass. You can feel free to use these if you prefer.

We will cover roughly chapters 2-6 of the Strang/Herman textbook. Topics are subject to change depending on the progress of the class, and various topics may be skipped due to time constraints.

It is strongly suggested that you read the sections of the textbook which correspond to the material covered during the lectures. The reading will enable you to answer my questions and ask your own focused questions during the lecture and help you to better understand the material.

It may be helpful to make use of calculators such as the TI-89 and mathematical programs such as MATLAB, Maple, or Mathematica periodically. However, our primary use of technology will be java applets and 3D visualization tools freely available on the internet.

Topics covered: Topics include vectors and vector-valued functions and their associated curves, functions of two and three variables and their associated surfaces, limits, continuity, partial derivatives, maximums and minimums, multiple integrals, and line integrals. Topics are subject to change depending on the progress of the class, and various topics may be skipped due to time constraints.

This course is an advanced calculus course dealing primarily with the calculus of several variables. The natural location to study several variables is in the Euclidean plane R 2 , in the Euclidean space R 3 , or in higher dimensional Euclidean spaces R n . These spaces contain various natural subsets such as lines, planes, curves, surfaces, and solid regions. Surfaces arise as the graphs of functions of two variables. Also, the Euclidean plane and the Euclidean space are the homes of vectors. Studying the algebra and calaculus of these yields understanding of concepts like perpendicularity and parallelism and enables us to work with lines and planes. The shape of the objects we are studying sometimes makes it convenient to depart from the usual coordinate systems and to work with alternate coordinate systems such as polar coordinates, cylindrical coordinates, or spherical coordinates.

As is the case with one variable calculus, calculus of several variables divides into two related parts, differentiation and integration. Differentiation is related to tangents, linear approximation, and motion in the plane or in higher dimensional space. In the case of two variables, we study tangent planes similar to the notion of tangent lines of single variable calculus. Differentiation also leads to a theory of maxima and minima for functions of several variables. Integration in several variables is related to areas and volumes. Among the applications are the computations of masses, averages, and probabilities. The evaluation of these higher dimensional integrals reduces to the iteration of the one variable process of integration. Finally, many physical problems such as the computations of work and of various fluxes reduce to the study of differential and integral calculus of vectors.

• Represent vectors analytically and geometrically, and compute dot and cross products for presentations of lines and planes,
• Analyze vector functions to find derivatives, tangent lines, integrals, arc length, and curvature,
• Compute limits and derivatives of functions of 2 and 3 variables,
• Apply derivative concepts to find tangent lines to level curves and to solve optimization problems,
• Evaluate double and triple integrals for area and volume,
• Differentiate vector fields,
• Determine gradient vector fields and find potential functions, and
• Evaluate line integrals directly and by the fundamental theorem.

• 16% - WeBWorK, Quizzes, and Class Participation
• 21% - Exam 1
• 21% - Exam 2
• 21% - Exam 3
• 21% - Final Exam

The letter grade you earn for the class will be based on the following breakdown of number grades:

Homework: Almost all the questions on the exams will be in the same spirit with the homework questions. Therefore understanding how to do all the homework questions will enable you to do well on the exams. Most homework will be done through the internet-based homework system called WeBWorK. However, there may occasionally be problems you must write out and hand in to me. All assignments must be completed by the given due date. Moreover, while it is not required that you complete a handwritten version of WeBWorK assignments, it is strongly encouraged. Writing a problem out by hand, showing all calculation steps, and keeping them collected in a notebook will greatly assist you as you prepare for exams.

Exams: The midterm exams and final exam are closed book, closed notes, closed friends, and open brain. Use of phones and other electronic devices will NOT be permitted during exams. Whether or not calculators are allowed on an exam will be determined at a later time.

Quizzes and Class Participation: There may be occasional (possibly unannounced) quizzes in class to make sure students are understanding and keeping up with the course material. Quizzes will be based on material from homework and previous lectures. NO MAKE-UP QUIZZES WILL BE GIVEN. Class participation will be based on your willingness to ASK and ANSWER questions in class.

It is essential not to fall behind because each lecture is based on previous work. If you have trouble with some material, SEEK HELP IMMEDIATELY in the following ways:

## Calculus Early Transcendentals Differential & Multi-Variable Calculus for Social Sciences

Calculus Early Transcendentals Differential & Multi-Variable Calculus for Social Sciences has been redesigned in the Department of Mathematics at Simon Fraser University from Calculus Early Transcendentals by Lyryx. Substantial portions of the content, examples, and diagrams have been redeveloped to meet the needs of social science calculus. Additional contributions have been provided by an experienced and practicing instructor. The textbook is approachable, cohesive, and suitable for standard differential calculus courses offering a comprehensive treatment of the necessary calculus techniques and concepts.

Information about what was changed in this adaptation is found in the Copyright statement on page iii of the textbook.

Based on this textbook, lecture and student notes have been created to provide 30 sets of slides for the integral calculus course. The student notes are skeleton versions of the lecture notes and come in two versions, either plain or with extra space on the side and legend to use a note taking system similar to the Cornell-style.