M408D: Sequences, Series, and Multivariable Calculus (Fall 2011)
This is the course page for sections 54550, 54555, and 54560 of M408D.
Table of Contents
Announcements
- FINALS WEEK OFFICE HOURS James Pascaleff will have office hours Monday 12/5, 10 am-12 pm in RLM 11.166. He will also hold usual office hours on Wednesday 12/7, 10-11 am and 3-4 pm.
- REVIEW SESSION Oscar Lopez will hold a review session Tuesday, 12/6, 4-6 pm, in room RLM 7.104
- The final homework, due Tuesday 12/6, is an extra credit assignment.
- James Pascaleff's office hours on Monday, October 17, will be 2:00 pm-3:00 pm instead of the usual 11:00 am-12:00 pm.
- The grader has requested that everyone staple their written homework before turning it in. Please do so, or you may lose points starting with the third assignment.
- If you receive a request to take an assessment test on Quest, you should go ahead and do it, as this will help the College of Natural Sciences develop new tests. Your score will not be counted toward your grade in this course.
Course Information
- Lecture
- MWF 1:00-2:00 pm in RLM 4.102
- Instructor: James Pascaleff
- Email: jpascaleff@math.utexas.edu Office: RLM 11.166 Office hours: M 11-12, W 10-11 & 3-4
- Teaching Assistant: Oscar Lopez
- Email: olopez@math.utexas.edu Office: RLM 13.156 Office hours: M 2-3:30, F 4-5:30
- Discussion Sections
-
Unique ID 54550 54555 54560 Time TTH 8:30-9:30 am TTH 4:00-5:00 pm TTH 5:00-6:00 pm Location RLM 5.118 ENS 126 RLM 6.124 - Textbook
- Calculus by James Stewart. 6th Edition, Brooks-Cole Cengage Learning.
- Prerequisites
- A grade of C- or better in M408C or M408L, or equivalent.
- Homework
- Starting September 6, Homework will be due in discussion section and on Quest.
- Midterm Exams
- Friday, September 23: L'Hospital's rule, improper integrals, testing sequences and series, power series Friday, October 21: Taylor series, parametric equations and polar coordinates, vectors, dot and cross products Friday, November 18: Vectors and the geometry of space, vector functions, partial derivatives up to Lagrange multipliers
- Final Exam
- Thursday, December 8, 2:00-5:00 pm, SAC 1.402.
- Grading
-
Written Homework 5% Quest Homework 5% Midterm Exams 45% (3 at 15% each) Final Exam 45% - Grade Scale
-
A 93-100 C 73-76 A- 90-92 C- 70-72 B+ 87-89 D+ 67-69 B 83-86 D 63-66 B- 80-82 D- 60-62 C+ 77-79 F 0-59
Course Description
M408D is the second semester of the standard calculus sequence aimed at students in the natural sciences, the social sciences, and engineering. The topics covered include infinite series, an introduction to vectors and vector calculus in two-dimensional and three-dimensional space, parametric equations, partial derivatives, gradients, and multiple integrals. The emphasis of the course is on computational methods, not proofs. The course meets three hours per week for lectures and two hours per week for discussion sections.
Note: The pace of M408C and M408D is brisk. For this reason, transfer students with one semester of calculus at another institution are requested to consult with the Undergraduate Adviser for Mathematics to determine whether M408D or an alternative, M308L, is the appropriate second course.
Course Plan & Lecture Notes
| Date | Topic | Lecture Notes |
| W 8/24 | 7.8 Indeterminate Forms and L'Hospital's Rule | notes |
| F 8/26 | 8.8 Improper Integrals | notes |
| M 8/29 | 12.1 Sequences | notes |
| W 8/31 | 12.2 Series | notes |
| F 9/2 | 12.3 The Integral Test and Estimates of Sums | notes |
| M 9/5 | Labor Day (no class) | |
| W 9/7 | 12.4 The Comparison Tests | notes |
| F 9/9 | 12.5 Alternating Series | notes |
| M 9/12 | 12.6 Absolute Convergence and the Ratio and Root Tests | notes |
| W 9/14 | 12.7 Strategy for Testing Series | notes |
| F 9/16 | 12.8 Power Series | notes |
| M 9/19 | 12.9 Representations of Functions as Power Series | notes |
| W 9/21 | 12.10 Taylor and Maclaurin Series | notes |
| F 9/23 | First Midterm Exam | |
| M 9/26 | 12.11 Applications of Taylor Polynomials | notes |
| W 9/28 | 11.1 Curves Defined by Parametric Equations | notes |
| F 9/30 | 11.2 Calculus with Parametric Curves | notes |
| M 10/3 | 11.3 Polar Coordinates | notes |
| W 10/5 | 11.4 Areas and Lengths in Polar Coordinates | notes |
| F 10/7 | 13.1 Three-Dimensional Coordinate Systems | notes |
| M 10/10 | 13.2 Vectors | notes |
| W 10/12 | 13.3 The Dot Product | notes |
| F 10/14 | 13.4 The Cross Product | notes |
| M 10/17 | 13.5 Equations of Lines and Planes | notes |
| W 10/19 | 13.6 Cylinders and Quadric Surfaces | notes |
| F 10/21 | Second Midterm Exam | |
| M 10/24 | 14.1 Vector Functions, 14.4 Velocity and Acceleration | notes |
| W 10/26 | 14.2 Calculus of Vector Functions | notes |
| F 10/28 | 14.3 Arclength, 15.1 Several Variables, 15.2 Limits and Continuity | notes |
| M 10/31 | 15.3 Partial Derivatives | notes |
| W 11/2 | 15.4 Tangent Planes and Linear Approximations | notes |
| F 11/4 | 15.5 The Chain Rule | notes (revised) |
| M 11/7 | 15.6 Directional Derivatives and the Gradient Vector | notes |
| W 11/9 | 15.7 Maximum and Minimum Values | notes |
| F 11/11 | 15.8 Lagrange Multipliers | notes |
| M 11/14 | 16.1 Double Integrals over Rectangles | notes |
| W 11/16 | 16.2 Iterated Integrals | notes |
| F 11/18 | Third Midterm Exam | |
| M 11/21 | 16.3 Double Integrals over General Regions | notes |
| W 11/23 | 16.4 Double Integrals in Polar Coordinates | notes |
| F 11/25 | Thanksgiving Holiday (no class) | |
| M 11/28 | 16.6 Triple Integrals | notes |
| W 11/30 | 16.9 Change of Variables in Multiple Integrals | notes |
| F 12/2 | Review | notes |
Textbook
The required textbook is Calculus, 6th edition, by James Stewart.
Homework
Written homework is due in your discussion section on the due date. Also do the Quest homework, due at 8:30 am on the due date.
| Due Date | Section in Stewart | Problems | Solution |
|---|---|---|---|
| T 9/6 | 7.8 | 56 | |
| 8.8 | 78 | ||
| 12.1 | 34, 64, 66, 68 | 68 | |
| 12.2 | 30, 32, 48, 52 | ||
| T 9/13 | 12.3 | 2, 30, 42 | |
| 12.4 | 26, 28, 30, 44 | 44 | |
| 12.5 | 16, 24, 34 | ||
| T 9/20 | 12.6 | 30, 32, 39 | 39 |
| 12.7 | 10, 22 | ||
| 12.8 | 30, 38, 39, 40 | ||
| T 9/27 | 12.9 | 32, 38 | 38 |
| 12.10 | 58, 62, 64 | ||
| T 10/04 | 12.11 | 26, 33, 37 | |
| 11.1 | 42, 43, 46 | ||
| 11.2 | 30, 32, 53 | 53 | |
| T 10/11 | 11.3 | 83 | |
| 11.4 | 18, 38, 46 | 38 | |
| 13.1 | 20, 21, 38 | ||
| T 10/18 | 13.2 | 28, 34, 38 | |
| 13.3 | 46, 52, 58 | 58 | |
| 13.4 | 38, 40, 42, 46 | ||
| T 10/25 | 13.5 | 60, 62, 66 | |
| 13.6 | 46, 49, 50 | 50 | |
| T 11/1 | 14.1 | 42 | |
| 14.2 | 50 | ||
| 14.4 | 28 | 28 | |
| 15.1 | 50 | ||
| 15.2 | 44 | ||
| T 11/8 | 15.3 | 77, 88 (computer part optional) | |
| 15.4 | 38, 42 | 42 | |
| 15.5 | 18, 50 | ||
| T 11/15 | 15.6 | 32, 38, 49, 56 | |
| 15.7 | 42, 44, 54 | ||
| 15.8 | 26, 30, 32 | 26 | |
| T 11/22 | 16.1 | 4, 8, 17, 18 | 17 |
| 16.2 | 31, 38 | ||
| T 11/29 | 16.3 | 40, 42, 58 | |
| 16.4 | 36 | 36 | |
| T 12/6 | Quest Only | EXTRA CREDIT |
ADDED The grader has requested that everyone staple their written homework before turning it in. Please do so, or you may lose points starting with the third assignment.
Homework policies
Starting September 6, homework will be due each Tuesday in the discussion section. The homework will consist of written exercises from the textbook and online exercises on Quest. The written homework will be posted on this website and announced in class one week before it is due. The online homework will be posted directly on Quest.
When grading written homework, one or two exercises will be chosen from the assignment and graded in depth, and the other exercises will be graded for completion.
The two lowest written homework scores and the two lowest Quest homework scores will be dropped when computing the homework score.
Late homework will not be accepted. Because the two lowest scores are dropped, you can miss one or two assignments without penalty.
Many of the problems on the written homework will require you not only to provide an answer but to justify it. This means that you must show the steps that lead to your answer, and that the correct answer by itself will not necessarily yield full credit.
You may work with other students on written homework, but you must write up your solutions and submit work to Quest by yourself. Please indicate on your homework the students that you work with.
Quest Fee
This course makes use of the web-based Quest content delivery and homework server system maintained by the College of Natural Sciences. This homework service will require a $22 charge per student for its use, which goes toward the maintenance and operation of the resource. Please go to http://quest.cns.utexas.edu to log in to the Quest system for this class. After the 12th day of class, when you log into Quest you will be asked to pay via credit card on a secure payment site. You have the option to wait up to 30 days to pay while still continuing to use Quest for your assignments. If you are taking more than one course using Quest, you will not be charged more than $50/semester. Quest provides mandatory instructional material for this course, just as is your textbook, etc. For payment questions, email quest.fees@cns.utexas.edu.
Exams
The three midterm exams will be given in lecture, at the usual time and location. The exams are cumulative, but each focuses on one portion of the course. The dates and topics of the exam are:
| Friday, September 23 | L'Hospital's rule, improper integrals, testing sequences and series, power series |
| Friday, October 21 | Taylor series, parametric equations and polar coordinates, vectors, dot and cross products |
| Friday, November 18 | Vectors and the geometry of space, vector functions, partial derivatives up to Lagrange multipliers |
The final exam will be held on Thursday, December 8 at 2:00-5:00 pm in SAC 1.402. The final exam is comprehensive.
Exam solutions
Exam 3 curve
The third exam was clearly more difficult than the first two, so there was a curve. To keep the bookkeeping simple, you will find your raw score on Quest, and you can use the following table to interpret it:
| Score | Grade |
|---|---|
| 89-110 | A |
| 85-88 | A- |
| 80-84 | B+ |
| 74-79 | B |
| 70-73 | B- |
| 65-69 | C+ |
| 59-64 | C |
| 55-58 | C- |
| 50-54 | D+ |
| 44-49 | D |
| 40-43 | D- |
Exam policies
No calculators or notes will be used on exams.
Students who have prior commitments that interfere with the exam times should let the instructor know before the 12th class day, September 9th, so that appropriate accomodations can be made.
If you are unable to take an exam due to an emergency, you must let the instructor know as soon as you yourself become aware that you are likely to miss the exam. It is particularly important that you notify the instructor before the beginning of the exam. Otherwise, you will recieve a grade of 0 on the exam. Make-up exams or other accomodations will be offered for excused absences as appropriate to each student's situation.
The final exam will be offered only at the time set by the Registrar. Extraordinary circumstances that cause a student to miss the final exam will be handled in accordance with the policies of the College of Natural Sciences and the University.
Grading
Homework contributes 10% to the final grade, with the written and Quest portions being worth 5% each. Each of the three midterm exams contributes 15%, and the final exam contributes 45%. Attendance does not contribute directly to the final grade.
Grade Scale
| A | 93-100 | C | 73-76 |
| A- | 90-92 | C- | 70-72 |
| B+ | 87-89 | D+ | 67-69 |
| B | 83-86 | D | 63-66 |
| B- | 80-82 | D- | 60-62 |
| C+ | 77-79 | F | 0-59 |
Under certain circumstances, and at the sole discretion of the instructor, this grading scale may be modified to make it easier, but never harder. It will not be possible to determine whether such a modification is appropriate until the final exam has been graded.
Deadlines for dropping the course
If you drop a class on or before September 9, the class will not show up on your transcript. If you drop a class after that date, the course will show up on the transcript with a grade of "Q". After November 1, it is not possible to drop a course except for extenuating (usually non-academic) circumstances.
Religious Holidays
In accordance with UT Austin policy, please notify the instructor at least 14 days prior to the date of observance of a religious holiday. If you cannot complete a homework assignment in order to observe a religious holiday, you will be excused from the assignment. If the holiday conflicts with an exam, you will be allowed to write a make-up exam within a reasonable time.
Special Needs
Students with disabilities may request appropriate academic accommodations from the Division of Diversity and Community Engagement, Services for Students with Disabilities at 471-6259 (voice), 232-2937 (video), or http://www.utexas.edu/diversity/ddce/ssd.
Academic Integrity
If you work with other students, indicate this on your homework. You must write up your homework by yourself. Read the University's standard on academic integrity found on the Student Judicial Services website.