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 |

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

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.

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

- Required Text: Calculus, Sixth Edition, By James Stewart, Brooks/Cole Publishing Co. 2008.
- Supplemental Materials: course notes and more available online at the course website.
- No graphing calculator is required for this course. Mathematica can do much more than even the best graphing calculator. I will allow (basic) scientific calculators during tests, but no graphing calculators, laptops, PDAs, IPODS,cell phones, bluetooth-type devices, or any other electronic device capable of either data storage or communication. If in doubt ask.

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:

- State and apply definitions and theorems relating to the topics listed above.
- Understanding the idea of approximations using power series.
- Understanding of the power of vectors to solve many real-world problems.
- Ability to manipulate aspects of derivative and integration of functions.
- Ability to model real systems using mathematics.
- Competence in appropriates problem-solving skills, and an appreciation of a variety of approaches to problem solving.
- Learn general intellectual skills such as observing, classifying, analyzing and synthesizing.

- Cognitive growth:
- Demonstrate proficiency in the ability to take the knowledge acquired and apply it to problem-solving situations.
- Appreciate mathematics as a powerful tool in their discipline.
- Product:
- For each hour in class each student needs to spend at least two hours of study time.
- 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.
- There will be homework assignments over material covered. These will be graded and returned.
- Announced and unannounced classroom quizzes may occur in this class. These will be graded and returned.
- Process:
- The method of instruction will consist of lecture and interaction with the students. There will be a free exchange of questions.
- The math lab will be available for help with assignments.
- There will be study groups formed from students taking this course.
- Student–Instructor conference will be used where appropriate.

- [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. - [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. - [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.
- [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 to replace the homework.
- [30pts] Tests: there will be three tests, I drop the lowest.
- [25pts] Comprehensive final exam.

91-100 = A

81-90 = B

71-80 = C

65-70 = D

0-64 = F

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

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.

- If you miss Homework Quiz(s) with good reason then I will increase the weight of your final exam. It is your responsibility to tell me why you missed it either by email or in office hours.
- If you fail to turn in the Homework Projects on or before the due date then it is counted as a zero (except in the case of a documented emergency absence)

Students are required to wear attire consistent with the

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 |

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.