MATH 223: Calculus III

Calculus, 5th edition, by James Stewart.

We will cover roughly chapters 13-17 of the textbook. Topics are subject to change depending on the progress of the class, and various topics may be skipped due to time constraints.

Please note that we will work on developing your independent reading skills in Mathematics. I certainly won't be able to cover in class all the material you will be required to learn. As a result, you will be expected to do a lot of reading. The reading assignments will be on topics to be discussed in the following week's lectures to enable you to ask focused questions in the class and to better understand the material.

We will probably make use of the TI-89 calculators. Therefore, it is probably in your best interest to have one (or something equivalent that can calculate integrals.)

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 differentiation, maximums and minimums, multiple integrals, and line integrals.

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 their higher dimensional 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. The Euclidean plane and the Euclidean space are the homes of vectors. Studying the algebra 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 linear approximation and to motion in the plane or in the space. In the case of two variables, this linear approximation is by tangent planes which replace the 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, of averages, and of 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.

Your overall grade will be determined as follows, with your lowest 20% being dropped.

• 20% - Homework, Quizzes, and Class Participation
• 20% - Exam 1
• 20% - Exam 2
• 20% - Exam 3
• 20% - Final Exam Part 1
• 20% - Final Exam Part 2

Your overall grade for the course will reflect how well the class is doing, and will be high if everyone is working hard on the homework and doing well on the exams. 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.

Homework: There will be weekly homework assignments which are due each Friday by 4:00 pm. Follow this link for a Description of Homework requirements.

Exams: There will be three Midterm Exams and one Final Exam. The Final Exam will have two parts. The first part is cumulative, covering material from the first three exams. The second part will cover material learned after the third midterm exam. Exams are closed book, closed notes, closed friends, and open brain. Cell phones, iPods, and other electronic devices will NOT be permitted in exams. Whether or not calculators are allowed on an exam will be determined at a later time.

Quizzes and Class Participation: There will be occasional, unannounced quizzes in class to make sure students are understanding and keeping up with the course material. Quizzes may be based on material from the reading assignment which we have not yet covered during lectures. Therefore, it is imperative that you keep up with the reading assignments. Any given quiz may cover topics from a previous lecture, from the reading assignment, or both. 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: