Calculus III

Math 2415: Calculus III

Fall 2012

Synonym: 14518, Section: 001, Northridge 2245
Monday / Wednesday  1:45 pm- 3:30 pm


Please make sure you have the necessary prerequisites for this course: MATH 2414 with a C or better 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.

Course Content:

Course Description: MATH 2415 CALCULUS III (4-4-0).  A standard third course in calculus. Topics include polar coordinates and polar curves; vectors and analytical geometry in three dimensions; vector-valued functions and curvature; components of acceleration; functions of several variables; limits and continuity in three-space; partial and directional derivatives; gradients, tangent planes, and extreme of functions of two variables; multiple integrals in rectangular, polar, spherical, and cylindrical coordinates; applications of multiple integrals to area, volume, moments, centroids, and surface area. the sine and cosine functions; numerical integration; and applications of the integral.
Instructional Methodology: This course is taught in the classroom primarily as a lecture/discussion course.
Course Rationale: The first two semesters of the calculus sequence dealt with material in two-dimensional rectangular Cartesian coordinates. A primary goal of Calculus III is to extend these ideas to three dimensions and to other coordinate systems. Therefore, in this course we introduce: (i) several methods for interpreting graphs of multivariable functions; (ii) properties of vectors; (iii) differentiation and integration of multivariable functions; (iv) parametric equations of curves in two and three dimensions; (v) a mathematical description of motion in space

Course Materials:

Text: Calculus: Concepts and Contexts, 4th ed., by James Stewart, Brooks/Cole 2010.  The text is sold in a full version and a shortened version, the “Single Variable” version.  Either may be used for Calculus I and II.  Students who will go on to Calculus III will need the full version.
Optional: Student Solutions Manual, Single Variable by Jeffrey A. Cole, Study Guide by Dan Clegg,
Technology required: The use of calculators or computers in order to perform routine computations is encouraged in order to give students more time on abstract concepts.  Mathematica software is available for student use.  You will be required to use Mathematica software for the course; you may choose to purchase this (there is a “student edition” and various time-limited versions available at a reduced price), but you are not required to do so.  This software is available in the classrooms and in the Learning Labs.


There will be 3 exams plus a final exam (part of which will be comprehensive).  In addition, you will be assigned several computer labs which will count for a substantial grade.  Grades will be weighted as follows:


Tests 1, 2, 3




Computer labs and assignments




Final Exam







Sometime after Test 3, there will be a single make-up exam over the material on tests 1-3; the grade on this exam can be used to replace your lowest grade on the first three tests, up to a maximum grade of 90 if you make complete corrections for tests 1-3 or 75 without the completed corrections.
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 do not take the test during that period, you will receive a 0 for that grade.  In that case, you will need to take the make-up exam to replace that 0.  
Grades will be assigned as follows:


90% or better and a grade of at least 80 on the final


60% - 69%


80% - 89% and a grade of at least 70 on the final


below 60%


70% - 79% and a grade of at least 60 on the final





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


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. An incomplete grade cannot be carried beyond the established date in the following semester. The completion date is determined by the instructor but may not be later than the final deadline for withdrawal in the subsequent semester.


You should bring your homework to class every day.  It will be collected regularly.  There may also be in-class assignments or quizzes collected for a grade (as part of your homework grade). There will be a penalty on late homework. Homework that is more than a week late might not receive any credit.  If you do not follow the instructions that will be announced in class about how to organize and submit your homework, you may not receive full (or any) credit for it.


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. After the last day to withdraw, neither the student nor the instructor may initiate a withdrawal. It is the responsibility of each student to ensure that his or her name is removed from the roll should he or she decide to withdraw from the class.  The instructor does, however, reserve the right to drop a student should he or she feel it is necessary. The student is also strongly encouraged to retain a copy of the withdrawal form for their records.
Students who enroll for the third or subsequent time in a course taken since Fall, 2002, may be charged a higher tuition rate, for that course. State law permits students to withdraw from no more than six courses during their entire undergraduate career at Texas public colleges or universities.  With certain exceptions, all course withdrawals automatically count towards this limit.  Details regarding this policy can be found in the ACC college catalog.
The withdrawal deadline for Fall 2012 is November 26, 2012.


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.

Classroom behavior:

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 on the web at:

Class participation:

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.

Keeping up:

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.

Ask questions:

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.

Always show your work:

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.

Time required and outside help:

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.
ACC main campuses have Learning Labs which offer free first-come, first-serve tutoring in mathematics courses. The locations, contact information and hours of availability of the Learning Labs are posted at:


STUDENT LEARNING OUTCOMES - A student who has taken this course should be able to:

  1. Demonstrate the ability to analyze and visualize curves, surfaces, and regions in 2 and 3 dimensions, in Cartesian, polar, cylindrical, and spherical coordinate systems.
  2. Perform calculus operations on vector-valued functions including limits, derivatives, integrals, curvature, and the description of motion in space.
  3. Perform calculus operations on functions of several variables including limits, partial derivatives, directional derivatives, and multiple integrals.
  4. Find and classify extrema and tangent planes of functions of two variables.
  5. Apply some of the theorems of vector calculus, such as the Fundamental Theorem of Line Integrals, Green’s Theorem, the Divergence Theorem, and Stokes' Theorem, to simplify integration problems.
  6. Apply the computational and conceptual principles of calculus to the solutions of various scientific and business applications.

Additional information about ACC's mathematics curriculum and faculty is available on the Internet at:

ACC College Course Policies

Attendance/Class Participation
Regular and punctual class and laboratory attendance is expected of all students.  If attendance or compliance with other course policies is unsatisfactory, the instructor may withdraw students from the class.

Withdrawal Policy
It is the responsibility of each student to ensure that his or her name is removed from the roll should he or she decide to withdraw from the class.  The instructor does, however, reserve the right to drop a student should he or she feel it is necessary.  If a student decides to withdraw, he or she should also verify that the withdrawal is submitted before the Final Withdrawal Date.  The student is also strongly encouraged to retain their copy of the withdrawal form for their records.
Students who enroll for the third or subsequent time in a course taken since Fall, 2002, may be charged a higher tuition rate, for that course.
State law permits students to withdraw from no more than six courses during their entire undergraduate career at Texas public colleges or universities.  With certain exceptions, all course withdrawals automatically count towards this limit.  Details regarding this policy can be found in the ACC college catalog.

Statement on Scholastic Dishonesty
A student attending ACC assumes responsibility for conduct compatible with the mission of the college as an educational institution.  Students have the responsibility to submit coursework that is the result of their own thought, research, or self-expression.  Students must follow all instructions given by faculty or designated college representatives when taking examinations, placement assessments, tests, quizzes, and evaluations.  Actions constituting scholastic dishonesty include, but are not limited to, plagiarism, cheating, fabrication, collusion, and falsifying documents.    Penalties for scholastic dishonesty will depend upon the nature of the violation and may range from lowering a grade on one assignment to an “F” in the course and/or expulsion from the college.  See the Student Standards of Conduct and Disciplinary Process and other policies at

Student Rights and Responsibilities
Students at the college have the rights accorded by the U.S. Constitution to freedom of speech, peaceful assembly, petition, and association. These rights carry with them the responsibility to accord the same rights to others in the college community and not to interfere with or disrupt the educational process. Opportunity for students to examine and question pertinent data and assumptions of a given discipline, guided by the evidence of scholarly research, is appropriate in a learning environment. This concept is accompanied by an equally demanding concept of responsibility on the part of the student. As willing partners in learning, students must comply with college rules and procedures.

Statement on Students with Disabilities
Each ACC campus offers support services for students with documented disabilities.  Students with disabilities who need classroom, academic or other accommodations must request them through the Office for Students with Disabilities (OSD).   Students are encouraged to request accommodations when they register for courses or at least three weeks before the start of the semester, otherwise the provision of accommodations may be delayed.  
Students who have received approval for accommodations from OSD for this course must provide the instructor with the ‘Notice of Approved Accommodations’ from OSD before accommodations will be provided.   Arrangements for academic accommodations can only be made after the instructor receives the ‘Notice of Approved Accommodations’ from the student.  
Students with approved accommodations are encouraged to submit the ‘Notice of Approved Accommodations’ to the instructor at the beginning of the semester because a reasonable amount of time may be needed to prepare and arrange for the accommodations.  Additional information about the Office for Students with Disabilities is available at

Safety Statement
Austin Community College is committed to providing a safe and healthy environment for study and work. You are expected to learn and comply with ACC environmental, health and safety procedures and agree to follow ACC safety policies. Additional information on these can be found at Because some health and safety circumstances are beyond our control, we ask that you become familiar with the Emergency Procedures poster and Campus Safety Plan map in each classroom. Additional information about emergency procedures and how to sign up for ACC Emergency Alerts to be notified in the event of a serious emergency can be found at
Please note, you are expected to conduct yourself professionally with respect and courtesy to all. Anyone who thoughtlessly or intentionally jeopardizes the health or safety of another individual will be dismissed from the day’s activity, may be withdrawn from the class, and/or barred from attending future activities.

Use of ACC email
All College e-mail communication to students will be sent solely to the student’s ACCmail account, with the expectation that such communications will be read in a timely fashion. ACC will send important information and will notify you of any college related emergencies using this account.  Students should only expect to receive email communication from their instructor using this account.  Likewise, students should use their ACCmail account when communicating with instructors and staff.  Instructions for activating an ACCmail account can be found at

Testing Center Policy
Under certain circumstances, an instructor may have students take an examination in a testing center.  Students using the Academic Testing Center must govern themselves according to the Student Guide for Use of ACC Testing Centers and should read the entire guide before going to take the exam.  To request an exam, one must have:
•           ACC Photo ID
•           Course Abbreviation (e.g., MATH or MATD)
•           Course Number (e.g.,0370 or 2413)
•           Course Synonym (e.g., 12345)
•           Course Section (e.g., 005)
Instructor's Name (Marcus McGuff)

Do NOT bring cell phones to the Testing Center.  Having your cell phone in the testing room, regardless of whether it is on or off, will revoke your testing privileges for the remainder of the semester.  ACC Testing Center policies can be found at

Student And Instructional Services
ACC strives to provide exemplary support to its students and offers a broad variety of opportunities and services.  Information on these services and support systems is available at:
Links to many student services and other information can be found at:
ACC Learning Labs provide free tutoring services to all ACC students currently enrolled in the course to be tutored.  The tutor schedule for each Learning Lab may be found at:
For help setting up your ACCeID, ACC Gmail, or ACC Blackboard, see a Learning Lab Technician at any ACC Learning Lab.

Course Outline and Approximate Calendar:
Please note:  schedule changes may occur during the semester. Any changes will be announced in class.







9.1, 9.2

3-dimensional coordinate systems, Vectors in 3-space




The dot product (scalar product)



Labor Day Holiday – No class today




The cross product (vector product)




Equations of lines and planes in 3-space




Functions and surfaces in 3 dimensions



10.1, 10.2

Review parametric curves, vector functions and curves in 3-space and their derivatives and integrals




More on curves, review for Test 1

Test 1 – Dates to be announced in class




An introduction to using Mathematica in higher level calculus




Arc length and curvature




Motion in space (velocity and acceleration)



11.1, 11.2

Functions of several variables, limits, and continuity



11.2, 11.3

More fun with limits, partial derivatives



11.3, 11.4

Partial derivatives, tangent planes, and linear approximations




The chain rule




Directional derivatives and the gradient vector, review for Test 2

Test 2 – Dates to be announced in class




Finding maximum/minimum values and applications




Constrained optimization – the Lagrange multiplier



12.1, 12.2

Double integrals over rectangles and iterated rectangles




Double integrals over general regions, describing general regions mathematically, Reversing the order of integration



12.4, 12.5

Double integrals in polar coordinates, Applications of double integrals




Triple integrals



9.7, 12.8

Cylindrical and spherical coordinate systems, integration in cylindrical and spherical coordinates




More integration in alternate coordinate systems, review for Test 3

Test 3 – Dates to be announced in class



13.1, 13.5

Vector fields and vector differential operators – the curl and the divergence



13.2, 13.3

Line integrals, the Fundamental Theorem for line integrals, conservative fields



13.6, 12.6

Surface integrals and surface area




Green’s Theorem




Stokes’ Theorem




Gauss’ Theorem



Final Exam, Part 1 (new material)



Final Exam, Part 2 (comprehensive)


This webpage was created by Marcus McGuff.
It was last updated on January 22, 2016 .