## MA241—Fall 2012

# MATH 241. Section 003

## Instructor

Francisco Blanco-Silva

**e-mail:** `blanco at math dot sc dot edu`

**office:** LeConte 307

## Meeting Times and Office Hours

Lectures: |
MWF |
12:20 AM – 1:10 PM | LeConte 115 | |

Office Hours: |
TTh |
1:00 PM – 4:00 PM | LeConte 307 |

## Important deadlines you need to know

The semester begins Thursday, August 23^{rd}, and ends Friday, December 7^{th}.

The deadline to drop/add and the last day to change credit/audit is Wednesday, August 29^{th}. The first day in which a “W” grade is assigned is therefore Thursday, August 30^{th}.

The last day to obtain a “W” grade or to elect a pass/fail grade is Thursday, October 11^{th}. The first day in which a “WF” grade is assigned is therefore Friday, October 12^{th}.

## Prerequisites

Qualifications through Placement or a grade of **C** or better in MATH 142

## Text

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

[Calculus: Early Transcendentals (Stewart’s Calculus Series) (See all Calculus Books)]

You will be required to use Enhanced WebAssign, the online homework system that accompanies your textbook, for my course. I strongly encourage you to purchase an access code that provides you access to Enhanced WebAssign and the eBook rather than a traditional hard copy of the text. (If you choose to purchase a hard copy, you will need to purchase the bundle that comes with the Enhanced WebAssign code.)

## Course Structure and Grading Policies

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

F = 0.15 * (HW + ME1 + ME2 + ME3 + ME4) + 0.25 * FE |

**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 www.webassign.net and click on [

**I have a Class Key**]. The class key for this section is`sc 9319 7695`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 17 **2**Mon, Oct 08 **3**Mon, Nov 05 **4**Fri, Nov 30 No make-up tests will be given. Only medical, death in the family, religious or official USC business reasons are valid excuses for missing a test and must be verified by letter from a doctor, guardian or supervisor to the instructor.

**Final Exam**: (up to 100 points) 25% of the course grade. The final exam is scheduled on Thursday, December 13^{th}from 12:30 PM to 3:00 PM.

The course grade will be determined as follows:

GRADE | RANGE |

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

- Remember to change your e-mail address on Blackboard if necessary [blackboard.sc.edu]
**ADA**: If you have special needs as addressed by the*Americans with Dissabilities Act*and need any assistance, please notify the instructor immediately.**Math Tutoring Center:**The Math Tutoring Center is a free tutoring service for MATH 111, 115, 122, 141, 142, 170, 221, 222, and 241. The center also 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 (www.math.sc.edu). No appointment is necessary.**Peer Tutoring:**Tutoring is available for this course to assist you in better understanding the course material. The Peer Tutoring Program at the Student Success Center provides free peer-facilitated study sessions led by qualified and trained undergraduate tutors who have previously taken and excelled in this course. Sessions are open to all students who want to improve their understanding of the material, as well as their grades. Tutoring is offered Sunday 6-10pm and Monday through Thursday 2-9pm. All tutoring sessions will take place on the Mezzanine Level of the Thomas Copper Library unless otherwise noted. Please visit www.sc.edu/tutoring to find the complete tutoring schedule and make an appointment. You may also contact the Student Success Center at 803-777-1000 and tutoring@sc.edu with additional questions. The tutor for your course is Emmaline Horton.

## 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, HW Assignments, Quizzes, Exams

**First part: Vector functions****Fri Aug 24**: 12.1 and 12.2: Coordinates in 3-space, distance, vectors [p.769 #1–8, 10–18, 20–22; p.777 #2-23]**Mon Aug 27**: 12.3: Dot product, projections [p.784 #3–10, 15–24, 29–33, 35–40]**Wed Aug 29**: 12.4: Cross and triple products [p.792 #1–5, 17–20, 27–38]**Fri Aug 31**: 12.5: Equations of lines and planes [p.802 #1–38, 43–46, 49–58, 67–72]**Wed Sep 05**: 12.6: Quadratic surfaces [p.810 #3–8, 29–36]**Fri Sep 07**: 13.1 and 13.2: Vector functions, derivatives and integrals [p.822 #2, 4, 5, 7, 10–18, 26–28, 35–38]**Mon Sep 10**: 13.3: Curvature, principal normal [p.828 #3–26; p.836 #1–6, 11, 12, 17–20, 27–29, 43, 44]**Wed Sep 12**: 13.4: Motion, velocity, acceleration [p.846 #3–14, 19]**Fri Sep 14**: Review for First midterm [Practice exam]**Mon Sep 17**: First Midterm—sections 12.1–12.6, 13.1–13.4

**Second Part: Functions of several variables****Wed Sep 19**: 14.1 and 14.2: Intro to functions of several variables, limits [p.866 #6, 8, 10–17, 21–29, 35–48]**Fri Sep 21**: 14.2 and 14.3: Limits and Continuity [p.877 #5–18, 29–34, 37, 38]**Mon Sep 24**: 14.3: Partial derivatives, higher order partials, mixed partials [p.889 #15–38, 43–48, 51–56, 77–85]**Wed Sep 26**: 14.4: Tangent planes, linear approximation [p.899 #1–6, 18, 19, 25–27, 31–37]**Fri Sep 28**: 14.5: Chain rule, Implicit differentiation [p.907 #1–12, 27–34]**Mon Oct 01**: 14.6: Directional derivatives, gradients [p.920 #4–35]**Wed Oct 03**: 14.7: Maxima and minima [p.930 #5–20, 29–36, 39–54]**Fri Oct 05**: 14.7: Maxima and minima II**Mon Oct 08**: Second Midterm—sections 14.1–14.7

**Third Part: Integration****Wed Oct 10**: 14.8: Lagrange multipliers [all story problems (39–54) from last section can be done with Lagrange multipliers. That’s today’s HW]**Fri Oct 12**: 15.1 and 15.2: Double integrals over rectangles, Iterated integrals [p.964 #3–22]**Mon Oct 15**: 15.3: Double integrals over general regions [p.972 #1–18]**Wed Oct 17**: 15.4: Double integrals in polar coordinates [p.978 #5–27]**Mon Oct 22**: 15.5: Applications [p.988 #3–20]**Wed Oct 24**: 15.6: Intro to Triple integrals [p.998 #9–22]**Fri Oct 26**: 15.7 and 15.8: Cylindrical and Spherical coordinates [No HW today]**Mon Oct 29**: 15.7: Triple integrals in cylindrical coordinates**Wed Oct 31**: 15.8: Triple integrals in spherical coordinates [p.1010 #11–14, 21–27, 39, 40]**Fri Nov 02**: 15.9: Change of variables in multiple integrals [p.1020 #1–15, 19–22]**Mon Nov 05**: Third Midterm—sections 15.1–15.9

**Fourth Part: Green’s Theorem****Wed Nov 07**: 16.1: Intro to Vector fields [p.1032 #1–4, 21–24]**Fri Nov 09**: 16.2: Line integrals I [p.1043 #1–16]**Mon Nov 12**: 16.2: Line integrals II [p.1043 #19–22]**Wed Nov 14**: 16.3: The Fundamental Theorem for Line integrals [p. 1053 #12–18]**Fri Nov 16**: 16.4: Green’s Theorem [p.1060 #1–14]**Mon Nov 19**: Overview of the course: putting it all together.**Mon Nov 26**: Fourth midterm—First session [Take-home]**Wed Nov 28**: Fourth midterm—Second session Second chances**Fri Nov 30**: Fourth Midterm—Third session [In-class test]

**Final Stretch:****Mon Dec 03**: [Review for Final Exam (1/3)]**Wed Dec 05**: [Review for Final Exam (2/3)]**Fri Dec 07**: [Review for Final Exam (3/3)]**Thu Dec 13**: 12:30 PM–3:00 PM

Comprehensive exam—Chapters 12, 13, 14, 15 and 16