MATH 113 Calculus IlI

Course Information

Here is some information in a .pdf file.

Multivariable Calculus: Early Transcendentals, 6^th edition, by James Stewart

MATH 113 is primarily 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 analogs. 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, the algebra of which wields 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 the 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, volumes, and to the general problem of finding a suitable summation of a function. Among the applications are the computation of masses, of averages, and of probabilities. The evaluation of these higher dimensional integrals reduces to the iteration of the one variable process of itegration. 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.
See also the Catalogue Description.

Your grade for the course will be based on your performance on three exams and WeBWorK assignments:

• WebWork: 30%

• Midterm Exam 1: 20%

• Midterm Exam 2: 20%

• Final Exam: 30%

Homework comes in two forms. One form consists of WeBWorK exercises. WeBWorK exercises are done online and provide instant feedback. When you have done a WeBWorK exercise correctly, your credit for the problem is immediately recorded in the database. You are encouraged to discuss problems with other students, however WeBWorK exercises are individualized for each student, so you must do your own assignment. There will be a WeBWork assignment posted for each section covered. For each WebWork section you will have at least one week to complete the assignment. Pay attention to the due time and start working on the problems long before it. (The due dates will be included in the WebWork system)
There will be 12 or 13 Webwork sets. Set 0 will not count. It is meant to familiarize you with Webwork.

The other form of homework consists of supplementary exercises that are listed in the course schedule. These exercises do not contribute directly to your total grade, but similar exercises will undoubtedly appear on exams. It is important to do both WeBWorK and supplementary exercises.

Throughout the semester we will offer extra credit for the solution of some challenging problems. They will be harder than the ones you see on homework or on exams. If N students (correctly) solve a problem (by the deadline), they each get 1/(N+1) points added to their final exam's score.

There will be two midterm exams and one final exam.

To study for exams, we recommend you review your notes, previous WeBWorK assignments, and previous supplementary homework exercises. Additionally, to study for the first part of the final exam, we recommend you review the midterm exams.

Calculators are not permitted during exams.

You may bring one formula card (1 sheet) to each exam.

It is essential not to fall behind because each lecture is based on previous work. If you are having trouble with some material, seek help in the following ways:

• Ask your instructor, either in class or privately.

• Go to the Math Clinic.

• Work with your classmates.

If you are having any difficulties, seek help immediately – do not wait until it is too late to recover from falling behind, or failing to understand a concept.