Quick Notes for Math 140 @ SIUC

The purpose of this blog is to have a list of pointers for my Math 140 class I am teaching.

There are 2 different questions on Limits one is Figure based and other is finding the limits using algebraic manipulation
Figure based limit
You need to know what you mean by left hand and right hand limits. Also you need to understand that a limit exists only if left hand limit = right hand limit. Whereas one sided limits can have value ranging from constant to positive or negative infinity.
If at the point you have to find the limit the graph is not continuous the limit doesn't exist.

For algebraic limit there could be five types of question.
Rationalizing

Derivative questions are easy to answer if you remember the product rule and quotient rule

2nd Derivative questions using boil down to product rule and quotient rules

By parts question remember the formula
Remember (LAE) The precedence

For maxima-minima question it is important that you come up with two equations

For graphing question make sure you know
how the sign change from + to - and - to + affect the equation

Sense and Sensibility

Well I am updating this blog from the 3rd Floor of Morris Library and its almost 9:45 pm. Yesterday was Orthodox Easter Celebration and I went out with Kyriakos to Herrin Orthodox Church to celebrate it. It was fun lightning the candle and going around the church. I had a good time and it was my first time going to an orthodox church. I had a minor trouble with my car and got it fixed by Tom. The stearing wheel and ignition was jammed. So it had to be broken as the other option of replacing the cylinder and lock was more expensive. Now I can start my car with a screw driver. Over the break I watched Sense and Sensibility. It was a BBC production. It has shades of resemblance to Pride and Prejudice. The women folk have only one thing in their head and that is to get married. The worth of each relation is based on how rich they are. The story is about two sisters one personifying sense and other sensibility and in the end they discover that each alone is not enough.
I had a pizza today and did read parts of Steven Covey's "Principle Centered Leadership". I also watched Eyewitness documentary on Arctic and Antartic which was good. Another one I watched was on plants. I did tutoring and I feel like I have missed my meditation and yoga for a while and I can see the effect on me. I need to relax and learn some new things.

Review "love actually"

There are several things I want to mention in this particular blog. First my Ping Pong game is getting better. I have been practicing with Akina and together we have improved a lot. In 449 we are doing Hypergraphs and its an interesting topic where the edge of the graph can contain more than 2 vertices. The edge is now the subset of the set.
I watched two movies yesterday including "All about Lily Chou - Chou" and "Love Actually". All about Lily Chou Chou is a long movie and is a tale about an eighth grader and I picked up because on the DVD cover it mentions to be among the favorite movie of Quentin Tarantino. So definitely I was curious. It's a long movie and touches on high school stuff. I may have to watch it again especially the making of the movie to appreciate it better. Love Actually is one of those sugary movies which are based on infatuation rather than love so the better name for the movie could be infatuation actually.

Earthquake in Carbondale, Illinois

Well I should have something nicer to begin my blog with. I usually wake up around 5 am these days. So today around between 4:30 and 5 when I woke up by a feeling of someone rattling my bed I realized that it was an earthquake. It did seem to last for a while. I think probably around 30 seconds. However I been so inured to earthquakes that I didn't mind even getting out of bed. I guess I was amused. I could hear my wooden cabinets making the cracking sound. I hope it didn't cause the damage but it had the intensity of one of the stronger earthquakes I have ever felt.

Avalokitesvara mantra, Sirshasana ..

It's 11:40 am and Saturday morning, in the background “Choo ker mere man ko “ song is playing while I am updating this blog. Yesterday I went out with Akina to Chinese Buffet and two days before I went with her to Golden Corrall. That means I am eating out a lot these days but I make sure that I balance that out with Grape Fruit juice. I have controlled my soda intake a whole lot now. I don't order Soda while I am at the restaurants.

In 449 we Dr. Porter taught Polya's Method of coloring. It's really neat and it gives insight into Burside's Lemma. I loved the problem where we had to prove that there are only 30 different possibilities of numbering a dice. Similarly for coloring the stick problem and necklace problems. I have enjoyed this class so much. We are now learning about Hypercube and one of the computer project is to verify the number of Hamiltonian paths in the Hypercube (Q3 and Q4). A Hypercube Qn is an n regular graph which has 2^n vertex i.e each vertex has n edges.

In 501 we did Fatou's lemma. I think now I am much clearer about limsup and liminf definitions after using Wikipedia. If I have to explain what I understand by Fatou's lemma is we take the limit outside the integral. We also proved the three main theorems in integration, Fatou's lemma, Monotone convergence theorem and dominating convergence theorem when we prove it on meaure.

My article on “Youtube and Siuc” is almost ready. I have to trim it down by another 200 words before I send it. I am doing Yoga everyday and now I can do Headstand or “Sirshasana” with the help of wall as support. I have made a new notebook for Dream log. I am looking forward to incorporating this in to my changing lifestyle which now includes minimum Internet, no television, yoga, getting up early in the morning, avoiding reading newspaper and only occasional reading of news headlines only, more reading of books on varied topics, lots of fruits, Namyo ho rin ge kyo chant. I finally found the mantras of Avalokitesvara on Youtube. It's from 'Tibetan Incantation” album. I had owned that cassette when I was in India and I loved this song so much but was unable to find it all those years. It's one of the best music I think that has ever been produced.

Some New Experience

I must log that I had several new experiences I watched "Pride and Prejudice". It starred Kiera Knightley and it reminded me of "Trishna" a soap on Doordarshan long time ago. I think one of the first few soaps. I also watched a piano recital at Shryock Auditorium by Emmanuel Ax. It was Beethoven's emperor Piano Concerto. I am enjoying the new ping pong paddle given to me by my wonderful friend Mei. I was among bevy of judges for the science fair. I helped judged the mathematics section and it was fun especially seeing the derangement problem. The other one was on variance of M&M and third one was on Golden Ratio. It took me and Dr. Tall almost half an hr to give points and we believe we did justice to the projects. I took time and look around other projects and some had great ideas.

Update

Well I haven't updated my blog in a while but I made sure that I was doing Yoga everyday and more or less I have incorporated getting up early in my life style too. I got myself registered for Vipassana and that means I will be going to Rockford, Illinois for a 10 day course. I am very excited about this. On the reading front I got Bhagavad Gita translation by Eknath Easwaran. It by far seems the most accessible translation. I was impressed by the preface and decided to search it on internet to found more about Eknath. He was the founder of blue mountain meditation center and was a professor of English at Nagpur University before he moved to Berkley. He also started the eight point meditation which seems interesting. I am convinced for now several years that we have to be very cautious about the mental diet and eight point meditation seems to reiterate that. Which means that I will be reading more about Eknath in future. He has penned over 27 books a contemporary of Gandhiji. I am sure each of these books will be a delight to read.

On Analysis front I will be taking a serious look at limsup and liminf definition. Go over montone convergence theorem, fatou’s lemma and dominated convergence theorem. On yoga front I am could finally do shirshasana using wall as a support. My flexibility is improving and that is a great joy.