## MA241—Spring 2014

## Instructor

Francisco Blanco-Silva

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

**office:** LeConte 307

## Meeting Times and Office Hours

Lectures: |
MWF |
10:50 AM – 11:40 AM | LeConte 112 | |

Office Hours: |
MWF |
9:30 AM -10:45 AM | LeConte 307 |

## Important deadlines you need to know

The semester begins Monday, January 13^{rd}, and ends Monday, April 28^{th}. The last day to obtain a “W” grade or to elect a pass/fail grade is Monday, March 3^{rd}. The first day in which a “WF” grade is assigned is therefore Tuesday, March 4^{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 | Student Solutions Manual |

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 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) + 0.40 * 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 5273 7839`Click [here] to retrieve further registration instructions.

**Midterm Exams**: (up to 100 points each) 45% of the course grade (15% each midterm). There will be three in-class midterm exams scheduled as follows:

Test # Date **1**Wed, Feb 05 **2**Wed, Mar 07 **3**Fri, Apr 11 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) 40% of the course grade. The final exam is scheduled on Monday, May 5^{th}from 9:00 AM to 11:30 AM.

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.

## 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****Mon Jan 13**: 12.1: Coordinates in 3-space, distance [p.769 #1–8, 10–18, 20–22]**Wed Jan 15**: 12.2: Vectors [p.777 #2-23]**Fri Jan 17**: 12.3: Dot product, projections [p.784 #3–10, 15–24, 29–33, 35–40]**Wed Jan 22**: 12.4: Cross and triple products [p.792 #1–5, 17–20, 27–38]**Fri Jan 24**: 12.5: Equations of lines and planes [p.802 #1–38, 43–46, 49–58, 67–72]**Mon Jan 27**: 12.5: Equations of lines and planes II**Wed Jan 29**: Winter weather advisory: Classes cancelled**Fri Jan 31**: 12.6: Cylinders and Quadratic surfaces [p.810 #3–8, 29–36]**Mon Feb 03**: 13.1: Intro to Vector functions [No HW today]**Wed Feb 05**: First Midterm—sections 12.1–12.5**Fri Feb 07**: 13.2: Derivatives and integrals of vector functions [p.822 #2, 4, 5, 7, 10–18, 26–28, 35–38]**Mon Feb 10**: 13.3: Curvature, principal normal [p.828 #3–26; p.836 #1–6, 11, 12, 17–20, 27–29, 43, 44]**Wed Feb 12**: Winter weather advisory: Classes cancelled**Fri Feb 14**: Winter weather advisory: Classes cancelled

**Second Part: Functions of several variables****Mon Feb 17**: 14.1 and 14.2: Intro to functions of several variables, limits [p.866 #6, 8, 10–17, 21–29, 35–48]**Wed Feb 19**: 14.2 and 14.3: Limits and Continuity [p.877 #5–18, 29–34, 37, 38]**Fri Feb 21**: 14.3: Partial derivatives, higher order partials, mixed partials [p.889 #15–38, 43–48, 51–56, 77–85]**Mon Feb 24**: 14.4: Tangent planes, linear approximation [p.899 #1–6, 18, 19, 25–27, 31–37]**Wed Feb 26**: 14.5: Chain rule, Implicit differentiation [p.907 #1–12, 27–34]**Fri Feb 28**: 14.6: Directional derivatives, gradients [p.920 #4–35]**Mon Mar 03**: 14.7: Maxima and minima [p.930 #5–20, 29–36, 39–54]**Wed Mar 05**: 14.7: Maxima and minima II**Fri Mar 07**: Second Midterm—sections 13.1–13.4, 14.1–14.7**Mon Mar 17**: 14.8: Lagrange multipliers [all story problems (39–54) from last section can be done with Lagrange multipliers. That’s today’s HW]**Wed Mar 19**: 14.8: Lagrange multipliers II

**Third Part: Integration****Fri Mar 21**: 15.1 and 15.2: Double integrals over rectangles, Iterated integrals [p.964 #3–22]**Mon Mar 24**: 15.3: Double integrals over general regions [p.972 #1–18]**Wed Mar 26**: 15.4: Double integrals in polar coordinates [p.978 #5–27]**Fri Mar 28**: 15.5: Applications [p.988 #3–20]**Mon Mar 31**: 15.6: Intro to Triple integrals [p.998 #9–22]**Wed Apr 02**: 15.7 and 15.8: Cylindrical and Spherical coordinates [No HW today]**Fri Apr 04**: 15.7: Triple integrals in cylindrical coordinates**Mon Apr 07**: 15.8: Triple integrals in spherical coordinates [p.1010 #11–14, 21–27, 39, 40]**Wed Apr 09**: 15.9: Change of variables in multiple integrals [p.1020 #1–15, 19–22]**Fri Apr 11**: Third Midterm—sections 15.1–15.9

**Fourth Part: Green’s Theorem****Mon Apr 14**: 16.1: Intro to Vector fields [p.1032 #1–4, 21–24]**Wed Apr 16**: 16.2: Line integrals I [p.1043 #1–16]**Fri Apr 18**: 16.2: Line integrals II [p.1043 #19–22]**Mon Apr 21**: 16.3: The Fundamental Theorem for Line integrals [p. 1053 #12–18]**Wed Apr 23**: 16.4: Green’s Theorem [p.1060 #1–14]**Fri Apr 25**: Overview of the course: putting it all together.**Mon Apr 28**: Review**Mon May 05**: 9:00 AM–11:30 AM

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