Math 220: Calculus I
Spring 2004: 4 credits, MWF, 9:00-9:50, R 8:00-8:50, MC 553
Instructor: Rich Maresh, Associate Professor of Mathematics, Dept. Chair
Office: MC 522, 796-3655, Hours: MWF 12-1, R 2-3 (Home: 526-4988)
Final Exam: Thursday, 6 May 2004, 9:50-11:50 am
Course Description: Limits and Continuity. Derivatives and applications. Differentiation of polynomial, rational, trigonometric, logarithmic and exponential functions. L’Hopital’s Rule.
Prerequisite: acceptable placement score (or ACT math score of at least 28), or at least 3 years of high school algebra and trigonometry with at least a B average, or a grade of C or better in MATH 180. Recommended as a general education liberal studies elective course.
Text: Calculus, Concepts and Contexts, 2nd Ed. (Stewart, Brooks/Cole, 2001)
CORE SKILL OBJECTIVES
1. Thinking Skills: Students engage in the process of inquiry and problem solving that involves both critical and creative thinking.
(a) Understands the “big problems” in the development of differential calculus, the tangent problem and the velocity problem.
(b) Understands the mathematical concept of Limit.
(c) Explores differentiation formulas for a variety of functions, including exponential and logarithmic, trigonometric and inverse trigonometric, hyperbolic and inverse hyperbolic functions.
(d) Investigates a wide variety of applications of differentiation, such as finding maximum and minimum values of functions, and instantaneous rates of change.
2. Communication Skills: Students communicate orally and in writing in an appropriate manner both personally and professionally.
(a) Does group work (labs and practice exams) is done throughout the course, involving both written and oral communication.
(b) Uses technology - graphing calculators and Maple V in the computer lab - to solve problems and to be able to communication solutions and explore options.
(c) Improves one’s ability to write logically valid and precise mathematical proofs and solutions.
3. Life Values: Students analyze, evaluate and respond to ethical issues from informed personal, professional, and social value systems.
(a) Develops an appreciation for the intellectual honesty of deductive reasoning.
(b) Understands the need to do one’s own work, to honestly challenge oneself to master the material.
4. Cultural Skills: Students understand their own and other cultural traditions and respect the diversity of the human experience.
(a) Develops and appreciation of the history of calculus and the role it has played in mathematics and in other disciplines.
(b) Learns to use the symbolic notation correctly and appropriately.
NCTM Goals: The NCTM (National Council of Teachers of Mathematics) gives the following set of overall goals for mathematics education in general, which are worth including here, since I think they are such fundamental reasons for studying mathematics.
1. Learn to value mathematics.
2. Learn to reason mathematically.
3. Learn to communicate mathematically.
4. Become confident in your mathematical ability.
5. Become problem solvers and posers.
Course Goals:
1. Students shall develop a solid foundation in the basic concepts and methods of Differential Calculus.
2. Students shall develop problem solving skills.
3. Students shall understand the appropriate use of technological tools in their mathematical work.
4. Students shall communicate mathematical ideas clearly and accurately.
Outcomes: This is a list of more specific mathematical outcomes this course should provide. The student shall...
Content:
1. ... demonstrate the knowledge of the theory and methods of Differential Calculus, specifically, limits, derivatives by definition, differentiation formulas, and applications of the derivative.
Problem-Solving:
2. …demonstrate the ability to apply appropriate mathematical tools and methods of novel or non-routine problems.
3. …demonstrate the ability to use various approaches in problem solving situations, and to see connections between these varied mathematical areas.
Technology:
4. …demonstrate the basic ability to perform computational and algebraic procedures using a calculator or computer.
5. …demonstrate the ability to efficiently and accurately graph functions using a calculator or computer.
6. …demonstrate the knowledge of the limitations of technological tools.
7. …demonstrate the ability to work effectively with a CAS, such as DERIVE, to do a variety of mathematical work.
Communication:
8. …use the language of mathematics accurately and appropriately.
9. …present mathematical content and argument in written form.
COURSE POLICIES AND PROCEDURES:
Probably the best single piece of wisdom I can pass on to you as you begin this course is: “Mathematics is not a spectator sport!” You need to view yourself as the LEARNER – and “learn” is an active verb, not a passive verb. I will do what I can to help structure things so that you have an appropriate sequence of topics and a useful collection of problems, but it is up to YOU to DO the problems and to READ the book and THINK ABOUT the topics.
You must develop a system that works for you, but let me suggest that it might include finding a study group or coming to me with your questions or going to tutoring sessions in the learning center. In any case you should expect to spend at least the traditional expectation of 2 hours outside of class for each hour in class – this is important! Class time is for exploring the topics and answering questions you might have, but you simply can’t master the material without putting in the time alone to really engage in the mathematics.
We are in the process of phasing in a new textbook and more than ever it is important that you actually READ the BOOK! The authors attempt to force the reader to think about the material and to develop an intuitive sense of what is going on; there is much emphasis on solving problems and much reliance on graphing technology as well as on symbolic manipulation.
HOMEWORK: In a nutshell, working problems is one of the key ways you will learn Calculus. Attending class is important, of course, but without doing problems you will not develop a solid foundation in the material. I will give you daily assignments and will expect that you will do as many as time allows (which I take to be roughly 2 hours per class period). I will not generally collect these assignments but I do see them as testing your understanding and as raising questions for you to ask in class.
LABS: Throughout the course there will be an occasional “lab”, a problem set you will work on during class time, and in a group setting. There are many ways we learn, and one way many people find helpful is working in a group, which allows discussion of the issues involved. A very good way to test your understanding of some concept is to try to explain it to a colleague. I hope you find these labs helpful.
EXAMS: There will be exams after each of the 4 chapters we will cover – these will be in two parts, a group practice problem set worth 20 points and then an individual exam worth 80 points, 100 points in total. The final exam will be cumulative and worth 150 points (25 on the group part, 125 on the individual part). By the way, I do not expect you to memorize the various formulas – you are allowed a page of notes for each exam, and you can bring all four pages in for the final exam.
GRADING POLICY: In general I use the rather traditional 90% of possible points for an “A”, 80% for a “B”, 70% for a “C”, and 60% for a “D”. I will try to make enough points available in non-test situations that “test-anxiety” should not entirely kill your chances for success, but I am a very firm believer in putting students through the exam experience so that I can see whether you, not your study group, understand the material.
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 me and/or Wayne Wojciechowski, the campus ADA coordinator (MC 320, 796-3085), within ten days to discuss your 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 220: Spring 2004 Schedule
12 Jan Intro., <1.1> Representing Functions p 22 # 1, 5-13 odd, 17-39 odd, 43, 45, 47
14 Jan more on <1.1>
15 Jan <1.2> Mathematical Modeling p 35 # 1-17 odd
16 Jan <1.3> New Functions From Old p 46 # 1-23 odd, 27-49 odd
19 Jan more on <1.3>
21 Jan <1.4> Graphing Technology p 55 # 1-23 odd
22 Jan Lab #1
23 Jan <1.5> Exponential Functions p 63 # 7-19 odd
26 Jan <1.6> Logarithms p 73 # 3-53 odd
28 Jan <1.7> Parametric Curves p 81 # 1-27 odd
29 Jan Lab #2
30 Jan Practice Exam #1 (20 Points)
2 Feb EXAM #1 (80 Points)
4 Feb <2.1> The Tangent and Velocity Problems p 99 # 1-7 odd
5 Feb <2.2> The Limit of a Function p 108 # 1-15 odd
6 Feb <2.3> The Geometry of Derivatives p 117 # 1-33 odd
9 Feb <2.4> Continuity p 128 # 1-29 odd
11 Feb Lab #3
12 Feb <2.5> Limits and Infinity. p 139 # 3-35 odd
13 Feb <2.6> Rates of Change p 148 # 1-21 odd
16 Feb <2.7> The Derivative p 155 # 1-31 odd
18 Feb <2.8> Derivatives as Functions p 167 # 1-27 odd, 33-41 odd
19 Feb <2.9> Linear Approximations p 173 # 1-11 odd
20 Feb Lab #4
23 Feb <2.10> f and f¢ p 178 # 1-7 odd, 15-23 odd
25 Feb Review …
26 Feb Group Practice Exam #2 (20 Points)
27 Feb EXAM #2 (80 Points)
1-5 Mar SPRING BREAK
8 Mar <3.1> Derivatives of Polyn. & Exp. Functions p 196 # 1-31 odd, 41-49 odd
10 Mar <3.2> Product and Quotient Rules p 204 # 1-19 odd, 23, 27
11 Mar <3.3> Derivative Applications p 215 # 1-11 odd, 17
12 Mar <3.4> Derivatives of Trigonometric Functions p 223 # 1-17 odd, 27, 31
15 Mar Lab #5
17 Mar <3.5> The Chain Rule p 233 # 1-33 odd, 47, 49, 53
18 Mar <3.6> Implicit Differentiation p 243 # 1-17 odd, 25-33 odd, 37
19 Mar <3.7> Derivatives of Logarithmic Functions p 250 # 1-31 odd
22 Mar Lab #6
24 Mar <3.8> Linear Approximation and Differentials p 256 # 1-13 odd
25 Mar Review …
26 Mar Group Practice Exam #3 (20 points)
29 Mar EXAM #3 (80 points)
31 Mar <4.1> Related Rates p 269 # 3-17 odd
1 Apr <4.2> Maximum and Minimum Values p 277 # 3-27 odd, 37-49 odd
2 Apr <4.3> Derivatives and Shapes of Curves p 288 # 1-19 odd
5 Apr <4.4> Calculators and Graphing Functions p 297 # 1-17 odd
7 Apr Lab #7
8-12 Apr EASTER BREAK
14 Apr <4.5> l’Hospital’s Rule p 305 # 5-35 odd
15 Apr <4.6> Optimization Problems p 313 # 5-23 odd
16 Apr more on <4.6>
19 Apr Lab #8
21 Apr <4.8> Newton’s Method p 327 # 1-17 odd
22 Apr <4.9> Antiderivatives p 334 # 1-25 odd, 31
23 Apr Review …
26 Apr Group Practice EXAM #4 (20 Points)
28 Apr EXAM #4 (80 Points)
29 Apr Review…
30 Apr GROUP PRACTICE FINAL EXAM (25 points)
FINAL EXAM: Wednesday, 10 Dec 2003, 9:50-11:50 (125 points)