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.

Calculus Volume 3, by Gilbert Strang and Edwin Herman.

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 R², in the Euclidean space R³, or in higher dimensional Euclidean spaces Rⁿ. 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.

Upon successful completion of this course, a student will be able to:

• 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.

Your overall grade will be determined as follows:

• 19% - WeBWorK, Quizzes, and Class Participation
• 27% - Exam 1
• 27% - Exam 2
• 27% - Final Exam

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

A	...	93-100				B+	...	87-89				C+	...	77-79				D	...	60-69
A-	...	90-92				B	...	83-86				C	...	73-76				E	...	0-59
						B-	...	80-82				C-	...	70-72

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:

Accommodations: SUNY Geneseo is dedicated to providing an equitable and inclusive educational experience for all students. The Office of Accessibility (OAS) will coordinate reasonable accommodations for persons with disabilities to ensure equal access to academic programs, activities, and services at Geneseo.

Students with approved accommodations may submit a semester request to renew their academic accommodations. More information on the process for requesting academic accommodations is on the OAS website.

If you have questions, contact the OAS by email, phone, or in-person:

Office of Accessibility Services - Erwin Hall 22, (585)245-5112, access@geneseo.edu.