MATH 241 Fall 2015

Section 6

Meeting Times

Lectures: MWF  9:40 AM - 10:30 AM LeConte 405
Office Hours: MTWThF  2:30 PM -  3:30 PM LeConte 314D

Important deadlines you need to know

  • The semester begins Thursday, August 20th, and ends Friday, December 4th.
  • The deadline to drop/add and the last day to change credit/audit is Wednesday, August 26th. The first day in which a "W" grade is assigned is therefore Thursday, August 27th.
  • The last day to obtain a "W" grade or to elect a pass/fail grade is Monday, October 12th. The first day in which a "WF" grade is assigned is therefore Tuesday, October 13th.


A grade of C or better in MATH 142.


Calculus. Early Transcendentals by James Stewart. Thompson Brooks/Cole 2008 (sixth edition)

Bundle: Custom USC Math 241 Calculus, 6th with Enhanced WebAssign and eBook

Calculus: Early Transcendentals (Stewart's Calculus Series) Student Solutions Manual for Stewart's Multivariable Calculus, 6th Edition

You will be required to use Enhanced WebAssign, the online homework system that accompanies your textbook, for my course. If you choose to purchase a hard copy of the textbook, you need to buy the bundle that comes with the Enhanced WebAssign code. Make yourself a favor, and purchase it directly from the publisher [follow this link]. Do NOT get it from the USC bookstore.

Course Structure and Grading Policies

Your final score for the course will be computed as follows:

  • Homework assignments: (up to 100 points) 15% of the course grade. Homework problems have been assigned for each lecture (you can see them at the end of this page, under Lesson Plan). A selection of those problems are posted on WebAssign on the day of the lecture, and will be graded. You will have until the end of the following day to complete the assignment (e.g. what is posted on Monday is due on Wednesday at 11:59PM; what is posted on Friday is due on Monday at 11:59PM) In order to sign up for your section of the course on WebAssign, visit and click on [Enter Class Key]. The class key is

    sc 9603 5676

    Click [here] to retrieve further registration instructions.
  • Midterm Exams: (up to 100 points each) 60% of the course grade (15% each midterm).
    There will be four in-class midterm exams scheduled as follows:
    Test # Date
    1 Mon, Sep 14
    2 Fri, Oct 16
    3 Wed, Nov 11
    4 Mon, Nov 23
  • Final Exam: (up to 100 points) 25% of the course grade.
    The final exam is scheduled on Friday, December 11th, 2015 at 9:00 AM.

The course grade will be determined as follows:

A 90%-100%
B+ 85%-89%
B 80%-84%
C+ 75%-79%
C 70%-74%
D+ 65%-69%
D 60%-64%
F below 60%

Further Information

  • Honor Code:
    The Honor Code applies to all work for this course. Please review the Honor Code at [this link]. Students found violating the Honor Code will be subject to discipline.
  • Some material will be stored in Dropbox. In that case, you will need an account to retrieve it. If you do not have one already, sign-in through [this link] with your academic e-mail address to receive a base 4GB storage, plus an extra 500MB, free of charge.
  • Remember to change your e-mail address on Blackboard if necessary []
  • Office of Student Disability Services:
    If you have special needs as addressed by the Americans with Disabilities Act and need any assistance, please notify the instructor immediately.
  • Math Tutoring Center:
    The Math Tutoring Center maintains a list of private tutors for math and statistics. The center is located in LeConte, room 105, and the schedule is available at the Department of Mathematics website ( No appointment is necessary.
  • Student Success Center:
    In partnership with University of South Carolina faculty, the Student Success Center (SSC) offers a number of programs to assist you in better understanding your course material and to aid you on your path to success. SSC programs are facilitated by trained undergraduate peer leaders who have previously excelled in their courses. Resources available to students in this course include:
    • Peer Tutoring: You can make a one-on-one appointment with a peer tutor by going to Drop-in Tutoring and Online Tutoring may also be available for this course. Visit the previous website for a full schedule of times, locations, and courses.
    • Success Connect: Throughout the semester, I may communicate with the SSC regarding your progress in the course. If contacted by the SSC, please schedule an appointment to discuss campus resources that are available to you. Success Connect referrals are not punitive and any information shared by me is confidential and subject to FERPA regulations.
    SSC services are offered to all USC undergraduates at no additional cost. You are invited to call the Student Success Hotline at (803) 777-1000 or visit to check schedules and make appointments. Success Consultants are available to assist you in navigating the University and connecting to available resources.

Learning Outcomes

A student who successfully completes Vector Calculus (MATH 241) should continue to develop as an independent learner with the ability to approach problems from a conceptual viewpoint, to utilize more than one idea in a single problem, and to apply appropriate calculus skills to problems in context. In particular, the successful student will master concepts and gain skills needed to solve problems related to:

  • Vectors and vector functions
  • Finding equations of lines and planes
  • Parametric curves
  • Differentiability, continuity and limits of functions of two or more variables.
  • Directional derivatives and gradients.
  • Maxima and minima of functions of more than one variable.
  • Double integrals
    • Over rectangular regions
    • Over non-rectangular regions
    • In polar coordinates
  • Triple Integrals
    • Over rectangular regions
    • In Cylindrical coordinates
    • In Spherical coordinates
  • Line Integrals
  • Green’s Theorem

Lesson plan

  • First part: Vector functions
    • Fri Aug 21: 12.1: Coordinates in 3-space, distance [p.769 #1--8, 10--18, 20--22]
    • Mon Aug 24: 12.2: Vectors [p.777 #2-23]
    • Wed Aug 26: 12.3: Dot product, projections [p.784 #3--10, 15--24, 29--33, 35--40]
    • Fri Aug 28: 12.4: Cross and triple products [p.792 #1--5, 17--20, 27--38]
    • Mon Aug 31: 12.5: Equations of lines and planes [p.802 #1--38, 43--46, 49--58, 67--72]
    • Wed Sep 02: 12.6: Cylinders and Quadratic surfaces [p.810 #3--8, 29--36]
    • Fri Sep 04: 13.1 and 13.2: Vector functions, derivatives and integrals [p.822 #2, 4, 5, 7, 10--18, 26--28, 35--38]
    • Wed Sep 09: 13.3: Curvature, principal normal [p.828 #3--26; p.836 #1--6, 11, 12, 17--20, 27--29, 43, 44]
    • Fri Sep 11: 13.4: Motion, velocity, acceleration [p.846 #3--14, 19]
    • Mon Sep 14: First Midterm---sections 12.1--12.6, 13.1--13.4
  • Second Part: Functions of several variables
    • Wed Sep 16: 14.1 and 14.2: Intro to functions of several variables, limits [p.866 #6, 8, 10--17, 21--29, 35--48]
    • Fri Sep 18: 14.2 and 14.3: Limits and Continuity [p.877 #5--18, 29--34, 37, 38]
    • Mon Sep 21: 14.3: Partial derivatives, higher order partials, mixed partials [p.889 #15--38, 43--48, 51--56, 77--85]
    • Wed Sep 23: 14.4: Tangent planes, linear approximation [p.899 #1--6, 18, 19, 25--27, 31--37]
    • Fri Sep 25: Review
    • Mon Sep 28: 14.5: Chain rule, Implicit differentiation [p.907 #1--12, 27--34]
    • Wed Sep 30: Review
    • Fri Oct 02: 14.6: Directional derivatives, gradients [p.920 #4--35]
    • Mon Oct 05: Classes canceled
    • Wed Oct 07: Classes canceled
    • Fri Oct 09: Classes canceled
    • Mon Oct 12: 14.7: Maxima and minima [p.930 #5--20, 29--36, 39--54]
    • Wed Oct 14: 14.8: Lagrange multipliers [most story problems from last section (39--54) can be done with Lagrange multipliers. That's today's HW]
    • Fri Oct 16: Second Midterm---sections 14.1--14.7
      Click [here] to retrieve the exam.</br>
  • Third Part: Integration
    • Mon Oct 19: 15.1 and 15.2: Double integrals over rectangles, Iterated integrals [p.964 #3--22]
      [Review of Integration techniques]</br>
    • Wed Oct 21: 15.3: Double integrals over general regions [p.972 #1--18]
    • Mon Oct 26: 15.4: Double integrals in polar coordinates [p.978 #5--27]
    • Wed Oct 28: 15.6: Intro to Triple integrals [p.998 #9--22]
    • Fri Oct 30: 15.7 and 15.8: Cylindrical and Spherical coordinates [No HW today]
    • Mon Nov 02: 15.7: Triple integrals in cylindrical coordinates
    • Wed Nov 04: 15.7: Triple integrals in spherical coordinates I
    • Fri Nov 06: 15.8: Triple integrals in spherical coordinates II [p.1010 #11--14, 21--27, 39, 40]
    • Mon Nov 09: 15.9: Change of variables in multiple integrals [p.1020 #1--15, 19--22]
    • Wed Nov 11: Third Midterm---sections 14.7, 14.8, 15.1--15.9
  • Fourth Part: Green's Theorem
    • Fri Nov 13: 16.1: Intro to Vector fields [p.1032 #1--4, 21--24]
    • Mon Nov 16: 16.2: Line integrals [p.1043 #1--16, 19--22]
    • Wed Nov 18: 16.3: The Fundamental Theorem for Line integrals [p.1053 #12--18]
    • Fri Nov 20: 16.4: Green's Theorem [p.1060 #1--14]
    • Mon Nov 23: Fourth midterm---sections 15.6--15.9
    • Mon Nov 30: Review for final exam
    • Wed Dec 02: Review for final exam
    • Dri Dec 04: Review for final exam