 |
SyllabusThe topic of the course is Single-Variable Calculus. Topics for this course include techniques of integration, sequences and series, and the basics of R3 including vector arithmetic. In particular, we will cover most of Chapters 9 through 13 in the single-variable calculus textbook and most of Chapter 1 in the multivariable textbook.In Chapter 9, "More Antidifferentiation Techniques," we will study some very important and powerful techniques for evaluating integrals, including integration by parts, partial fractions and trig substitution. In Chapter 10, "Improper Integrals," we will study integrals over 'infinite' regions, grapple with how such things can make sense and how to compute them. We will also learn at an important tool for evaluating certain limits, namely l'Hôpital's Rule. We will spend a lot of time in Chapter 11, "Infinite Series." We will learn what a mathematician means by the word 'series,' how to determine when such things 'converge' and 'diverge,' and consider special series called power series and Taylor series. Taylor series allow us to find nice approximations to certain functions, which is one important reason for studying series in the first place. After studying them, among other things you'll know how your calculator actually calculates things like sin pi. In Chapter 12, "Differential Equations," we'll learn the basics of diff eqs and how to solve certain diff eqs graphically via direction fields and symoblically via separation of variables. In Chapter 13, "Polar Coordinates," we'll learn the basics of this very different, but very important way of looking at the real plane, R2. We'll also learn to do calculus in this new coordinate system.
Finally, in Chapter 1 of the multivariable book, "Curves and Vectors,"
we'll look at the basics of R3 with special attention given to
a new object known as a 'vector.' We'll learn about vectors and vector arithmetic
including addition and the three multiplications: scalar multiplication,
dot product, and cross product.
We'll also learn how to find equations of lines and planes using
these operations on vectors.
Sometimes they will be affectionately referred to as OZ-2 and OZ-3.
Unless reported to me before January 11th,
a scheduling conflict is not a sufficient excuse to take
an exam at any time other than the official time listed below.
The Final Exam will occur between March 12th and March 16th.
If you must make travel plans before the schedule for final exams appears,
Do Not make plans to leave Hanover on or before March 16th.
The Final Exam Will Not be given early to accommodate travel plans.
For this course, no calculators or computers may be used during the exams.
Please keep this in mind while working on your homework.
The exams will take place at the following times and places:
You are expected to attend every class.
You have invested a large sum of money for the opportunity to come to class and
I will invest a large amount of time in preparing for class;
I do not want any of us wasting the investments we have made.
Reading assignments will be given daily and should be read before coming to class.
For some of my thoughts on reading mathematics texts,
click here.
Quizzes will be administered at the end of class on Monday covering material presented in
class the previous week.
They will consist of a couple of questions and should only take 10 - 15 minutes to complete.
If you do the homework for the lectures given the previous week (including Friday's homework),
then you should do fine on the quizzes.
Homework problems will be assigned daily and collected the following class period.
Homework will be turned in and picked up from the boxes outside of Cook Auditorium.
Late homework will not be accepted and a grade of 0 will be assigned
(of course, exceptions can be made for emergencies such as illness, death, natural disasters...).
The solutions you present must be coherent and written in complete sentences whenever possible.
Simply stating answers or turning in garbled, unclear solutions will result in a grade of 0.
For further details consult the
Homework Schedule.
Also, consider visiting the course Chat Page.
This is probably a very good venue for those late night questions, especially those that arise
the night before the exams...
During class, I will use Maple (a computer algebra system) to illustrate various ideas.
If you are interested, you can obtain a copy of Maple from the Public server;
basic instructions for downloading and using Maple can be found at:
Collaboration on homework is encouraged (and expected);
although, you should first spend some time in individual concentration to gain
the full benefit of the homework. On the other hand, copying is discouraged.
You should not be leaving a study group (or a tutorial) with your homework ready
to be turned in; write up your solution sets by yourself.
|
| ||||||||||||||||||||||||||||||||||
