Instructor:	David Barsky
Telephone:	750-4201 (with voice mail)
E-mail:		djbarsky@csusm.edu
URL:		http://www.csusm.edu/public/DJBarskyWebs/mainpage.html
Office:		Craven Hall, Room 6231
Office Hours:	To Be Announced

Recommended: One or two floppy diskettes formatted for Macintosh computers.

Supplements: Volume One of the two volume set of Study Guides by Richard St. Andre covers the material for the first two-thirds of this course (and also MATH 160). It is not required, but many students have found this study guide to be useful. If you find the first volume helpful you might want to order Volume Two for use in the last third of the course. The bookstore has also stocked Volume One of the Student Solutions Manual. If you decide to purchase this, make certain that you do not become reliant on it.

Prerequisite: MATH 160 with a grade of C or better. (Note: a C- is not a grade of C or better.)

I. Catalog Description. A continuation of the differential and integral calculus: inverse trigonometric and hyperbolic functions, integration methods, indeterminate forms, coordinate systems, planes and lines in space, sequences and series, applications, historical perspectives. Includes a laboratory experience using either computers or graphics calculators.

II. Expanded Description. In this course we will cover the following chapters in Stewart's text:

6. (second half of chapter) Inverse Trigonometric Functions
5. (middle of the chapter) Applications of Integration
7. Techniques of Integration
8. Further Applications of Integration
10. Infinite Sequences and Series

As the preceding listing indicates, we will not always follow the order of the text; when we cover chapters 5, 7 and 8 we will alternate between sections on techniques, and sections on applications. See Section VII for a tentative ordering of the sections that we will be covering.

There are many different facets to this course; four primary aspects are described below.

First, like every other course at CSUSM, this class has a 2500 word writing requirement. We will substantially exceed that minimum requirement. In your homework, you will need to do more than just "get the answer in the back of the book." You will need to present your work in a clear, organized fashion so that anyone looking at your solution will be able to understand how you arrived at your conclusion. To repeat the author of our text,

	Part of the aim of this course is to train you to think logically.  Learn
	to write the solutions of the exercises in a connected step-by-step fashion
	with explanatory words and symbols - not just a string of disconnected
	equations or formulas.

Third, this is a calculus course with applications. Just as problems in physics historically served as the impetus for the development of calculus, we will often use real-world problems to motivate the mathematics. Throughout the course we will spend time (both in lecture and in homework) working on real-world problems. You will be expected to be able to take a real-world problem (i.e., a word problem), formulate it as a mathematics problem, solve that mathematical problem, and decide what the implications that solution has for the original real-world problem. Not only will you have to know how to set up the correct integral for an application, but you will be asked to explain why this is the necessary integral.

Fourth, part of this class is a computer laboratory. On Mondays we will be meeting in Macintosh computer laboratory. We will use a powerful Computer Algebra System (CAS) called Maple running on Macintosh computers to help improve our intuition about the mathematics we are learning. In particular, this program will be very helpful in helping us go back and forth between graphical, tabular and symbolic representations of functions. Let me place an important warning here: Maple is not a substitute for thinking! This program can be a valuable tool for gaining insight into a particular problem ... if it is used intelligently; but we shall see lots of examples in the laboratory where a naive, unsophisticated use of Maple will lead us to a wrong conclusion. The more calculus we learn, the easier it will become to determine when Maple is giving us a correct answer. (A useful side-benefit of this laboratory is that it should help give you some of the skills that you need in order to satisfy the CSUSM Computer Competency Requirement.) We will not always use the computers when we are in the lab (I anticipate using them roughly a half-dozen times over the course of the semester), but it is recommended that you bring your Macintosh-formatted diskette with you on Mondays so that you can save the Maple worksheets when we work on them.

III. Course Goals. This course is a sequel to MATH 160. The basic goal of this course is for you to improve your skills in some basic methods of calculus (such as integration) that were introduced in MATH 160, and to learn some additional methods of calculus (e.g., infinite series). You will be expected to know the theory behind these concepts, and how to prove some elementary properties. You will be expected to model real-world situations, apply these operations to solve the corresponding mathematical problem, and then interpret your solution in the context of the original situation. You will be expected to express your work in an easily understandable form. You will acquire the ability to use a CAS on a computer to help you in your work, and you will learn how to evaluate the output of this program in order to determine when it is reasonable and when it is wrong.

IV. Grades. Your grade will be based on:

			Homework Grade	12%
			Four Hour Exams	16, 16, 16, and 12%,
			Final Exam	28%

V. Homework. Homework, and its due date, will be posted on the chalkboard (or whiteboard) at lecture. The general rule of thumb is that an assignment made on a Wednesday or Friday will be due the Friday of the following week, while assignments announced on Monday will be due the Friday of that week. I will try to arrange my office hours (a handout listing them will be distributed at the end of the first week of the semester) so that you should always have the opportunity to attempt the homework first, then come see me if you have difficulty, and finally go back and finish the assignment by the due date (if you start it early enough). Late homework will generally not be accepted. If you have to miss a lecture, you should make arrangements to have your homework placed under my door no later than 1:00pm of the day on which it is due; it is your responsibility to get the next homework assignment - you may call me at my office or check the class web site (see Section X). The importance of homework cannot be overstressed: one only learns mathematics by doing it!

As the university writing requirement will be satisfied through the homework, your homework assignments will be graded for both the correctness of your solutions and the level of your exposition. Even if the problem simply asks you evaluate the integral int(x^3 cos(x^4 + 2), x) [this is how we would write the integral in Maple]- which can be easily done by making a u-substitution (see Example 1 on page 296 of the course text), you should always include at least one complete English sentence explaining what you did. For example, in the case of the integral given above you might write, "I noticed that the factor of x^3 differed from the derivative of the x^4+2 'inside' the cosine by only a constant factor. Thus I decided to make the substitution u = x^4+2. Having done this, I was left with the integral of a cosine which I know how to evaluate."

One way to improve the style of your mathematical writing is to study the writing of an accomplished author: Stewart. Here are two suggestions that will make you a better writer and thinker of mathematics.
(1) Every time that you sit down to work on the homework, begin by copying one of the examples out of the book. By doing this, you will reap a two-fold benefit. On the one hand, having written it out, you will understand the example better than if you only read it. Additionally, you will become attuned to some of the finer points of mathematical writing, and the style of your writing will improve.
(2) Begin your homework by trying to solve the problems on a piece of scratch paper. After you are satisfied with your conclusion, look over your work and ask yourself, "What did I do to solve this problem?" Your answer (to yourself) should be the starting point for writing up the solution that you will submit for grading. It is important to realize that if you can get the right answer, but you just cannot explain how you did it, then your grasp of the material is extremely shaky and you need to get help quickly (see Section IX).

I encourage you to form study groups and to work together (this allows you to gain valuable oral communication skills in addition to learning the material) but you must write up your solutions separately (this allows you to gain valuable written communication skills and it keeps you from cheating yourself). Writing up the solutions alone allows you to test yourself to see whether you really understand the material, and this helps to keep you from being "surprised" on the exams. A good strategy is to try first to solve all of the problems yourself, and then meet with some of your classmates who have also already attempted all of the problems to discuss the problems that you have been unable to solve. To facilitate the formation of study groups, I will pass around a study group sign-up sheet.

I would greatly appreciate it if you would staple your homework pages together, but, please, do not write your solutions in the corner of the paper that will be hidden underneath the staple. Do not use red ink, or a red pencil. I will return the homework after it has been graded before (and for those who arrive late, after) lecture.

I want to warn you that not all of the homework will be graded; typically only a few representative problems will be examined. This makes it extremely important that you do all of the homework in each set - so that you don't find yourself in the unfortunate situation of having done most of the problems, but not the ones that were graded. Even if this does happen to you once or twice, you should still have an excellent homework grade if you are following the material (if not, get help - see Section IX) and handing in every homework assignment. For your information, in both of the last two times that I taught this course, homework grades that averaged 80% throughout the semester were what I considered to be "A" homework grades; I expect that this will roughly be the case for MATH 162 this semester.

Finally, if you have purchased the Student Solutions Manual, make certain that you don't develop the bad habit of looking to soon at the solutions in it. Remember: There are no solutions manuals distributed with the exams!

VI. Exams. I will be giving four (4) hour exams (see Section XI for tentative dates). I will not "drop" any of the exams, but I will count your worst hour exam score as only 12% of your grade; the other scores will each be 16% of your grade. I will not directly assign letter grades to the exams, but I will give some rough indications of how the numerical scores correlate with grades for the sole purpose of helping you evaluate your performance.

If you feel that a problem on your exam was misgraded or unfairly graded, you have one week from the day that exams are handed back to see me about that. After that one week period is over there will be no regrading of problems. (Of course, if the number of points on your exam has been mistallied, that can always be corrected.)

There will be no makeups for the exams. If a single hour exam is missed for a valid reason (justified in writing), then the three remaining exams will each count for 20% of your grade.

It is my intent to help you prepare for the exams in the following ways. (You have my promise that I will always try to do everything described below in this paragraph, but as I cannot foresee events that may limit my time during the semester, that is all that I can absolutely guarantee.) I will usually distribute a review sheet two classes before the exam that will help you to direct and focus your preparation for the exam. At the lecture preceding the exam period, I will give you a practice exam together with a solutions page. Try working through the exam in a mock-exam atmosphere before taking a peek at the solutions. I will also schedule a review period (out of class) before each exam.

Regarding the format of the exams, most exam questions will be similar to homework problems or examples from lecture and the text, but some others will be less routine and more challenging. There will be problems that require written answers; in your answers to the latter you must use complete sentences and correct punctuation, and your work must be legible. Depending on class size, there may be some multiple choice questions. Initially, the practice exam and real exam will be quite similar. As the semester progresses, the real exams will increasingly deviate from their practice versions, as I expect you to be growing mathematically. I view the process of preparing for and taking the exams as a "learning experience" for you. Accordingly, I will provide answer sheets for the exams to culminate these experiences.

The best strategy for preparing for these exams is to
1. stay current with the course,
2. do all of the homework,
3. get help (see Section IX) as soon as you realize that you're having difficulty with some of the material, and
4. get a good night's sleep the night before the exam, so that you are rested and ready to think when you walk into the classroom.

I believe that the final exam is scheduled for 9:45 - 11:45 a.m. on Wednesday, December 17. I will post the location of the exam on my web page for this class (see Section X) toward the end of the semester. The final exam will be cumulative. As stated in the class schedule, "No make-up financial examination will be given except for reasons of illness or other verified emergencies."

VII. Order of Topics. The table that follows below lists all of the sections in the book that we will be trying to cover this semester in their tentative order of appearance. This ordering is being provided to you so that you can tell what material we will be covering next and read ahead in the course - a practise that I strongly recommend. It may occasionally become necessary for us to rearrange a few of these topics. Whenever that hapens, I will try to give you advance warning so that you can adjust your readings.

1.	Section 6.1*		12.	Section 8.1		23.	Section 10.2
2.	Section 6.6		13.	Section 7.4***		24.	Section 10.3
3.	Section 6.7		14.	Section 7.5****		25.	Section 10.4
4.	Section 6.8		15.	Section 8.2		26.	Section 10.6
5.	Section 7.1		16.	Section 7.7		27.	Section 10.8
6.	Section 5.2		17.	Section 8.3		28.	Section 10.5
7.	Section 7.4**		18.	Section 7.8		29.	Section 10.9
8.	Section 5.3		19.	Section 8.4		30.	Section 10.10
9.	Section 7.2		20.	Section 7.9		31.	Section 10.11
10.	Section 5.4		21.	Section 10.12*****	32.	Section 10.12
11.	Section 7.3		22.	Section 10.1

*	A very quick review			**	Cases I and II
***	Cases III and IV			****	The first half of the section
*****	Includes an overview of Chapter 10

VIII. Classroom Procedure. I strongly encourage your participation in the lectures. When I ask a question, please don't be afraid to answer it if you think that you can. You probably are right, and even if you aren't, I'm not going to ridicule you. Also, if you have a question (about mathematics) in lecture, please feel free to ask it as it occurs to you. However, I will not answer specific questions about grading in class - see me in my office hours for that. Note also that "Is this going to be on the exam?" is an inappropriate question which will not be answered in the middle of a lecture. When we're working with Maple, if you're having difficulty working out the calculations on the computer, just raise your hand and I'll come over to help you; that's part of why I'm there.

IX. How To Get Help. There are several ways to get help for this course. First and foremost, you can come see me. I will be running several office hours a week; don't wait for the special review sessions before the exams. You can also contact me by telephone or by e-mail (the number/address is on the first page of this syllabus). Second, you can try the Mathematics Learning Assistance Center (Math Lab) in Craven 3106-I (phone number 750-4102); this is staffed by upper-division and graduate students who should be quite capable of helping you with any of the material covered in this course. The current plan is for the Math Lab to be open from 10:30-4:00 Monday through Thursday, and from 8:30-10:30 on Friday mornings. Third, you can try the Academic Support Program for Intellectual Rewards and Enhancement (ASPIRE) in Craven 5201 (phone number 750-4014); there is an application process to get into this program, and it is limited to approximately 250 participants, so I encourage you to apply early if you meet the admission criteria.

IX. Internet. [Note there are no active links in this paragraph, but if you're already here, you don't need them anyway.] I will produce and maintain a Web page for this course. The URL is http://www.csusm.edu/public/DJBarskyWebs/162page.html. You can also reach it from the San Marcos home page (http://www.csusm.edu) by going to CSUSM CWIS (the whole thing) [near the top of the page], then to Faculty [under Personal Home Pages, near the bottom of the page], then to David Barsky [about the third screen down], and finally to MATH 162 Calculus with Applications, II [about the second screen down]. My MATH 162 page will serve as a repository for official course announcements such as the location of the final exam and out-of-class review sessions, reading assignments, homework assignments, rescheduled hour exams (if that becomes necessary), and (perhaps) capsule summaries of the class lectures. During the one of the lab periods I will show you how to use Netscape Navigator to reach this site.

XI. Important Dates. Mark these on your calendar.

Add/Drop period begins				Tuesday, September 2
First lecture					Wednesday, September 3
Last day to add classes or drop with no record	Monday, September 15
Last day to change grading option		Monday, September 22
1st Hour Exam (tentatively)			Friday, September 26
2nd Hour Exam (tentatively)			Wednesday, October 15
Last day to withdraw with a grade of W		Monday, October 20
3rd Hour Exam (tentatively)			Wednesday, November 5
Thanksgiving Break - No class			Friday, November 28
4th Hour Exam (tentatively)			Friday, December 5
Last class					Friday, December 12
Final Exam					9:45 - 11:45 a.m.
						Wednesday, December 17

XII. Grade Statistics. You may be interested in the distribution of grades in MATH 162 when I taught the course each of the last two Springs. Keep in mind that these are merely historical facts and do not necessarily reflect the way that grades will be assigned this semester. (Due to rounding off, the percentages do not sum to 100.)

		B+	2%	C+	 2%	D+	 4%	F	 0%	
A	19%	B	9%	C	13%	D	13%
A-	 2%	B-	2%	C-	 4%	D-	 2%	W*	23%

XIII. Your Responsibilities. I propose a metaphor for this course. We are embarking on a mathematical journey, and I am your guide: I will lead you, but I will not carry you. You, and you alone, are ultimately responsible for your own learning. It is very important that you do the reading assignments when they are assigned, and that you carefully study the examples in the text (as Stewart says, with "paper and pencil at hand"). You have to do all of the homework, and if you miss any of the lectures, you need to make arrangements to get the notes from someone.

XIV. Our Contract. By enrolling in and attending this course, you are agreeing to conduct yourself with complete academic honesty at all times. In particular, you are promising to neither receive nor provide assistance on examinations, and the solutions to all of the homework problems that you submit must be composed by yourself. This handout is a contract between you and me. My commitment is to teach the course as described in the preceding sections of this document. By remaining in this course, you affirm that you have read and understood this contract, and that you agree to it.

XV. Welcome to Calculus with Applications, II. - David Barsky

Go back to the main 162 page.

This page posted 9/6/97
Classroom location corrected 9/8/97