Some course policies

What the course is about:
Classifying very broadly, this course is about three main topics- Linear Algebra (Chapters 7 & 8), Vector Calculus (Chapter 9) and Differential Equations (Chapters 2, 3, 4, 5 & 10).
The first topic deals with vector spaces and (linear) maps between them, matrices, properties of matrices. We will also see some applications of matrices e.g. solving systems of equations. Later, in the third part of the course, we will use whatever Linear Algebra we learnt to solve systems of differential equations.
Then, we are going to study some vector calculus, and Stokes' Theorem and its applications. (By Stokes' Theorem, I mean not just Stokes' but also Green's and Divergence Theorems.)
Finally, we look at differential equations. After quickly brushing over what we saw in Math 114, we will try to solve other types of differential equations e.g. Cauchy-Euler, Bernoulli, etc. and then see an effective method to solve higher degree differential equations and systems of linear differential equations. We will see how to solve differential equations by the method of power series. We will also learn how to use Laplace transforms to solve differential equations.

Prerequisites:
I won't be assuming anything for the Linear Algebra part of the course as I will start from scratch. However, Calculus- Differentiation and Integration (esp. Substitution and Integration by parts) and basic Trigonometry should be on your fingertips.
Among other things, I will be assuming a reasonably sound knowledge of Math 114. More specifically, functions of several variables and vector calculus and differential equations are two topics with which you should have some familiarity.
Regarding Maple, I do not require the use of Maple in the course. However, I think Maple is a powerful software and especially, when we deal with functions of several variables, it is not so easy to visualise the graphs and Maple often helps us visualise by drawing three-dimensional graphs. Using Maple is also a good way to verify ones answers. (For best results, you should work out the problem on your own and then use Maple to verify your answer.)

Goals of the course:
Though, we will be trying to complete the syllabus mentioned, more importance will be paid to understanding the stuff well than just trying to "cover" the syllabus. What we will be learning (linear algebra, calculus of functions of several variables, differential equations) are foundational topics required and used in all spheres of mathematics and other sciences (including physics, engineering), and so, if the basics are not clear, one might face problems. So, though the emphasis might be on solving problems, if you want to be at the top of the class, you should understand things clearly too.

Homework/ Quizzes:
Homeworks will be assigned once/ twice a week mainly based on the core problems for the topics completed that week. Homework need not be handed in. However, this does not mean homework is not to be done. The ability to do homework regularly will be a good indicator of your performance in class. Also, I will be taking short (~10-minute) quizzes in class (with or without prior notice) and these quizzes will be closely based on the homework problems. (I might choose a problem verbatim from the homework.) So, there is more than one incentive in doing homework. The homeworks are mainly intended to ensure that one does not fall behind what is being done in class. The homeworks will be posted on the homework page, and the quiz/ exam scores will be posted on Blackboard. (Please make sure that you cross-check your scores on Blackboard, and in case of any discrepancy, please inform me as early as possible.) Some of the core problems may be assigned as homework while others may not. It is your responsibility to make sure that you have solved all of the core problems as well as all the questions in the sample examinations as preparation for the exams.
You are strongly encouraged to discuss the solutions to the homeworks with ones classmates or anybody else (including me).

Exams:
There will be a total of four exams- three (~1-hour) exams in the middle of the semester and a final exam. Other than that, there will be quizzes (as mentioned above). The final exam will be held on the final day of classes. I will announce the specific dates for the other examinations in proper time. The syllabus for the final exam shall be whatever is taught till the last day of class.

Schedule:
Exam 1: 30th May (tentative)
Exam 2: 12th June (tentative)
Exam 3: 21st June (tentative)
Final Exam: 28th June

Weightage:
Final Exam                        :  40%
Other Exams  (15% * 3 =) :  45%
Quizzes                              :  15%
(Extra credit may also be awarded if a consistently good performance is noted.)

Grading:
Please note that I shall not take attendance into consideration while awarding you grades. If you think you know the subject material and you feel attending classes are not going to help you, you may feel free not to attend classes. But please make sure you turn up for quizzes and exams. I will not be offended if you do not show up for classes. But please make sure you keep in touch with the subject material, because otherwise, you might be in trouble during the exams.
Also, typically the course should have 33% A's, 33% B's and 33% C's. However, if I notice a good performance, I might relax the percentage of A's and B's. Hypothetically, the entire class could get A's but for that everybody has to peform really well.

What is expected of you:
Though I will be discussing all the relevant topics in class, and elaborately treat the more important and subtle ones, it will not be possible to speak about everything in entire detail in this limited time. So, you are expected to do a lot of reading at home after class hours. Also, as the class meets for more than eight hours a week, not being up-to-date with what is being done can turn out to be expensive. I'll be mentioning in class what you should read before the next day's class. You should make sure that you are able to solve each and every problem that is assigned on the homework, and also the core problems assigned for the course. At the end of this course, you should make sure that you are not just able to compute, but also have an understanding of what was done in class. You should also be able to write reasonably decent proofs at the end of this course.

Resources:
Other than the resources already mentioned, you may feel free to come and ask me questions during office hours and during or after class.

About me:
I have just completed my second year of the graduate program in mathematics here. I've had "some" experience in teaching/ "TA'ing". I taught Math 115 last summer and was a TA for Math 114 and Math 240 in Fall 2006 and Spring 2007 respectively and have enjoyed all my experiences so far, and am confident I'll enjoy it this summer too. I hope to provide a friendly and informal classroom atmosphere conducive to learning as well as enjoying oneself. I am sure I will be making mistakes (if one can comment from one's past experience!) and I look forward to being interrupted during class. PLEASE do correct me whenever you think I am wrong (however trivial the slip may be, because someone else might not have noticed it), that way we all get to learn. You may or may not be correct all the time but I am sure our understanding will improve at the end of it. If you feel the pace of the class is too fast/ slow, please do not hesitate to bring it to my notice. Also, I'm not a native speaker of english and so you might have trouble understanding me. Please feel free to stop me and make me repeat something which I have not been clear about or something which you don't understand. I look forward to a very rewarding semester for all of us. Best of Luck!