Math 231-001 Calculus and Analytic Geometry III, Fall 2008 Liberty University, Lynchburg Virginia
James S. Cook, Assistant Professor of Mathematics
Office Hours: M-T-W-R-F from 7:00am-9:00am
and M-W-F from 2:45pm-3:45pm
Applied Science 105
Email: jcook4@liberty.edu
office phone: 434-582-2476
Matthew 7:7-8 Lectures and tests are in DeMoss Learning Center room 1107
Lecture Times: T-R 12:25pm - 1:40 pm


Course Description:
A continuation of Math 132. Infinite series, power series, geometry of the plane and space, vectors, functions of several variables, multiple integrals, and an introduction to differential equations. 3 hours credit

Rationale:
Calculus can be exciting; this subject offers a student so much new scope and power. The student will learn how to set up and solve calculus problems. This course is aimed at mainstream calculus students and strives for an optimal balance of intuition and rigor. Many diverse applications will be considered in order to service the ever-expanding clientele, which includes many students outside the field of mathematics, physics, and engineering.

Prerequisites:
To enroll in this course you must have successfully completed Math 131 and Math 132, or equivalent.

Materials List:
Learning Outcomes/Requirements

  • Objectives:
    This course will be intense in the following areas: different coordinate systems, power series, vectors, functions of two variables, and double and triple integration and pragmatic use of these ideas in problem-solving endeavors.

    Each student is accountable for the following:
    1. State and apply definitions and theorems relating to the topics listed above.
    2. Understanding the idea of approximations using power series.
    3. Understanding of the power of vectors to solve many real-world problems.
    4. Ability to manipulate aspects of derivative and integration of functions.
    5. Ability to model real systems using mathematics.
    6. Competence in appropriates problem-solving skills, and an appreciation of a variety of approaches to problem solving.
    7. Learn general intellectual skills such as observing, classifying, analyzing and synthesizing.
  • Requirements:
    1. Cognitive growth:
      1. Demonstrate proficiency in the ability to take the knowledge acquired and apply it to problem-solving situations.
      2. Appreciate mathematics as a powerful tool in their discipline.
    2. Product:
      1. For each hour in class each student needs to spend at least two hours of study time.
      2. Each student from memory will write three one-hour examinations over related material covered in class. There will be a final comprehensive examination at the designated time.
      3. There will be homework assignments over material covered. These will be graded and returned.
      4. Announced and unannounced classroom quizzes may occur in this class. These will be graded and returned.
    3. Process:
      1. The method of instruction will consist of lecture and interaction with the students. There will be a free exchange of questions.
      2. The math lab will be available for help with assignments.
      3. There will be study groups formed from students taking this course.
      4. Student–Instructor conference will be used where appropriate.
    Grading Policies:
  • Students are expected to abide by the Liberty University Honor Code as stated in The Liberty Way.
  • The total number of points towards the course grade for each segment of work.
    1. [19pts] In class Homework Quizzes: you will know what the possible problems are, I select one or two and give you several minutes to copy solution neatly. Usually these are problems from your text. You have a complete list of all such problems posted on the course website. You should monitor lectures and email for any updates/hints on the list.
    2. [24pts] Out of class Homework Projects: these typically consist of problems which are designed to challenge you beyond the usual homework from the text. There will be three such assignments. It is my intention for these to be returned to you before the test.
    3. [2pts] Test reviews, mid-term evaluation survey, working Liberty University email. The test reviews are to aid your test preparation. The test reviews are multiple choice and include both conceptual questions and reminders about what's on the test, they will be available through Blackboard. The mid-term evaluation survey is an assessment tool whose goal is facilitating improvement of course before its finish. Finally, I require you have a working LU email account. Failure to keep the LU account in working order could deduct 2pts from your final grade, I sincerely hope this deduction is never enacted.
    4. [0pts] Quizzes: if the class responsibly completes the homework before the due date then no pop quizzes. If the class fails its duty to give the homework a serious effort then I will institute daily quizzes to replace the homework.
    5. [30pts] Tests: there will be three tests, I drop the lowest.
    6. [25pts] Comprehensive final exam.
  • Forming study groups is encouraged. However, it is important that you do not simply copy other student's homework. You may check answers, but you should not replicate steps. Exceptions to this rule should be clear; no group work on tests and no group work when I outlaw it. For example, I typically outlaw group work on an easy take-home test.

  • Missed Tests: If you have an emergency absence then the weight of the final will be increased. For example, if you had to help your mom evade an attacking elephant (I would need documentation and/or witnesses) during the test time then I would drop the lowest of the three tests you took and the final examination would be worth 25+15=40pts. If your absence is known ahead of time then you need to notify me so we can make arrangements.

  • Final Grade: Your final course grade will be determined by the following point scale (no rounding)
    91-100 = A
    81-90 = B
    71-80 = C
    65-70 = D
    0-64 = F

  • Warning: the purpose of Blackboard's gradebook is to provide you a complete record of your grades in this course. The correct final average will probably not be posted in Blackboard.

  • Documented Disabilities:
    Students with a documented disability may contact the Office of Disability Academic Support (ODAS) in TE 127 for arrangements for academic accommodations."

    Attendance Policies:
    Class attendance at each session is expected. If you are unable to attend, please let me know by sending me an e-mail regarding the absence. Your e-mail should be sent with-in two days of your absence. Also, if you do not attend, please send your Homework Project(s) with a roommate or other person because I do not accept late assignments. The reason that make-up work is rarely given is that I post solutions soon after the due date so accepting late assignments is typically unfair to the other students. If you know you will be absent in advance (as you would with a university authorized participation in a sporting event) then you should make arrangements to turn in an alternate assignment in early in place of the Homework Quiz or Project. It is your responsibility to notify me by email or stop by office hours so we can make these arrangements.

    Dress Code:
    Students are required to wear attire consistent with the Liberty Way.

    Agenda of Class Sessions:
    Homework Quizzes may be given during any lecture as described in the course schedule. The following is a tentative schedule which may be modified as the semester progesses. Modifications will made be known by announcements in lecture.

    Assignment Due Date
    Homework Project 1 Friday, Sept. 5 give hardcopy to me during office hours
    Test 1 Tuesday, Sept. 11
    Homework Project 2 Friday, Oct. 17, give hardcopy to me during office hours
    Test 2 Tuesday, Oct. 23
    Homework Project 3 Friday, Nov. 14, give hardcopy to me during office hours
    Test 3 Tuesday, Dec. 2
    Comprehensive Final Exam. Dec. 10 from 10:30am-12:30pm

    Section # My Notes Due Date Assignment Description / Hints / Mathematica helps
    Sec. 13.1 236-239 Aug. 21 7, 11, 13, 15, 20, 23-31(odds), 39, 40 3d-Cartesian Coordinates
    Sec. 13.2 240-250 Aug. 26 4, 5, 7, 13, 17, 21, 24, 26, 29, 31, 35 vectors
    Sec. 13.3 240-250 Aug. 26 3, 5, 7, 9, 11, 13*, 17, 19, 21, 23, 29, 31, 35-40, 45, 57* dot product
    Sec. 13.4 240-250 Aug. 26 1, 3, 5, 7, 10, 20, 33, 39, 43 cross product
    Sec. 13.5 251-256 Aug. 26 3, 5, 7, 10, 11, 14, 16, 17, 18, 25, 26, 30, 31, 35, 40, 49, 55 lines and planes
    Sec. 13.6 257-262 Aug. 28 21, 23, 25, 27, 49* functions of several variables
    Sec. 14.1 263-268 Sep. 4 7, 9, 11, 13, 19, 23, 25*, 41, 42* vector-valued functions
    Sec. 14.2 263-268 Sep. 4 5, 9, 11, 13, 15, 16, 27-33, 35, 43, 45 calculus of vector-valued functions
    Sec. 14.3 269-279 Sep. 4 1, 13 arclength and moving TNB-frame
    Sec. 14.4 280-283 Sep. 4 9, 11, 13, 15, 19, 21*, 33, motion in space
    . . Sep. 5 Homework Project I .
    Sec. 15.2 290-291 Sep. 9 5, 7, 9 limits and continuity
    Sec. 15.3 292-295 Sep. 9 5, 15-38, 41, 43*, 45, 47, 49, 50, 51, 53, 55, 56, 61, 65, 70, 71 basic partial derivatives
    Sec. 15.5 296-299 Sep. 9 1, 2, 7, 8, 10, 11, 21, 22, 25, 38, 39, 40, 45, 53 chain rule for several variables
    N/A 300-305 Sep. 9 will give in lecture, see my notes for examples* constrained partial differentiation
    Test I . Sep. 11 Test I .
    Sec. 15.4 311-313, 317-319 Sep. 23 1, 3, 11, 17, 19, 25, 27, 29, 39, 42 tangent plane and linearization
    Sec. 15.6 311-319 Sep 23 5, 8-15, 20-22, 25, 29, 31, 38, 39, 43, 53 directional derivative
    Sec. 15.7 320-324 Sep 23 5, 7, 9, 14, 29, 33, 35, 45*, 49 extrema in functions of several variables
    Sec. 17.6a 402-406 Sep. 30 1, 3, 4, 5, 6, 13, 19-26, 33-36(graph optional), parametrized surfaces and surface area
    Sec. 16.2 330-342 Oct. 7 3, 6, 7, 10, 12, 13, 15, 21, 25, 31 basic double integrals
    Sec. 16.3 330-342 Oct. 7 1, 3, 5, 7, 9, 11, 13, 16, 18, 19, 21, 33, 40, 41, 43 double integrals over general regions
    Sec. 16.6 339-343 Oct. 7 3, 5, 6, 7, 9, 10, 13, 19, 32 basic triple integrals
    Sec. 16.9 343-359 Oct. 14 1, 3, 4, 5, 6, 7, 10, 13*, 17a, 21 the Jacobian
    Sec. 16.4 343-359 Oct. 16 9, 10, 11, 13, 15, 16, 17, 19, 23, 25, 28, 31 double integrals in polar coordinates
    . . Oct. 17 Homework Project II .
    Sec. 16.7 343-359 Oct. 21 1, 3, 5, 7, 9, 11, 15, 17-20, 26*, 27 triple integrals in cylindrical coordinates
    Sec. 16.8 343-359 Oct. 21 1-27(odd), 36* triple integrals in spherical coordinates
    Test II . Oct. 23 Test II .
    Sec. 13.1 360-365 Nov. 4 1, 3, 5, 7, 15, 17, 21, 23, 24, 25, 29, 35 vector fields
    Sec. 13.5 366-368, 369-372, 373-374 Nov. 4 1, 3, 4, 5, 11, 12, 13, 15, 19-22, 30, 31, 32, 39(wildcard) curl and divergence
    Sec. 13.2 385-394 Nov. 11 1-5, 8, 11, 12, 15, 17, 18, 19-22, 39, 41, 42 line integrals
    Sec. 13.3 395-401, 400-401 Nov. 13 3, 5, 7, 11, 13, 17, 19, 21, 27, 28, 29-33, 34a FTC for line integrals, conservative forces
    Sec. 17.6b 402-406 Nov. 13 37, 41, 43 surface area
    Sec. 13.6 407-411 Nov. 13 5, 7, 11, 14, 18, 21, 23, 29, 40*, 41, 43, 44, 47* surface integrals
    . . Nov. 14 Homework Project III .
    Sec. 13.4 412-419 Nov 18 1, 3, 5, 7, 9, 11, 29(wildcard) Greene's Theorem
    Sec. 13.7 412-419 Nov. 20 2, 3, 4, 5, 6, 7, 9, 10*, 16*, 17* Stoke's Theorem
    Sec. 13.8 421-423 Nov. 20 5, 7, 9, 10, 13, 17*, 23 Divergence Theorem
    N/A . Nov. 20 See handout "Added Vector Calculus" additional problems in vector calculus
    Event . Nov. 24-28 . Thanksgiving Break
    Test III . Dec. 2 Test III .
    Final . Dec. 10 10:30am-12:30pm comprehensive

  • "wildcard" exercises can be turned in anytime before the last test. If they are nearly correct then I allow you to substitute your wildcard grade for some unsatisfactory Homework Quiz grade, or if you missed one it can substitute for the missed Homework Quiz. (Recall that if you miss a Homework Quiz then you are supposed to contact me and explain why so we can arrange to increase the weight of the final. Finals are risky so this is a good option if you have time)


  • Disclaimer : While I have attempted to completely specify the content of this course, I reserve the right to change this syllabus if necessary. It is your responsibility to monitor your Liberty University email account for any changes in the syllabus. I will notify you via email and announce in class in the event something needs modification.

    Motivational thoughts from your instructor:
    This is the last of a 3-semester course on Calculus. The methods and concepts presented in this course are fundamental to most, if not all, technical disciplines. Three dimensional coordinate geometry and vector analysis are used throughout many disciplines to describe where things reside in a careful analytic manner. The calculus of parametrized curves in two or three dimenions describes the motion of physical bodies in the plane or space. Newton's Laws are stated in terms of this calculus and vector analysis. We can derive Kepler's Laws, Centripetal Forces, Coriolis Forces and much more under this framework. Integral and differential vector calculus provide the langauge needed to analyze the electric and magnetic fields of electromagnetism. Maxwell's equations are written in terms of the curl and divergence. Vector calculus also is essential to discussing fluid dynamics and much more. Therefore, calculus is used to phrase many of the laws of physics describe the natural world. This means that if we know calculus then we can better appreciate the general revelation of God.

    It is important that you master the techniques of MATH 231. I look forward to helping you toward that goal, but ultimately you must think for yourself. The ability to think in math comes from practice (for most of us anyway) so make sure you set aside plenty of time thoughout the week to work out the subject for yourself.

    It is possible that you may not use calculus in your daily life, but there is still something to be gained by its study. As Christians we are called to sharpen our minds towards the purpose of defending our faith and winning others to Christ. Mathematics demands that we think more precisely than in many other avenues of discussion. In short, I argue that mathematics can help you think better. Think of it as weight lifting for your brain. No pain, no gain.

    Finally, there is beauty. Mathematics can be beautiful. We can thank our Creator for this beauty. Often this is sufficient reason for the pure mathematician. For example, in MATH 231 we will learn that there are several different coordinate systems that describe the same underlying geometry. I find this idea of intrinsic geometry to be beautiful. I hope some of you can also find beauty in the calculus.