Mathematics

Math 220: Calculus I

Instructor: Rich Maresh, Associate Professor

Office: MC 522, 796-3655, Hours: MWF 12-1, TW 2-3(Home: 526-4988)

Final Exam: Thursday, 13 Dec 01, 7:40-9:40 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, From Graphical, Numerical, and Symbolic Points of View (Ostebee & Zorn, Saunders CollegePublishing, 1997)

CORE SKILL OBJECTIVES

1.Thinking Skills:

A.Uses reasoned standards in solving problems and presenting arguments.

2.Communication Skills:

A.Reads with comprehension and the ability to analyze and evaluate.

B.Listens with an open mind and responds with respect.

C.Information and communicates using current technology.

3.Life Values:

A.Analyzes, evaluates and responds to ethical issues from an informed personal value system.

4.Cultural Skills:

A.Understands culture as an evolving set of world views with diverse historical roots that provides a framework for guiding, expressing, and interpreting human behavior.

B.Demonstrates knowledge of the signs and symbols of another culture.

C.Participates in activity that broadens the student’s customary way of thinking.

5.Aesthetic Skills:

A.Develops an aesthetic sensitivity.

 

 

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:

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 OBJECTIVES

1.Thinking Skills:

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:

A.Collects a portfolio of one’s work during the course and write a reflection paper.

B.Does group work (labs and practice exams) is done throughout the course, involving both written and oral communication.

C.Uses technology - graphing calculators and Maple V in the computer lab - to solve problems and to be able to communication solutions and explore options.

D.Improves one’s ability to write logically valid and precise mathematical proofs and solutions.

3.Life Value Skills:

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:

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.

5.Aesthetic Skills:

A.Develops an appreciation for the austere intellectual beauty of deductive reasoning.

B.Develops an appreciation for mathematical elegance.

Objectives: This is a list of more specific outcomes this course should provide. The student should...

1.... gain a better understanding of the concept of a function.

2.... use graphs to estimate related values, relative rates, extreme values, limits, and derivatives.

3.... develop a concept of limit.

4.... understand the derivative.

5.... apply concepts and techniques to calculus to analyze functions and find relative rates, extreme values.

6.... use numerical methods to evaluate derivatives and use calculators and computers efficiently as tools.

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. 

READING THE TEXT: Because it is so important that you read the book, I am going to ask you to OUTLINE the text. You can’t read a mathematics text like you might read a novel – it is important that you actually understand what you are reading! Each week I will take a brief look at your growing outline and will check off your name for acceptable work. This will be worth 5 points per week. 

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 first 3 chapters – 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). Because chapter 4 will take us up to the end of the course, there will not be a separate exam on that chapter, but the final will more heavily emphasize that final chapter than the previous three – this is very reasonable in a course like this, in which the material builds in such a sequential manner. 

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.

 

MATH 220: Fall 2001 Schedule

 

27 Aug     <1.1>  Functions                        p 10 # 1-4, 6-8, 11-13, 17, 18, 20

29 Aug    <1.2> Graphs                              p 21 # 1, 2, 4-10, 16-24, 25, 27, 28-37, 41-43, 48, 49, 51, 53, 56-69

31 Aug    Lab #1

4 Sep    <1.3> Machine Graphics               p 34 # 1-17 odd, 20, 21

5 Sep    <1.4> What is a Function?             p 46 # 1-9 odd, 10, 11-51 odd, 57

7 Sep    Lab #2

10 Sep    <1.5> Elementary Functions        p 65 # 1-43 odd, 51, 53, 59

11 Sep    <1.6> New Functions From Old  p 78 # 1-29 odd, 30-32, 35-43 odd, 47, 53, 61

12 Sep    <1.7> Modeling                            p 90 # 1, 3, 5

14 Sep    GROUP PRACTICE EXAM #1

17 Sep    Review …

18 Sep    - EXAM # 1 –

19 Sep    <2.1> The Idea of the Derivative    p 105 # 1, 2, 3, 5, 7, 8, 10, 11, 13, 17, 18, 19, 21, 25, 27, 29

21 Sep    <2.2> Estimating the Derivative     p 114 # 1, 3, 4, 5, 7, 9, 11, 13, 23, 25, 29, 33

24 Sep    Lab #3

25 Sep    <2.3> The Geometry of Derivatives    p 127 # 1, 3, 5, 7, 9, 19, 23, 25, 27

26 Sep

28 Sep    <2.4> Higher-Order Derivatives          p 135 # 1, 3, 5, 6, 7, 9, 13, 17, 19, 21, 23, 27

1 Oct     <2.5> Rates of Change: Avg, Inst.        p 148 # 1, 3, 4, 5, 7, 11, 12, 13, 14, 17

2 Oct     Lab #4

3 Oct    <2.6> Limits and Continuity                 p 160 # 1, 3, 5, 7, 16, 17, 19, 21, 27-41 odd, 44, 45, 49-57 odd

5 Oct    <2.7> Limits and Infinity                      p 173 #1, 3, 5, 7, 9, 10, 11, 14, 15, 19, 23, 25

8 Oct

9 Oct     GROUP PRACTICE EXAM #2

10 Oct   Review …

12 Oct    - EXAM # 2 -

15 Oct    <3.1> Derivatives of Polynomials      p 191 # 1-7 odd, 11-17 odd, 21-27 odd, 31-43 odd, 73, 75, 80, 85, 96

16 Oct    <3.2> Using Derivative Formulas       p 197 # 1-13 odd, 16, 20, 21, 23, 24, 25, 26, 29

17 Oct    <3.3> Deriv. of Exponential Fcns       p 206 # 1-45, 48, 54, 57, 58, 60, 62, 65, 67, 83, 87

22 Oct     Lab #5

23 Oct    <3.4> Deriv of Trigonometric Fcns    p 213 # 1-8, 15, 17, 21, 23, 25, 31, 33, 41, 43, 55, 56, 57, 59, 61

24 Oct    <3.5> Product and Quotient Rules     p 221 # 1-43 odd, 51, 53 , 56

26 Oct    <3.6> The Chain Rule                         p 230 # 1-49 odd, 50, 51, 53, 55

29 Oct     Lab #6

30 Oct    <3.7> Implicit Differentiation            p 236 # 1, 3, 5, 9, 11

31 Oct    <3.8> Deriv of Inverse Trig Fcns       p 245 # 1-10, 13-49 odd

2 Nov

5 Nov     GROUP PRACTICE EXAM #3

6 Nov    Review …

7 Nov    - EXAM #3 -

9 Nov    <4.1> Differential Equations                p 254 # 1-11 odd, 15, 17, 20

12 Nov    <4.2> Modeling Growth                     p 264 # 1-6, 8, 9, 11

13 Nov    <4.3> Linear and Quadratic Approx   p 277 # 1-11 odd, 12, 13, 15, 17, 19, 23

14 Nov    <4.4> Newton’s Method                    p 286 # 1, 3, 4, 5, 8, 11, 15

16 Nov    <4.5> Splines: Connecting Points       p 295 # 1, 2, 3, 7, 9, 11, 13

19 Nov     <4.6>Optimization                            p 303 # 1, 2, 3, 6, 8, 9, 11, 12, 14, 15, 16, 18, 19, 21

20 Nov      Lab #7

26 Nov    <4.8> Related Rates                            p 314 # 1-7, 9-19 odd, 23, 24

27 Nov

28 Nov    <4.9>Parametric Functions                 p 324 # 1-6, 9-11

30 Nov    Lab #8

3 Dec    <4.10> Why Continuity Matters          p 330 # 1-5, 7, 9

4 Dec    <4.11> Mean Value Theorem                p 338 # 1-5, 7, 8, 11

5 Dec    Lab #9

6 Dec    GROUP PRACTICE FINAL EXAM

FINAL EXAM:Thursday, 13 Dec 2001, 7:40-9:40