CLASS Connections Template

Calculus III
92.231

CLASS Connections TITLE

INSTRUCTOR:

Konstantin Rybnikov

Office Hours: Monday, Thursday 2:15 –3:30 PM or by appointment.

COURSE DESCRIPTION:

In Calculus I and II you studied derivatives and integrals of functions of one variable. Many physical quantities, however, depend on more than one variable. For example, the air temperature ina room depends on where you measure the temperature and on the time, so temperature is a function of 4 variables (3 space coordinates and time). Temperature is an example of a scalar quantity - it can be described by a single number (e.g. 70°). Some quantities, e.g. wind velocity, are vector quantities that require more than a single number to describe them. (In the case of wind velocity this is three numbers.) In Calculus III you will study scalar-valued functions and vector-valued functions of several variables. You will learn how to extend the concept of derivative and integral to functions of several variables, and you will learn some applications of these concepts. The skills you develop in Calculus III will be useful to you in some of your upper-level engineering courses, e.g. heat transfer, thermodynamics, fluid mechanics, and electromagnetic theory.

COURSE OBJECTIVES:

My goals for this course are for you to

· learn elements of vector and matrix algebra,
· develop a qualitative understanding of and be able to calculate the following: partial derivatives, gradient, and directional derivative of a scalar-valued function; divergence and curl of a vector-valued function; definite integral of a scalar-valued function over a region in 2-space or 3-space; line integral; and surface integral
· be able to give mathematical descriptions of curves and surfaces in 3-space
· be able to state and to apply the two major theorems of vector calculus: the Divergence Theorem and Stokes' Theorem

I would appreciate hearing your goals for the course.

Specific objectives for each topic we cover will be distributed in class. You should use these to help you prepare for exams.

GENERAL COURSE INFORMATION:

Prerequisites: Calculus I and II (92.131 and 92.132 or equivalent). Your grade in Calculus II must be at least C.

Class attendance is required. You are responsible for all information (course material, assignments, changes in exam dates, etc.) presented in class, whether you attend or not.

INSTRUCTIONAL RESOURCES:

The campus has a license for Mathematica. Engineering Departments have Matlab. The 5-th floor Lab across the hall from the dean's office in Olney Hall has Maple. Tutors are available to help you in the Tutoring Center (Southwick 321).

GRADING POLICY:

Course grades

Course grades will be based on participation, homework, 3 in-class exams (midterms), and a comprehensive final exam. Homework accounts for 10%. Participation accounts for 5%. The participation grade is, of course, subjective. Two major factors are active participation in class (e.g. answering my questions or posing good questions) and attendance. Although I do not formally ``take attendance", I have very good visual memory and I will remember if you missed classes. Each midterm accounts for 15%. The final exam accounts for 40%.

Suppose you scored, in percents of the maximal possible score, M1, M2, M3 on the midterms and X on the final. If (M1+M2+M3)/3 is less than X, I will use the final exam score instead of your midterm scores (which is obviously to your benefit).

Your letter grade for the course will be determined from your course average according to the following rules.

The ``table grade" will be determined according to the table below. Also, the ``curve grade" will be determined by fitting the scores to a bell curve, centered somewhere near B-. Your final grade will be the maximum of the two.

Percentage

[90,100]

[85,90)

[80,85)

[75,80)

[65,75)

[60, 65)

[55, 60)

[50, 55)

[45, 50)

[40,45)

Grade

A-

B+

B-

C+

C-

D+

Tentative first exam date: second Wednesday of February.

Exam Policy

It is important that everyone take the same exams under the same conditions for maximum fairness and reliability of testing. I therefore do not give makeup exams unless you have a valid reason (for example, illness or religious holiday) for missing the scheduled exam, and I do not allow extra time on exams unless you have a note from Disability Services. No makeups unless for the above-mentioned reasons with a prior notice.

There will be no ``practice tests" given before the midterms. I may, at my discretion, give a ``practice final" at the end of the course.

Homework

In order for you to understand the material in this course, it is extremely important that you do the assigned homework problems. Working with your classmates can be a great help, and I strongly encourage it. I also urge you to ask questions about any problems that give you trouble.

Homework problems are due in one week unless stated otherwise. Late homework will not be accepted. Some homework assignments will be optional; by default a homework assignment is mandatory. Some homework papers will be collected and graded. Your grade on such an assignment will be based on the on the correctness of your solutions to two or three randomly selected problems. If the problem is solved in the book or the solution is given, you still have to work through it, but I will probably not choose it for grading.

Most homework papers will be returned at the end of the semester. If you had difficulties with homework problems, let me know and I will solve such problems in class or post solutions on the website or invite you to see me during office hours.

You should spend at least 6 hours a week on this course apart from class attendance, office hour or Tutoring center visits, etc.