Introduction
Students in my tutorial batch may refer to the live document which I maintain for this course. This document is constructed almost entirely out of interactions with students in my tutorial batch: their doubts and from discussing approaches to solving the tutorial sheets of MA 105. Other students may consult their own Teaching Assistants before refering to the above document. Those who are here just to learn the subject, may proceed as they wish.
Logistics
- Short Quiz every week at the start of tutorial Wednesday 2pm, this will be graded and returned to you every week by the next tutrial session.
- Quiz 1 Sept 11
- Midsem Sept 16-21
- Quiz 2 October 25
Notes
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Notes will keep updating as the course proceeds.
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Historical Comments : You will be surprised to know that the concept of function is not very old. Till 1837 it was believed that every function could be traced with “free motion of the hand”. Gustav Dirichlet in 1837 gave the definition of function which we use most often now. He also gave the example of the indicator function of the set of rationals in (0,1). Do you think you can graph the function?
Q/A
Question: How many months have 28 days? Mathematician’s answer: All of them.
Q) This is in response to many queries: how to write answers in exam (so that no mark is cut)?
Here are some suggestions (follow the at your own risk :-) :
Think before you write. Write what you thought (you will be evaluated on what you have written, and not what you had in mind). Rather than merely make an assertion, say where it comes from. Each step in your answer should be logically correct and well supported by facts. In any writing, saying what you mean is important - and difficult. Mathematics is highly symbolic, but using lots of mathematical symbols does not make an argument a mathematical one. Avoid using quantifiers for “for all”, ‘for every”, “there exists”, etc., unless you are sure. It is better to write a line or two extra to make your conclusions more clear rather than letting the reader to guess. If needed, add a figure, but for reference only. Write clearly what is given and what you are trying to prove (Classic geometry proofs are good examples). Always proofread your work. Read what you have written, at least your own writing should make sense to you. Reading a well written, without too many cuts, arrows, etc., document is always a pleasure. Reflect on your answer, of course if time permits. -Prof. Inder K. Rana
References:
- Prof. Ghorpade’s (Course Instructor) page
- Prof. I.K. Rana’s NPTEL Course: Single and Multivariable Calculus
- Co-TA Aryaman Maithani’s MA 105 page, also thanks to his tech savviness without which this page would not have existed either.
- UBC’s Calculus online notebook
- Stewart
- Apostol
- Div, curl, grad and all that (library reading section 512.9)
- Gradients and Normals
Further Reading (beyond the scope of this course):
- Size of infinities
- Walter Rudin- Principles of Mathematical Analysis
- Lang- Undergraduate Analysis
- Modern Master gives his exposition Tao- Analysis
- Munkres- Analysis on Manifolds