### Meeting Times

Lectures: |
TTh 9:30 AM - 10:45 AM |
LeConte 113 |

Problem Sessions: |
Sect 001. M 8:00 AM - 8:50 AM |
LeConte 121 |

Sect 002. M 9:05 AM - 9:55 AM |
LeConte 121 | |

Computer Labs: |
Sect 001. F 8:00 AM - 8:50 AM |
LeConte 102 |

Sect 002. F 9:05 AM - 9:55 AM |
LeConte 102 |

### Office Hours

TTh 2:00 PM — 3.00 PM in LeConte 307.

### Teaching Assistant

**Office Hours**: MF 10.00am--11.00am, W 12.00pm--1.00pm in LC400K

`brylev at email dot sc dot edu`

### Prerequisites

Qualifications through placement or a grade of **C** or better in MATH 141. The deadline to drop/add is Wednesday, August 24^{th}. The first day in which a "W" grade is assigned is therefore August 25^{th}. The last day to obtain a "W" grade or to elect a pass/fail grade is Thursday, October 13^{th}. The first day in which a "WF" grade is assigned is therefore Friday, October 14^{th}.

### Text

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

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

### Course Structure and Grading Policies

Homework problems will be assigned at the end of each lecture. They might be collected and graded. In that case, the grade will count as a quiz. Your final score for the course will be computed as follows:

- Computer Labs: 15% of the course grade. [http://www.math.sc.edu/calclab/141L-S10/]
- Quizzes: 15% of the course grade.
**Only the 10 best scores are counted.**A ten-minute quiz will be given during the problem session. There will be no make-up quizzes, since only the best 10 grades count towards the course grade. - Midterms: each test counts 15%, for a total of 45% of the course grade.There will be three in-class midterm exams scheduled as follows:

Test # Date **1**Thursday Sep 08 **2**Tuesday Oct 04 **3**Tuesday Nov 08 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: 25% of the course grade.The final exam is scheduled on Tuesday, December 6
^{th}, at 2:00 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% |

**ATTENDANCE POLICY**: Attendance is mandatory. Penalties to your final grade apply as follows:

- Students missing four sessions without a valid excuse will have their final grade lowered by half a letter grade (e.g. from C to D+).
- Students missing six sessions without a valid excuse will have their final grade lowered by a full letter grade (e.g. from B to C)
- Students missing eight sessions without a valid excuse will have their final grade lowered by a letter-and-a-half (e.g. from A to C+)

### Further Information

Some useful 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.- 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.
- The
**Student Success Center**and one of four**Academic Centers for Excellence (ACE)**are on the mezzanine level of the Thomas Cooper Library and can be reached by phone at (803) 777-0684 or by going online at www.sc.edu/academicsuccess Other ACE locations around campus make access to these resources easy (Sims Hall, Bates House, Columbia Hall). The centers are at the crossroads of services and information about many special resources for stucents, including advice on developing successful study habits, time management, and effective learning strategies as well as availability of tutoring. - The Supplemental Instructor for this course is Kevin Wood. Kevin will be holding three sessions a week (after August 28) in the Student Success Center (SSC#2) located in the top floor of the library. His schedule is as follows:

**Sunday**8:00 PM **Tuesday**5:00 PM **Thursday**6:00 PM

### Learning Outcomes

A student who successfully completes Calculus II (MATH 142) 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:

- Techniques of integration
- Substitution
- Integration by parts
- Trigonometric integrals and trigonometric substitution
- Partial fractions

- Improper integrals
- Applications of integration in Geometry, Science and Engineering
- Area
- Volume by disks and shells
- Average value

- Convergence of sequences and series
- $latex n$—th term test (for divergence)
- Integral test
- Comparison test
- Ratio test
- Root test
- Alternating series test

- Power series
- Taylor and Maclaurin series
- Application of Taylor polynomials
- Polar coordinates
- Area and length in polar coordinates

### HW Assignments, Quizzes, Exams

**Thu Aug 18**: 5.3. The Fundamental Theorem of Calculus

[p.388 #7--10, 13, 14, 19--31, 35--40, 53--56]

Extra Credit (2pts, due Thursday Aug 25):$latex \text{If }F(x)=\displaystyle{\int_1^x} f(t)\, dt, \text{where } f(t) = \displaystyle{\int_1^{t^3} \frac{\sqrt{1+u^2}}{u}}\, du, \text{find }F''(2).\text{ Do not simplify}$**Mon Aug 22**: [Quiz#1]**Tue Aug 23**: 5.5. The Substitution Rule**[HW due Monday Aug 29]**

[p.406 #1--16, 19, 21--26, 28--32, 34, 36, 37, 40, 42, 45, 51--55, 58]

Extra Credit (2pts, due Thursday Sep 01):$latex \text{Evaluate the following integrals.}$

$latex \text{To receive credit, indicate the substitutions made, and all the necessary steps.}$$latex \displaystyle{\int \frac{\sin 2x}{1+ \cos^2 x}\, dx \qquad \int \frac{x^2}{\sqrt{1-x}}\, dx}$**Thu Aug 25**: 6.1 & 6.2. Area and Volume

[p.420 #1--28; p.430 #1--18]

Extra Credit (2pts, due Tuesday Sep 06):$latex \text{Find the area between the curves }y=\sin x, y=\cos x, x=0, x=2\pi.$$latex \text{To receive credit, indicate clearly all the integrals used.}$**Mon Aug 29**: [Quiz#2] [HW from Aug 23 due today (counts as Quiz#3)]**Tue Aug 30**: 6.3. Volume by cylindrical shells

[p.436 #3--7, 10--14, 21]**Thu Sep 01**: 6.5. The mean-value Theorem

[p.445 #1--10, 13, 14]**Tue Sep 06**: 7.1. Integration by parts

[p.457 #1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 30, 32, 34, 36, 38]

Extra Credit (2pts, due Tuesday Sep 13):$latex \text{Evaluate the following integrals }\displaystyle{\int \big( \ln x\big)^2 \, dx, \quad \int x^4 \big( \ln x\big)^2 \, dx, \quad \int \big( \ln x\big)^3 dx.}$**Thu Sep 08**: First Midterm. Chapters 5 and 6 [Practice Test]**Mon Sep 12**:**Tue Sep 13**: 7.2. Trigonometric Integration

[p.465 #1--48, 55, 57, 58, 61--64]

Extra Credit (2pts, due Tuesday Sep 20):$latex \text{Evaluate the following integral: }\displaystyle{\int \sec x\, dx = \ln \lvert \sec x + \tan x \rvert.}$**Thu Sep 15**: 7.3. Trigonometric substitutions**[HW due Monday Sep 19]**

[p.472 #4--29]

Extra Credit (2pts, due Tuesday Sep 20):$latex \text{Evaluate the following integral: }\displaystyle{\int \frac{\sqrt{1+x^2}}{x}\, dx}$**Mon Sep 19**: [Quiz #4] [HW from Sep 15 due today (counts as Quiz#5)]**Tue Sep 20**: 7.4. Integration of rational functions by partial fraction decomposition

[p.481 #7--38]

Extra Credit (2pts, due Tuesday Sep 27):$latex \text{Evaluate the following integral: }\displaystyle{\int \ln (x^2-x+2)\, dx}$**Thu Sep 22**: 7.8. Improper integrals

[p.515 #5--40]**Mon Sep 26**: [Quiz #6]**Tue Sep 27**: 7.5. Putting it all together: Integration Techniques. [Quiz#7]

Your HW for today is the [Practice Test]**Thu Sep 29**: 11.1. Sequences

[p.684 #3--46]**Mon Oct 03**: Review Second Midterm**Tue Oct 04**: Second Midterm. Chapter 7 [Practice Test]**Thu Oct 06**: 11.2. Introduction to series [Quiz #8]

[p.694 #9, 11-40]**Mon Oct 10**:**Tue Oct 11**: 11.3. The Integral test

[p.703 #3--26]**Thu Oct 13**: 11.4. The Comparison test [Quiz #9]

[p.709 #3--32]**Mon Oct 17**: [Quiz #10]**Tue Oct 18**: 11.5-11.6. Absolute convergence. The ratio and root tests [Quiz #11]

[p.713 #2--20, p.719 #2--28]**Mon Oct 24**: [Quiz #12]**Tue Oct 25**: 11.8. Power series

[p.727 #3-28]**Thu Oct 27**: 11.9. Functions as Power Series [Quiz #13]

[p.733 #3--12, 15--17]**Mon Oct 31**: [Quiz #14]**Tue Nov 01**: 11.10. Taylor and MacLaurin Series I

[p.746 #5--20]**Thu Nov 03**: 11.10. Taylor and MacLaurin Series II**Mon Nov 07****Tue Nov 08**: Third Midterm. Chapter 11 (sections 1--10) [Review: Convergence of Series]**Thu Nov 10**: 10.3. Polar coordinates

[p.647 #1ab, 3ab, 5i, 7--12, 21--26, 29--48]**Mon Nov 14**:**Tue Nov 15**: 10.4**Thu Nov 17**: Review**Mon Nov 21**:**Tue Nov 22**: Review**Mon Nov 28**:**Tue Nov 29**: Review**Thu Dec 01**: Review

**Tue Dec 06**: Final Exam. Chapters 5, 6, 7, 10 and 11