FINAL EXAM will be SATURDAY DEC 11, 2pm-5pm. It will be held in the usual classroom RLM 4.102

Here are ANSWERS TO TEST 3. Other answers may also be correct.

Instructor: Dave Rusin (rusin@math.utexas.edu) Office hrs: T, Th 11-2 and by appointment, in RLM 9.140 Teaching asst: Zhihui Xie (zxie@math.utexas.edu) Office hrs: M 9-10am and (new!) T,Th 7:30-8:30 pm in RLM 11.134 Text: Calculus (6th Edition) by James Stewart Lecture: RLM 4.102, T,Th 3:30-5pm Discussions: MW 8-9am RLM 6.118 (54750), MW 3-4 RLM 6.104 (54755), MW 4-5 JES A307A (54760)

Course webpage: http://www.ma.utexas.edu/~rusin/408D/

This course is a continuation of M408C and covers a variety of topics in the theory of functions of one or more variables: indeterminate limits, improper integrals, infinite sequences, power and Taylor series, parametric curves, and derivatives and integrals of vector and multivariable functions with applications. Its objective is to provide students with practical mathematical skills necessary for advanced studies in all areas of science and engineering. The prerequisite is a grade of at least C in Mathematics 408C or 408L.

Your semester grade will be based on a number of components. This structure is designed to encourage you to stay actively involved in the course all the way through the semester. Any adjustments to the schedules or policies will be announced multiple times in lecture and on Blackboard and on the course website shown above.

Homeworks: I would like to try something new: the Quest homework system. This will enable you to get constant feedback on how well you are understanding the material. When the system is properly set up and functioning, you will be able to see your assignments at https://quest.cns.utexas.edu/ The homework must be completed online by the date posted, typically about one week after it becomes available. You will accumulate points during the semester, and your "Homework score" will be the number of points earned divided by the possible number of points you could have earned, times 100.

Quizzes: There will be a quiz (almost) every Wednesday. As with the homeworks, this will give you a "Quiz score" of up to 100 points.

Exams: There will be 3 mid-term exams, on September 23, October 21,
and November **23**, during the usual class period. Each is worth 100 points.
The final exam will be Saturday, December 11 2010 from 2pm until 5pm; it
is worth 200 points. (Location to be announced.) Textbooks, notes, and
electronic devices (including phones and calculators) are not permitted
during exams.

Your semester grade is based only on the number of points accumulated from this mix of 700 possible points. Your grade will be no lower than what is indicated from this table:

Point total | Semester grade |

650-700 | A |

630-649 | A- |

610-629 | B+ |

580-609 | B |

560-579 | B- |

540-559 | C+ |

510-539 | C |

490-509 | C- |

470-489 | D+ |

440-469 | D |

420-439 | D- |

0-419 | F |

Students with disabilities: The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities. For more information, contact the Office of the Dean of Students at 471-6259, 471-4641 TTY.

Drop dates: The last day to drop the course without possible academic penalty is Sept 22, 2010. For more information about deadlines for adding and dropping the course under different circumstances, please consult the Registrar's web page, http://registrar.utexas.edu/calendars/10-11/

- Drop-In Tutoring -- A free, walk-in study environment supported by Sanger's mathematics tutors (for students enrolled in 302, 303D, 305G, 408C/D, 408K/L/M, 408N/S)
- Appointment Tutoring -- Individualized one-hour meetings with one of the mathematics tutors (for students enrolled in 302, 303D, 305G, 315C, 316, 316K/L, 325K, 408C/D, 408K/L/M, 408N/S, 427K)
- Small Group Tutoring -- Arranged group study for students enrolled in a common class, supported by the mathematic tutors (for students enrolled in 302, 305G, 408C/D, 408K/L/M, 408N/S and possibly more -- by request)

My tentative plan (subject to change!):

- Thursday, August 26: 7.8 - LHopital's Rule
- Tuesday, August 31: 8.8- Improper integrals
- Thursday, September 2: 12.1 - Sequences
- Tuesday, September 7: 12.2 - Series
- Thursday, September 9: 12.3, 12.4 - integral test, comparison
- Tuesday, September 14: 12.5, 12.6 - alternating series; absolute cvg
- Thursday, September 16: 12.7 - strategies for testing convergence
- Tuesday, September 21: 12.8, 12.9 - power series, series as functions
- Thursday, September 23: Midterm exam
- Tuesday, September 28: 12.10 - Taylor series
- Thursday, September 30: 12.10, 12.11 - Taylor series and applications
- Tuesday, October 5: 11.1, 11.2 - parametric curves
- Thursday, October 7: 11.2, 11.3 - calculus on curves, polar coords
- Tuesday, October 12: 11.3, 11.4 - polar coordinates
- Thursday, October 14: 13.1, 13.2 - 3D coordinates, vectors
- Tuesday, October 19: 13.3, 13.4 - dot product, cross product
- Thursday, October 21: Midterm exam
- Tuesday, October 26: 13.5, 13.6 - lines, planes, surfaces in R^3
- Thursday, October 28: 14.1 - vector functions
- Tuesday, November 2: 14.2 (14.3 14.4) - vector calculus
- Thursday, November 4: 15.1, 15.2 - functions on R^n
- Tuesday, November 9: 15.3 - partial derivatives
- Thursday, November 11: 15.4 - tangent planes, linearization
- Tuesday, November 16: 15.5, 15.6 - Chain Rule, directional derivatives
- Thursday, November 18: 15.7, 15.8 - min/max problems in R^n
- Tuesday, November 23: Midterm exam
- Thursday, November 25: No class -- Thanksgiving holiday
- Tuesday, November 30: 16.1, 16.2 - iterated integrals
- Thursday, December 2: 16.3, 16.4 - surface integrals