Math 131-004 Calculus and Analytic Geometry I, 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 in B.R. Lakin School of Religion room 108
Lecture Times: M-W-F 4:05-4:55pm, T-R 3:35 - 4:50pm


Course Description:
Functions and graphs, limits and continuity; differentiation and integration of algebraic, exponential, trigonometric and logarithmic functions; applications and conic sections.

Rationale:
This course, along with MATH 132, provides a standard introduction to the study of calculus. It presents the theory and applications of elementary calculus necessary for further study of mathematics.

Prerequisites:
Algebra and trigonometry at the level of MATH 121-122 or MATH 128.

Materials List:
Learning Outcomes/Requirements

  • Objectives:
    This course will emphasize understanding calculus principles as well as skill. It will focus mainly on functions and graphs; limits and continuity; differentiation and its applications; and integration and some of its applications.

    The students are accountable for the following:
    1. Be able to perform accurately any algebraic calculations necessary.
    2. Be able to sketch and discuss the graphs of polynomial functions and trigonometric functions.
    3. Be able to carry out the differentiation of the elementary functions.
    4. Be able to carry out integration of simple algebraic and simple trigonometric functions.
    5. Appreciate the power of calculus as a tool for solving problems not possible by other means.
    6. Appreciate calculus as playing a major role in the development of science as well as mathematics.
    7. Appreciate calculus as a logical system aside from its applications.
    8. Gain an appreciation for mathematics as a major factor in modern society and as a marketable major.
    9. Value the communication of mathematics to others.
    10. Be able to use the computer and a mathematical language to solve some problems.
  • Requirements:
    1. Cognitive growth:
      1. Demonstrate his ability to apply the concepts of differentiation in solving problems and the concepts of integration in solving problems with and without the computer.
      2. Demonstrate his mathematical proficiency by analyzing and criticizing proof.
      3. Demonstrate his mathematical proficiency by constructing proofs of specified theorems.
    2. Product:
      1. Four (4) exams plus a comprehensive final exam.
      2. Daily assignments.
      3. Quizzes – announced and unannounced
    3. Process:
      1. Instructor lectures/demonstrations.
      2. Student demonstrations of solutions to problems.
      3. Student-instructor conferences as 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. [12pts] 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. There is a tentative list at towards the end of this syllabus. You should monitor lectures and email for any updates/hints on the list.
    2. [16pts] 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 four 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. [45pts] Tests: there will be four (4) 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:
    The Test and Homework Project due dates are as follows:

    Assignment Due Date
    Homework Project I Friday, Sept. 5
    Test 1 Tuesday, Sept. 9
    Homework Project II Friday, Sept. 26
    Test 2 Tuesday, Sept. 30
    Homework Project III Friday, Oct. 24
    Test 3 Tuesday, Oct. 28
    Homework Project IV Friday, Nov. 14
    Test 4 Thursday, Nov. 20
    Comprehensive Final Exam. Dec. 10, 3:30-5:30pm

    Homework Quizzes may be given during any lecture as described in the course schedule (see the course schedule online for additional details). The following is a tentative course schedule. Any modifications of this schedule will be announced in lecture.

    Section # My Lecture Notes "Due Date" Assignment Description / Hints / Mathematica helps
    Event c1 Aug 18 Read through the introduction to my notes. First day of classes
    Event . Aug 20 Calculus Readiness Test. (counts as two homework quizzes)
    Sec. 1.1 c2.1, c2.2, c2.3 Aug. 21 2, 8*, 28, 30, 45, 50*, 56*, 64, 65* equations and models (p.21)
    Sec. 1.2 c2.4 Aug. 22 1, 6, 7, 8*, 9* functions and curve fitting (p.34)
    Sec. 1.3 c2.5 Aug. 25 3, 31, 59, 63*, 65*, 66* manipulating functions and their graphs (p.46)
    Sec. 7.1a c2.6 Aug. 25 1, 2, 11*, 17, 21, 22*, 23, 25 inverse functions (p.391)
    Sec. 7.2a c2.4.8, c2.4.9 Aug. 25 1, 2*, 10, 17* exponential functions (p.402)
    Sec. 7.3a c2.4.8, c2.4.9 Aug. 25 1, 2, 8, 11, 17, 27*, 28 logarithmic functions (p.409)
    Sec. 7.6a c2.4.7 Aug. 25 1, 2, 10*, 11* inverse trig functions (p.461)
    Sec. 7.7a c2.4.10 Aug. 27 1, 3, 7, 11*, 13*, 26 hyperbolic functions (p.468),(hint: for 26 see Example 3 p.466-467)
    Sec. 2.2 c3.1 Aug. 29 2, 6, 14, 25*, 26, 27, 40* limits (p.74)
    Sec. 2.3 c3.2, c3.3, c3.4, c3.5, c3.6, c3.7 Sept. 1 3*, 4, 5, 6, 10, 13, 17, 19*, 25, 26*, 27, 37*, 58, 61 limit laws (p.84), (hint: for 19 need to factor out an (x+2) in the denominator)
    Sec. 2.4 c3.8 Sept. 4 15, 19, 24, 44(wildcard) technical limits (p.96)
    Sec. 2.5 c3.2, c3.3 Sept. 5 1, 2, 4, 6, 32, 40*, 42*, 45*, 48*, 55 continuity (p.106)
    Event . Sept. 5 Homework Project I due functions and limits
    Sec. 3.1 c4.1 Sept. 8 4, 6, 10*, 14*, 16*, 32, 33 definition of derivative at a point, tangent lines (p.121)
    . . Sept. 8 Review for Test I day your questions, my hints.
    Event Test I Sept. 9 Sections 1.1, 1.2, 1.3, 2.1, 2.2, 2.3, 2.4, 2.5, 3.1, 7.1a, 7.2a, 7.3a, 7.7a functions, algebra, limits and definition of derivative
    Sec. 3.2 c4.1, c4.2 Sept. 15 3, 27*, 39, 41*, 53 derivative as a function (p.131)
    Sec. 3.3 c4.3, c4.6, c4.7, Sept. 16 1, 3, 5, 7, 9, 11, 13*, 15*, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35*, 37, 39, 41*, 43*, 49, 57*, 59, 61, 65, 69*, 71*, 79, 83*, 85, 93, 96* derivatives involving linearity, products, and quotient rule (p.144)
    Sec. 3.4 c4.3, c4.5, c4.6, c4.7 Sept. 16 1, 3, 5, 7, 9*, 11*, 13, 15, 37, 49 derivatives of sine and cosine and their products, reciprocals etc... (p.154)
    Sec. 3.5 c4.8 Sept. 19 1, 3, 5, 7, 9, 11, 13*, 15*, 17, 19, 21, 23, 25, 27*, 29, 31, 33, 41, 43*, 48*, 59, 79, 84, 87*, 89* chain rule for composite functions (p.160)
    Sec. 3.6 c4.9 Sept. 23 5, 7, 9, 11, 13, 23, 25*, 33, 40, 45*, 53* implicit differentiation (p.169)
    Sec. 7.2b c4.4, c4.6, c4.7, c4.8 Sept. 23 31, 33, 35, 37, 39, 41, 43, 45, 49*, 53* derivatives involving exponential functions (p.402)
    Sec. 7.4a c4.9, c4.10 Sept. 25 3, 7, 11, 13, 17, 25, 41, 43, 45*, 47*, 49*, 51* derivatives of logarithms and logarithmic differentiation (p.419)
    Sec. 7.6b c4.9 Sep. 25 19, 29, 31 derivatives of inverse trig functions (p.461)
    Sec. 7.7b c4.11 Sep. 26 29(wildcard), 31, 33, 35 differentiation of hyperbolic functions (p.469)
    Event . Sept. 26 Homework Project II due differentiation
    Event . Sept. 29 Review for Test II day your questions, my hints.
    Event Test II Sept. 30 Sections 3.2, 3.3, 7.2b, 3.4, 3.5, 3.6, 7.4a techniques of differentiation
    Sec. 3.8 c5.1 Oct. 6 1, 3, 5, 11, 13, 15, 17, 23, 33, 43 related rates (p.186)
    Sec. 3.9 c5.2 Oct. 7 1, 11, 15, 19, 33 linearizations and differentials (p.191)
    Sec. 4.1 c5.3 Oct. 10 7, 9, 29, 31, 33, 35, 45, 49, 57, 59, 63, 72 extreme values (p.211)
    Sec. 4.2 c5.4 Oct. 13 1, 5, 11, 17, 21 Rolle's Theorem, Mean Value Theorem (p.219)
    Sec. 4.3 c5.5 Oct. 13 1, 3, 4, 5, 7, 9, 11, 13, 21, 23, 29, 40, 53, 67(wildcard) derivatives and shape of graphs (p.227)
    Sec. 4.4 c5.6 Oct. 14 3, 7, 9, 11, 19, 22, 25, 27, 29, 67*, 69* limits at infinity (p.240), algebra and/or logic will resolve the indeterminancy.
    Sec. 4.5 c5.7 Oct. 15 1, 9, 13, 25, 39, 40*, 42* the big picture (p.248)
    Sec. 4.7 c5.8 Oct. 20 3, 5, 7, 17, 19, 21, 23, 33, 37*, 41*, 43, 49, 71 optimization (p.262)
    Sec. 7.6c c5.8 Oct. 20 47 optimization (p.461)
    Sec. 5.1 c6.1 Oct. 21 3, 15 the area problem (p.298)
    Sec. 5.2 c6.2 Oct. 21 5, 21, 27*, 65 definition and properties of the definite integral (p.310)
    Sec. 4.9 c6.3 Oct. 22 1, 3, 5, 7, 9, 11, 13, 15, 17, 23*, 25*, 33, 37, 41, 45 antiderivatives (p.279)
    Sec. 5.3 c6.4 Oct. 24 7, 13, 15, 19, 21, 23, 25, 27, 29, 31, 33, 37*, 45, 49, 69, 71, 73* Fundamental Theorem of Calculus (FTC)(p.321)
    Event . Oct. 24 Homework Project III due applications of differentiation and foundations of integration
    Event . Oct. 27 Review for Test III day your questions, my hints.
    Event Test III Oct. 28 Sections 3.8, 3.9, 4.1, 4.2, 4.3, 4.4, 4.5, 4.7, 4.9, 5.1, 5.2, 5.3, 7.2c, 7.4b, 7.6c applications of differentiation and fundamentals of integration
    Sec. 5.4 c7.1 Nov. 3 5, 7, 9, 11, 13, 15, 31, 41*, 48, 52, 53, 55, 57, 59, 67*, 69, 71, 72 indefinite integrals (most general antiderivative), integrals as sums for computing net change (p.329)
    Sec. 5.5 c7.2 Nov. 6 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 35, 37, 39, 41, 43, 45, 47, 49, 59, 63*, 64, 65, 67, 69, 71, 73, 75*, 77*, 79, 81 u-substitution (p.338)
    Sec. 7.2d c7.2 Nov. 7 73, 77, 79, 81 integrals involving exponential function, some problems need u-substitution technique here. (p.404)
    Sec. 7.4c c7.2 Nov. 7 69, 71, 73, 79 integrals that yield logarithms, some problems need u-substitution technique here. (p.421)
    Sec. 7.6d c7.2 Nov. 7 63*, 65*, 69, 71 integrals that yield inverse trig. functions, some problems need u-substitution here. (p.462)
    Sec. 6.1 c8.1 Nov. 14 5, 7, 9, 11, 13, 19, 21, 29*, 49 areas bounded by curves (p.352)
    Sec. 6.2 c8.2 Nov. 14 1, 3, 5, 7, 9, 49, 51, 53, 57*, 65*, 70* volumes by the slice (p.362)
    Sec. 6.3 c8.3 Nov. 17 5, 7, 9, 11, 46 volumes by the shell (p.368)
    Event . Nov. 14 Homework Project IV due u-substitution, areas and volumes
    Event . Nov. 19 Review for Test IV day your questions, my hints.
    Event Test IV Nov. 20 Sections 5.4, 5.5, 6.1, 6.2, 6.3, 7.2d, 7.4c, 7.6d basic integration and select applications
    Event . Nov. 24-28 . Thanksgiving Break
    Sec. 7.8 c9 Dec. 3 5, 7, 9, 11, 13, 15, 17, 19, 21*, 23, 25*, 27*, 29*, 43*, 49, 55*, 59*, 63*, 85, 93, 94, 99(wildcard) L'Hopital's Rule (p.478)
    Event . Dec. 3 review for final exam Last day of classes
    Event Final Exam Dec. 10, 3:30-5:30 comprehensive, covers everything tested on Tests I,II,III and IV AND section 7.8 tests I, II,III,IV and 7.8

    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 comments from your instructor:
    This is the first in a 3-semester course on Calculus. The methods and concepts presented in this course are fundamental to most, if not all, technical disciplines. Differentiation allows us to analyze the change in a variable. Integration allows us to analyze the total value of a variable. Calculus is used to phrase many of the laws of physics which describe much of 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 131. 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 throughout 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 and we can thank our Creator for allowing us to comprehend that beauty. A well crafted proof can be appreciated much the same way as other fine art. This is often sufficient motivation for pure mathematicians.