Math 180: Elementary Functions
Spring 2007, MRC 346, MWRF 8:00-8:50 a.m.
Professor: Richard Maresh, MRC 521, 796-3655, rjmaresh@viterbo.edu
Office Hours: MWF 10-11, R 9-10, M 1-2
Final Exam: Thursday, 10 May 2007, 7:40-9:40 a.m.
Course Description: Functions: graphs of functions, algebra of functions, inverse functions, polynomial and rational functions, zeros and asymptotes of functions. Exponential and logarithmic functions. Trigonometry: right-angle trigonometry, trigonometric functions, graphs of trigonometric functions, trigonometric identities, inverse trig functions. Law of Sines, Law of Cosines.
Prerequisite: Acceptable placement score, or two years of high school algebra with a B or higher average grade, or a grade of C or higher in Math 110. Recommended as general education liberal studies elective course (G9).
Text: Precalculus: Functions and Graphs (10th Edition), by Swokowski and Cole. (Thompson-Brooks/Cole, 2005)
Core Skill AbilitiesThe following general education skills are addressed in this course:
- Communication Skills
- Writes competently within the major and for a variety of purposes and audiences.
- Reads with comprehension and the ability to analyze and evaluate.
- Speaks effectively, both formally and informally.
- Listens with an open mind and responds with respect.
- Accesses information and communicates using current technology.
- Thinking Skills
- Uses reasoned standards in solving problems and presenting arguments.
- Applies the skills of planning, monitoring and evaluating.
- Life Values
- Analyzes, evaluates and responds to ethical issues from an informed personal value system.
General Education Objectives:
- – the students will:
- Use graphs to represent mathematical behavior.
- Communicate solutions to a variety of problems in a mathematically correct manner.
- Model problems from geometry and other disciplines using function concepts.
- Thinking Skills – the students will:
- Gain a better understanding of the concept of function.
- Represent quantitative relationships arithmetically, symbolically, geometrically and graphically.
- Utilize transformation of functions to obtain new functions (translation, rotation, reflection, dilation).
- Understand the structure of the real numbers
- Use a problem-solving approach to investigate and understand mathematical content.
- Justifies answers with logic and sound reasoning.
- Life Values – the students will:
- Adhere to the Academic Honesty Policy.
Specific Course Content:
- Functions – definition, notation, graphs, operations
- Polynomials – definition, division, zeros, rational functions, inverse functions
- Exponential and Logarithmic Functions
- Trigonometry – trig functions and graphs, solving triangles, trig identities, laws of sines and cosines, sum and difference formulas, inverse trig functions, DeMoivre’s theorem
- Additional topics – conic sections, parametric functions, polar coordinates
Course Procedures and Notes
Attendance: I do not formally use attendance as part of the grading system, but I can assure you that regular attendance is very important to being successful in the course. I include a detailed schedule so that if you do have to miss a class you can keep up with the material, but it’s not the same – you simply miss out on a key part of the learning process if you miss a class meeting.
Technology: I urge you to either purchase or borrow a graphing calculator if you do not already have one. I think a TI-84 type calculator would be a good one for this course. I will frequently use the overhead display unit with a TI-84 as we work through the material.
Homework: There are two big differences between a high school mathematics course and a college mathematics course: (a) the pace is about 3 times greater in college, and (b) you are expected to do most of your actual learning outside of class. As a general rule, students will need to put in about 2 hours outside of class doing problems for every hour inside the classroom. Not very many students actually do this, and not very many students do as well in their math course as they could. You want to somehow try to structure your life over the next four months so that you can perform to your ability, and this means doing lots of homework problems.
Students will often say they “drew a blank” during a test, or that they understood the problem when the teacher did it in class, but couldn’t do it later on their own. Research shows that in fact these students study for an exam by glancing over the ideas but don’t actually do problems. You can’t say that you know how to do the problems unless you actually test yourself. The “think method” doesn’t work in learning to play the piano or trumpet, and it doesn’t work in learning mathematics!
As far as the specific problems I have assigned, I have pretty randomly assigned 1, 5, 9, …, i.e. every fourth problem. That way you will attempt problems from all the various categories. I think you should view these assignments as a minimum. Anytime you have trouble doing a problem, you should probably do more of that type of problem. It is human nature to avoid things we aren’t good at doing, but that route will not lead to growth. You have to work hardest on your weaknesses.
I will not be collecting these homework assignments – I don’t think they should be part of the grade in any formal sense – but this is where the learning actually does take place. College courses cost you money – don’t short-change yourself!
Mathematics is not a spectator sport! You can’t learn by watching someone else do it.
Active Learning: You should also assess your own learning. If you are having trouble with some material don’t just “live with it”. You can get tutoring help in the learning center, you can come see me for help, or you can form a study group and learn from each other. If you are doing the homework problems, you will also be in much better position to follow what is happening in class, or to have questions to ask in class. There is a tendency in a math class to just come and listen, figuring that if nothing is to actually be handed in that day, then there is no assignment – but this is all wrong! You only get out of a class what you put into it.
My style in the classroom is what I would call “lecture-discussion”. I will entertain questions from students, I will often ask questions if only to make sure you are following as we move through the material. I will work many problems because that’s how I think we actually learn the material. If you can’t do the problems, then you haven’t mastered the material yet.
There are a couple of techniques of “active learning” that I will employ on occasion. The “Think-Pair-Share” method is one where I ask a question, give you a bit of time to think about it, then have you discuss it with a classmate (“pair”) and then discuss it in the whole class (“share”). Another thing I will do on occasion is to give a little quiz or brief problem set, just to see if you are on top of things.
Blackboard: Because we meet four times per week I do not make extensive use of Blackboard, but I will use it for several things. I will store a copy of the syllabus there, under Course Documents. I will make occasional announcements through Blackboard. I might also use it for old exams or notes on some topic. Finally, I will use it to make available your in-progress grade throughout the semester.
Exams: When you take exams you may use your calculator and you may also construct a 1-page (both sides OK) set of notes. For the comprehensive exam you may use the notes from all your previous exams. I usually encourage students to basically outline the material and to write down what you think will be useful to you.
Academic Honesty: Cheating will not be tolerated. Exam questions and problems will be open-ended rather than multiple-choice, so it is harder to get answers from your classmates, and I generally ask you to show your work to receive full credit on a problem, which again makes it harder to lift answers from another. If I detect cheating on an exam you will be given a score of ZERO for that exam – it’s not worth it to cheat, and it is also unethical.
Grading: I generally use a scale of 90% for an A, 87% for an AB, 80% for a B, 77% for a BC, 70% for a C, 67% for a CD, and 60% for a D. Over the semester we will probably have about 700 points possible.
In my courses, there is not such thing as “extra credit” – I think your grade should reflect how well you have demonstrated your understanding of the material by successfully working problems.
As a general rule your grade for the course will be computed by including the final exam at its face value. However, I will adjust your grade upward if your score on the final exam is higher than your overall average throughout the course – in this case you will receive as a grade what you earned on the final exam.
Getting Help: The learning center makes tutoring help available, including drop-in math help (M 9-10, 2:30-3:30; T 9-10, 1:30-2:30; W 11-12, 2:30-3:30; R 11-12; F 10-11). If you seek tutoring help, make sure that you do not rely on it to the extent that you aren’t working problems on your own. The tutor won’t be at your side during an exam. Also feel free to come see me if you are having difficulty. Unfortunately, it is often only the strongest students who take advantage of the instructor’s office hours.
Disclaimer: I reserve the right to make adjustments to the schedule and the syllabus in general as we move through the course. This is a new edition of the text and it may turn out that some changes may be necessary.
Americans with Disabilities Act: If you are a person with a disability and require any auxiliary aids, services or other accommodations for this class, please see Wayne Wojciechowski in Murphy Center, Room 335 (796-3085) within ten days to discuss your accommodation needs.
I want to include taking exams in the learning center under this category; you will need a written request from Wayne Wojciechowski before I will allow you to take exams there.
Math 180 Schedule – Spring 2007
Jan 15 [1.1] Real Number Properties p 16 # 1, 5, 9, …, 57
Jan 17 [1.2] Exponents, [1.3] Polynomials p 29 # 1, 5, 9, …, 97; p 45 # 1, 5, 9, …, 93
Jan 18 [1.4] Solving Equations p 61 # 1, 5, 9, …, 85
Jan 19 [1.5] Complex Numbers, [1.6] Inequalities p 74 # 1, 5, 9, …, 45; p 85 # 1, 5, 9, …, 61
Jan 22 [2.1] Rectangular Coordinate Systems p 101 # 1-29 odd
Jan 24 [2.2] Graphs of Equations p 116 # 1, 5, 9, …, 81
Jan 25 [2.3] Lines p 132 # 1, 5, 9, …, 65
Jan 26 [2.4] Functions p 150 # 1, 5, 9, …, 77
Jan 29 [2.5] Graphs of Functions p 169 # 1, 5, 9, …, 73
Jan 31 [2.6] Quadratic Functions p 183 # 1, 5, 9, …, 61
Feb 1 [2.7] Operations on Functions p 196 # 1, 5, 9, …, 55
Feb 2 Group Practice Exam #1 (Chapters 1-2, 25 points)
Feb 5 EXAM #1 (Chapters 1-2, 75 points)
Feb 7 [3.1] Polynomial Functions p 215 # 1, 5, 9, …, 57
Feb 8 [3.2] Polynomial Division p 225 # 1, 5, 9, …, 49
Feb 9 [3.3] Zeros of Polynomials p 237 # 1, 5, 9, …, 57
Feb 12 [3.4] Complex and Rational Zeros p 247 # 1, 5, 9, …, 41
Feb 14 [3.5] Rational Functions p 265 # 1, 5, 9, …, 57
Feb 15 [3.6] Variation p 272 # 1, 5, 9, …, 25
Feb 16 [4.1] Inverse Functions p 288 # 1, 5, 9, … , 57
Feb 19 [4.2] Exponential Functions p 299 # 1, 5, 9, …, 49
Feb 21 [4.3] The Natural Exponential Function p 311 # 1, 5, 9, …, 53
Feb 22 [4.4] Logarithmic Functions p 325 # 1, 5, 9, …, 73
Feb 23 [4.5] Properties of Logarithms p 336 # 1, 5, 9, …, 61
Feb 26 [4.6] Exponential and Logarithmic Equations p 348 # 1, 5, 9, …, 73
Feb 28 Review …
Mar 1 Group Practice Exam #2 (Chapters 3-4, 25 points)
Mar 2 EXAM #2 (Chapters 3-4, 75 points)
S P R I N G B R E A K
Mar 12 [5.1] Angles p 369 # 1, 5, 9, …, 49
Mar 14 [5.2] Trigonometric Functions of Angles p 385 # 1, 5, 9, …, 85
Mar 15 [5.3] Trigonometric Functions of Real Numbers p 404 # 1, 5, 9, …, 81
Mar 16 [5.4] Values of the Trigonometric Functions p 414 # 1, 5, 9, …, 41
Mar 19 [5.5] Trigonometric Graphs p 426 # 1, 5, 9, …, 49
Mar 21 [5.6] Additional Trigonometric Graphs p 437 # 1, 5, 9, …, 73
Mar 22 [5.7] Applied Problems p 446 # 1, 5, 9, …, 41
Mar 23 [6.1] Trigonometric Identities p 466 # 1, 5, 9, …, 57
Mar 26 [6.2] Trigonometric Equations p 479 # 1, 5, 9, …, 73
Mar 28 [6.3] Addition and Subtractions Formulas p 490 # 1, 5, 9, …, 41
Mar 29 [6.4] Multiple-Angle Formulas p 500 # 1, 5, 9, …, 49
Mar 30 [6.5] Product-to-Sum, Sum-to-Product Formulas p 508 # 1, 5, 9, …, 33
Apr 2 [6.6] Inverse Trigonometric Functions p 521 # 1, 5, 9, …, 57
Apr 4 Lab
E A S T E R B R E A K
Apr 11 Review…
Apr 12 Group Practice Exam #3 (Chapters 5-6, 25 points)
Apr 13 EXAM #3 (Chapters 5-6, 75 points)
Apr 16 [7.1] Law of Sines p 537 # 1, 5, 9, …, 25
Apr 18 [7.2] Law of Cosines p 546 # 1, 5, 9, …, 29
Apr 19 [7.3] Vectors p 561 # 1, 5, 9, …, 65
Apr 20 [7.5] Trigonometric Form for Complex Numbers p 582 # 1, 5, 9, …, 65
Apr 23 [7.6] DeMoivre’s Theorem p 589 # 1, 5, 9, …, 29
Apr 25 [10.1] Parabolas p 783 # 1, 5, 9, …, 49
Apr 26 [10.2] Ellipses p 796 # 1, 5, 9, …, 29
Apr 27 [10.3] Hyperbolas p 808 # 1, 5, 9, …, 29
Apr 30 [10.4] Parametric Functions p 824 # 1, 5, 9, …, 25
May 2 [10.5] Polar Coordinates p 842 # 1, 5, 9, …, 29
May 3 Review …
May 4 Group/Practice Final Exam (25 points)
Final Comprehensive Exam: Thursday, 10 May 07, 7:40 – 9:40 a.m. (125 points)