Vector Calculus

About the Textbook

Vector Calculus

Description: This is a text on elementary multivariable calculus, designed for students who have completed courses in single-variable calculus.The traditional topics are covered: basic vector algebra; lines, planes and surfaces; vector-valued functions; functions of 2 or 3 variables; partial derivatives; optimization; multiple integrals; line and surface integrals.

The book also includes discussion of numerical methods: Newton's method for optimization, and the Monte Carlo method for evaluating multiple integrals. There is a section dealing with applications to probability. Appendices include a proof of the right-hand rule for the cross product, and a short tutorial on using Gnuplot for graphing functions of 2 variables. 

Additionally, there are 420 exercises in the book, while answers to selected exercises are included.

Authors: 

• Michael Corral - Schoolcraft College
  

Formats:  

This book is only available as a PDF file

Supplemental resources: 

The author of the textbook provides the following resources for the book:

• For those who want to view and/or compile the book's source files, the LaTeX source code is available here: calc3book-1.0-src.tar.gz
•  The Java programs and source code for Newton's algorithm (Ch. 2) and the Monte Carlo method (Ch. 3) can be downloaded here: calc3book_java.zip
• Matlab/Octave equivalents of the above Java programs can be downloaded here: ParallelizationArea.zip

I have supplemented the course with the following:

• WebWork 
• SAGE

Cost savings:

I previously used Essential Calculus by James Stewart, which retails for $192 on Amazon. Since I teach this class to about 25 students each year, this is a total savings of $4,800.

License:

There is not a Creative Commons license for this book. However, the book is distributed under the terms of the GNU Free Documentation License, Version 1.2. 

About the Course

MAT 211: Calculus III

Description: Multivariable calculus: analytic geometry, scalar and vector products, partial differentiation, multiple integration, change of coordinates, gradient, optimization, line integrals, Green's theorem, Divergence theorem and Stokes theorem, elements of vector calculus.

Students are mostly Math and Physics major (both subjects require this course), occasionally there are students from other majors. 

Prerequisites: MAT 193 (Calculus II) C grade or better.

Credit: 5 units 

Learning outcomes:

• Demonstrate an intuitive understanding of functions of several variables via level curves and surfaces, and related concepts of limit, continuity and differentiability.
• Perform partial differentiation and multiple integration of functions of several variables.
• Change from Cartesian co-ordinates to polar, cylindrical or spherical co-ordinates and vice versa, perform differential (partial or ordinary) and integration (multiple or single) in curvilinear co-ordinate systems and effect transformation via the Jacobian..
• Utilize vectors to deal with spatial curves and surfaces, and calculus of several variables
• Use the concepts of vector calculus: gradient, curl, divergence, line and surface integrals, Green's, Stokes' and the divergence theorem.
• Apply calculus of several variables to solve problems of optimization, differential geometry and physics.

Curricular changes: 

There were no changes made to the curriculum.

Teaching and learning impacts:

Collaborate more with other faculty: No       
Use wider range of teaching materials: Yes
Student learning improved: Unsure
Student retention improved: No
Any unexpected results: No

The textbook has an appendix on gnuplot which is a free software for plotting all sort of graphs, including graphs of functions. This prompted me using SAGE (a computer algebra system) which is easier for student to access and can do more things.

Sample syllabus and assignment:

Syllabus
This is the syllabus I use for this course.

Assignment 1
This is a sample of a WebWorks assignment.

Assignment 2
This is another type of assignment for the class.

Textbook Adoption

OER Adoption Process

I found this book through a search on the internet. Michael Corral's book, Vector Calculus provides a straight-forward account to mult-variable calculus that is suitable to the level of my students at no cost. It has more than enough materials for a semester course (5 units) and covers all the essential topics of the course. 

 I supplement the textbook with exercises from WebWork which is also freely available to the students. It provides much more computational exercises and instant feedbacks to students. 

Student access:  

The electronic version of the textbook (pdf) is available for free public access. Our department runs a WebWork server for our students. 

Student feedback or participation: 

We did not do any formal survey with students about the textbook this time. It should be done next time when I use this textbook again. 

From the conversations that I had with the students, it is clear that they use this textbook the same way as they use any other textbook: they consult the textbook when they need to work on homework problems and look for examples that are similar to the questions at hand. Other than that they seldom read the textbook for proofs and explanation of the mathematics.  

Wai Yan Pong, Ph.D.

I am a Mathematics professor at the CSU Dominguez Hills. I teach all sorts of undergraduate courses in mathematics regularly.

I am not fixated on a certain teaching style. Sometimes I lecture, sometimes I have students present their works. Sometimes I ask students to work individually and sometimes I have them works in groups. It all depends on what the course and the readiness of the students. In fact, I often mix these ways of teaching in the same course. This makes it more fun for me and less boring for the students. I believe math is best learned by doing it.

I always tell my students that they should not only learn how to solve problems but also understand what they are solving for. Computation without understanding
is the job of a computer.

As for research, I am interested in number theory, differential algebra, model theory and the interaction between them. My current research is on topologies and derivations on the ring of arithmetic functions.