Course Description:  CALCULUS IV (4-4-0) . This course develops the calculus of real- and vector-valued functions of one and several variables. Topics include matrix algebra and linear maps; vector-valued functions and their analysis; the geometry of Euclidean n-space; functions of several variables and their differentiation; gradients and directional derivatives; partial derivative; arc length; vector fields, divergence, and curl; Taylor's theorem for several variables; extreme of real-valued functions in n-space; LaGrange multipliers; multiple integrals and the chain rule; improper integrals; line integrals; area of surface; surface integrals; Green's Theorem; Gauss' Theorem; Stokes' Theorem; conservative fields

Instructional Methodology : This course is taught in the classroom primarily as a lecture/discussion course. There is also a computer lab component.

Course Rationale: This course serves as an extension of the traditional calculus sequence and contains additional topics relevant to students majoring in engineering, physics, and applied mathematics, including:  

1. differentiability generalized to multivariable functions  

2. an introduction to vector fields and flow lines  

3. a description of four differential operators: gradient, divergence, curl, and Laplacian  

4. the change-or-variables theorem for double and triple integrals  

5. path integrals and line integrals;  parametrization of surfaces;   surface integrals  

6. Green's theorem, Stokes' theorem, the divergence theorem  

7. conservative vector fields; Maxwell's equations  

Please make sure you have the necessary prerequisites for this course. That means you need a C or better in MATH 2415 (Calculus III) or its equivalent.  If I feel you are not prepared for this course, I may choose to withdraw you. If you have any questions about your preparation for the course, please come and talk to me about it.

Textbook : Vector Calculus , 5th edition(ISBN 0716749920), Marsden & Tromba, W.H. Freeman and Co., 2003.

Technology Required : You must have access to technology that enables you to (1) Graph a function. (2) Find the zeroes of a function. (3) Do numerical integration.

Optional:   Mathematicaversion 6 (student edition) by Wolfram Research. (This is available for your use at several locations on campus as well as most ACC campuses.)

There will be 4 exams during the term, each of which will count equally towards your grade. There will also be a series of computer labs that together will count as another test grade.

You may earn bonus points on each test, except for the final test, by correcting all errors and submitting them to me within one week of receiving the graded test back. If you take any test late for any reason, there will be a penalty of 10 points off your test grade. However, no late tests will be allowed after I hand the graded tests back in class.  

If you miss a test, you must try to take it during this “late” period. If you miss this deadline as well, I may consider allowing you to hand in corrections on all tests and replace all or part of the missed test with your grade on the final, but only in the case of serious illness or emergency.  This is solely at my discretion. Otherwise, you will receive a 0 on the test. All tests and assignments must be turned in on or before the last class meeting. Grades will be assigned as follows:

Grades will be assigned as follows:

A

90% or better

D

60% - 69%

B

80% - 89%

F

below 60%

C

70% - 79%

W

Withdrawn by student or instructor prior to last withdrawal date on school calendar

I

Incomplete grades (I) will be given only in very rare circumstances. Generally, to receive a grade of "I", a student must have taken all tests, be passing, and after the last date to withdraw, have a personal tragedy occur which prevents course completion.

You should bring your homework to class every day.  Homework will be assigned regularly and is required for success in this course.  There may be occasional quizzes on homework material if it seems necessary to motivate homework participation.  If this is the case, these quizzes may make up as much as 5% of the following test grade.

Attendance is required in this course.  It is extremely important for you to attend class regularly. Although I may not take regular attendance, I MAY drop you from the course for excessive absences, although I make no commitment to do so.

It is the student's responsibility to initiate all withdrawals in this course. The instructor may withdraw students for excessive absences (4) but makes no commitment to do this for the student. (If you decide to stop coming, you had best make sure that you drop the course. While we MIGHT do this, it is YOUR responsibility. If you fail to do so, you could receive an F on your permanent record.) After the withdrawal deadline, neither the student nor the instructor may initiate a withdrawal. If you are withdrawn by mistake, I will only consider reinstating you if you have taken all necessary tests, are current in your homework, and have not missed an excessive number of classes. The withdrawal deadline for Spring 2008 is April 21, 2008.

Classroom behavior should support and enhance learning. Behavior that disrupts the learning process will be dealt with appropriately, which may include having the student leave class for the rest of that day. In serious cases, disruptive behavior may lead to a student being withdrawn from the class. ACC's policy on student discipline can be found in the Student Handbook page 32 or on the web at: http://www.austincc.edu/handbook

All students are expected to actively participate in this class. This can include asking relevant questions in class, participating in class discussions and other in-class activities, helping other students, coming to office hours with questions, and doing other things that contribute to the class.

Please, try to keep up with the homework and with the lecture in class. There just isn't much time to catch up. This means you have to be sure to allow yourself plenty of time to do the homework and to study.

Please, please, please, if you don't understand something, or you aren't clear about something, or if you think I (or the book) have made a mistake (it has been known to happen), or if you have any other questions, please ask. Don't let confusion accumulate. If you don't want to ask in class, come to our office hours (or call) and ask. It is much easier to ask a question now than to miss it on the test.  I expect all students to participate in class discussions and other activities. Trust me, you will get much more out of the class if you become actively involved in it.

It is much more important that you understand the processes involved in solving problems than that you just give me the right answer. If I see from your work that you understand what you are doing, I will usually give partial credit for a problem, even if you made a mistake somewhere along the line. If you don't show your work (unless I believe you could reasonably do it in your head), I may not give you full credit, even if the answer is right. If you can really do something in your head, that's great, but when in doubt, write it down.  It is also very important that you write what you mean. I will correct your notation the first few times, but I will start counting it wrong if you continue to write things incorrectly. In addition, please write clearly and legibly. If I can't read it, I won't grade it.

To do homework and study requires two or three times as much time outside of class as the time you spend in class in order to succeed in this course. If you need more out-of-class help than you can obtain in your instructor's office hours, free tutoring is available in any of ACC's Learning Labs.

The locations, contact information and hours of availability of the Learning Labs are posted at: http://www.austincc.edu/tutor

Institutions of higher education are conducted for the common good.  The common good depends upon a search for truth and upon free expression.  In this course the professor and students shall strive to protect free inquiry and the open exchange of facts, ideas, and opinions.  Students are free to take exception to views offered in this course and to reserve judgment about debatable issues. Grades will not be affected by personal views.  With this freedom comes the responsibility of civility and a respect for a diversity of ideas and opinions.  This means that students must take turns speaking, listen to others speak without interruption, and refrain from name-calling or other personal attacks.

Acts prohibited by the college for which discipline may be administered include scholastic dishonesty, including but not limited to, cheating on an exam or quiz, plagiarizing, and unauthorized collaboration with another in preparing outside work.  Academic work submitted by students shall be the result of their thought, work, research or self-expression.  Academic work is defined as, but not limited to, tests, quizzes, whether taken electronically or on paper; projects, either individual or group; classroom presentations; and homework.

Students who violate the rules concerning scholastic dishonesty will be assessed an academic penalty which the instructor determines is in keeping with the seriousness of the offense. This academic penalty may range from a grade penalty on the particular assignment to an overall grade penalty in the course, including possibly an F in the course. ACC's policy can be found in the Student Handbook on the web at: http://www.austincc.edu/handbook .  

Testing Center Policies: ACC Testing Center policies can be found at: http://www.austincc.edu/testctr/. Deadlines for all tests will be announced in class. Any tests taken after the announced deadline are considered late.

Student Services: The web address for student services is: http://www.austincc.edu/support. The ACC student handbook can be found at: http://www.austincc.edu/handbook

Each ACC campus offers support services for students with documented physical or psychological disabilities.  Students with disabilities must request reasonable accommodations through the Office of Students with Disabilities on the campus where they expect to take the majority of their classes.  Students are encouraged to do this three weeks before the start of the semester.

Students who are requesting accommodation must provide the instructor with a letter of accommodation from the Office of Students with Disabilities (OSD) at the beginning of the semester.   Accommodations can only be made after the instructor receives the letter of accommodation from OSD

Sections

Sections

Review, Sections 2.2-2.3

Sections 7.1

Sections 2.4-2.5

Section 7.2

Section 2.6

Sections 7.3-7.4

Sections 4.1, (4.2), 4.3, Test 1

Sections 7.5-7.6

Sections 4.4, 5.1

Sections 7.6(cont), Test 3, 8.1

Sections 5.2-5.4

Sections 8.2-8.3

Sections 5.5, 6.1

Sections 8.3(cont)-8.4

Sections 6.2-6.3, Test 2

Review, Exam