Welcome to Math 103 with Clark Bray
Summer 2005, Session 2


Instructor

Clark Bray, 022 Physics Building, 660-2822, cbray@math.duke.edu
Office hours: TBA
Textbook:  Calculus, 6th Edition, by Edwards and Penney; Math 103 Notes on Linear Algebra ; Math 103 Notes on Multivariable Derivatives (and Figures).  Note that these last two documents are currently in development, and may be updated throughout the term.  I will make an announcement if there are any significant changes.

Links and Downloads

Syllabus -- This document includes a list of topics in this course in the order that they will be covered.  Homework problems for given sections are posted here.  Adjustments to the syllabus may be made throughout the semester; if any significant changes are made, I will send out an email announcement.

Additional Homework Problems (AHP) -- This is a collection of problems that will be assigned along with the book problems throughout the term.

Solutions to the Additional Homework Problems -- You can use these solutions to check your computations, or to get started in the right direction if you are stuck and don't know where to begin on a problem.  Obviously though, copying these solutions and turning them in as your own work would violate the honor code; furthermore, such action would deprive you of the opportunity to learn from the problems, and to gauge your understanding of the material.

Solutions to E&P, section 13.6, problems 44-46 -- These problems gave many students trouble, so I wrote out detailed solutions for your reference and study.

Math 103 Course Homepage  -- This page contains much of the information for the 103 course.  The syllabus listed there, however, is NOT the one we will be using in this course. 

Math Information for First-Year Students -- This page has many useful links; make sure to familiarize yourself with it.

Blackboard -- This will only be used for recording and reporting grades in this class.  Your grades will be (securely) posted there so that you can know your grades as quickly as possible, and so that you can verify that they have been recorded correctly.  Make sure to log in after each assignment is returned to make sure that the grade was recorded correctly; if it was not, contact me as soon as possible so that the correction can be made.

Schedule of Lectures -- This schedule has the dates of all of the exams, and a rough schedule indicating which lecture (from the syllabus) will be given on each class day.  Students are urged to read the appropriate section of the book BEFORE the lecture, so that they will have a general idea of what problems will be addressed and what approaches will be taken so that they can make better use of class time.

Note, the schedule of lectures is just an approximation; we may find ourselves ahead of or behind schedule, depending on some unknowns. 

Exam 1 Solutions

Exam 2 Solutions

Final Exam Solutions

Values of Sine and Cosine at Standard Angles -- All students are strongly advised to know the values of the six trig functions at the standard angles (all multiples of pi/4 and pi/6); this short commentary and the linked diagram will help you both remember these values, and understand the fundamental relationship between trigonometry and the unit circle.

The Remainder Theorem and the Factor Theorem -- These are fundamental facts about polynomial algebra, and they are simply stated and easy to prove; but for some reason they are not covered in most high school curricula any more.  I strongly encourage students to look at this brief description and ensure an understanding of these theorems and their proofs.

Some comments about Single Variable Integrals -- Make sure to download and read this very carefully! 

A different point of view on Single Variable Derivatives -- Make sure to download and read this very carefully!

Hierarchy of Derivative Properties -- This diagram shows the different properties a function can have at a given point, relating to taking derivatives at that point, and which ones imply which other ones.

Diagram, Vector Calculus in R^2 -- Students should use this diagram to help see the symmetries and relationships between the Fundamental Theorem of Line Integrals (in R^2) and Green's Theorem.

Diagram, Vector Calculus in R^3 -- Students should use this to help mentally organize the constructions and theorems that we have talked about in Chapter 15 (except for Green's Theorem).  Note the symmetrical relationships between the three boundary theorems, and how the lifetime theorems can help suggest what type of integral is appropriate for a given problem.

Math 103, Fall '04 -- Students can find here all of the exams (with solutions) that I gave when I taught this course in Fall '04.

Math 103, Summer '05 (Term 1) -- Students can find here all of the exams (with solutions) that I gave when I taught this course in Fall '04.

Java Applets -- This is a site that was created by a colleague at Stanford; several of the tools there could be useful to you for visualizing multivariable functions.  In particular, be sure to try the "3D Graph" tool, and enter the following details into the controls:  f(x,y) = (3x^2y - y^3)/(x^2 + y^2), xsteps = 61, ysteps = 60...  It is easy to check that f = r sin(3(theta)) and thus that at the origin all of the directional derivatives exist -- but, when you play with the perspective controls (labelled "theta" and "phi"), you will see that this function is definitely NOT differentiable at the origin.  Here is a picture of the graph from one perspective.  See "Math 103 Notes on Multivariable Derivatives" for a more detailed discussion.


Homework

Homework problems are assigned for every lecture, and students should complete each assignment on the day of the lecture.  The problems assigned for that day will be due on the second following class day, at the beginning of class -- this should give you time to start the problems the day they are assigned, seek out help if needed on the next day, and then have time to finish them that night before being due the following day.  They will be graded and returned to you as soon as possible.

Make sure you staple your homeworks!  We cannot give credit to students for work that was lost as a result of not being stapled.  Also, make sure to put at the top of the front page your name, the lecture number(s) for those problems (indicated on the syllabus), and the course information (Math 103, Clark Bray)

No late homework will be accepted. 

In calculating homework grades, the lowest of your homework scores will be dropped.  The purpose of this policy is to handle exceptional circumstances such as a serious illness.  Please do not request to have late homework accepted.  Also, it is inadvisable to skip a homework unless absolutely necessary, since only one homework will be dropped.

Working together in groups on homeworks is strongly encouraged!   You will find that the people you are working with either (1) understand something you don't, in which case they can explain it to you; (2) understand something that you do understand, but from a different point of view -- these additional perspectives can prove to be very useful; or (3), don't understand something that you do understand -- in which case you have the opportunity to explain it to them...  I think you will find that in the process of explaining something, very often you will achieve a better understanding yourself.

Of course, it goes without saying that even though you may work in groups, the homeworks you turn in must be your own work.   You may share ideas, perspectives, approaches to problems, but copying is not allowed.  Furthermore, keep in mind that the homeworks are primarily a learning tool, and count for a fairly low percentage of your grade.  Do not deprive yourself of this invaluable learning opportunity!




Grading and Exams

Final grades for the class will be determined by the total number of points earned in the class.  These points are given based on performance on the items below, with the following maximum possible scores:

Homework average:   30 possible points (the lowest homework score is dropped)
Tests:                           200 possible points (2 exams x 100 points each)
Final Exam:                 200 possible points
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Total:                            430 possible points


The student should be prepared for the fact that the grading system for these exams is NOT the same as the one most students became accustomed to in high school. There are two main properties in particular of the high school system that will not be used in this class :

1) In most high school grading systems, there are fixed, arbitrary numbers that determine the cutoffs between different letter grades -- these cutoffs were invariant, and independent of the exam. The problem with this that it forces the instructor to create exams that are always the same difficulty; in other words, the instructor must make sure that all exams will yield the same mean score. Furthermore, it requires that the distribution of scores also be roughly constant. Achieving both of these goals is not only difficult, but impossible to perform perfectly.

This system ties the instructor's hands severely, and is totally unnecessary! Of course it is important that final letter grades for a class follow a prescribed plan, so that those letter grades have some meaning outside of the context of that class. Ensuring that is actually easier if the instructor chooses the cutoff numbers after having seen the distribution of student scores. The cutoffs can then be chosen while incorporating important considerations such as the difficulty of the exam, or any other points about the exam that may be relevant.

2) The class average on exams in most high schools was usually expected to be somewhere in the mid-eighties. While this is reasonable considering the nature of high school, it is not always appropriate for a college setting.

In this class, certainly, there are expectations for the student that are much more demanding than those of most high schools. We expect that the student will achieve much more than the mere ability to reproduce what he or she has seen in class. In particular, we expect that the student will achieve an understanding of the ideas that are at the foundation of the methods -- and thereby gain the ability to apply those ideas to situations that he or she has not already been exposed to.

Since the expectations of this class are more difficult than those of high school, it stands to reason that the exams, designed to test the students mastery of these more lofty goals, must involve more difficult questions; and therefore, the exams must be more difficult. Clearly this will result in class averages that are lower than what one would expect if the exams were more like those of high school. It will also tend to result in score distributions that are more broad, since the students responses can be expected to be more varied.

The student should be fully aware of these points before taking an exam in this class.

It is very dangerous to associate letter grades with performances on individual exams, because it is very difficult to predict how the distributions for those exams will interact when the total score distribution is formed. Therefore, the class will usually be informed only of the class median and mean for a given exam -- letter grades will not be assigned. 

I will periodically distribute a list of all student total scores in the class (with names removed), so that students can see exactly how their own total scores compare to the rest of the class. 



Calculators

We will not be using calculators in any aspect of this course.  You may use a calculator on a homework problem if you feel that it will help you understand the concepts, but you may not make any reference to the use of a calculator on the homework you turn in.

Calculators will NOT be allowed on the final exam or on the in-class exams.  I also generally discourage their use on the homeworks, since students may develop a dependency that will hurt them on the exams.


Getting help

There are several resources that students should be aware of; make sure to read the Sources of Help for First-Year Students.

You are highly encouraged to make good use of the Summer Help Room.  It is located on West Campus in Physics 216, and is staffed from 12:00pm-5:00pm Monday through Friday.  You can also come to my office hours, or just swing by sometime to see if I'm available.  If you need to make a special appointment to see me, send me an email.

I'd also like to emphasize that classmates can be an excellent resource as well.  I refer you above to my comments on this in the homework section.

Be sure to realize that you are encouraged to use these resources for more than just help on the homework...  Ask questions about general ideas you are having trouble with, specific parts of the lectures that you did not understand...  Of course you should also seek help with homework if you find yourself stuck on a problem for an extended period of time.


Honor Code

The Honor Code is taken very seriously on Duke campus, and you are all reminded to make certain you are familiar with it. 

In this course some collaboration is allowed and encouraged, but of course your work must all be your own.  Here are some specific comments about the graded items in this class:

Homeworks -- You are encouraged to work in groups to exchange ideas and help each other understand how to approach problems, but the student's work must be his or her own.  Copying and dictating are not allowed. 

Exams and Quizzes -- Students are not allowed to have any outside help during exams or quizzes. 


Attendance

Attendance at all lectures is required . If you miss a lecture, it is your responsibility to catch up on the topics that you missed. You should keep in mind that in this course, the material builds on itself; if you miss some of the material, subsequent lectures will seem more difficult to you.

Absences from exams and quizzes will be excused only for reasons such as serious illness or appropriate official university activities.  In either case, a written notification from the dean is required.  In the case of illness, this must be done with the Short-term Illness Notification form.  In the case that an absence from an exam is excused, the grade will be determined based on your performance on the final exam for the course, and relative to the performance of the rest of the class on that exam.